Average slope gradient, slope length, and exposure of the sections I–III.
We studied the effectiveness of grassland vegetation of a temporary capping system consisting of differently compacted boulder marl and its impact on the water balance components. This study presents the modelled water balances for the period between 2008 and 2015, performed with HELP 3.95 D (German edition). The model requires landfill design and weather data as well as soil physical and evapotranspiration parameters including the leaf area indices and evaporative zone depth with regard to the grassland vegetation. The modelled average annual actual evapotranspiration rates ranged between 277 and 390 mm year-1 or rather 33 and 66% of the annual precipitation (10-year average of 728 mm). The actual evapotranspiration rates are strongly influenced by the maximum leaf area indices that increased between 2008 and 2015 from 1.0 to 3.5 as well as the evaporative zone depth that also increased from 20 cm in 2008 to 50 cm in 2015. The empirical-mathematical–based HELP model is a useful option to successfully determine the water balance components of a landfill capping system under the given weather and site conditions including the development of the grassland vegetation.
- HELP model
- water balance
- actual evapotranspiration
- leachate generation
- vegetation growth
In a global perspective, landfill sites still represent the major option of waste disposal not only in developing countries . In Germany, the qualitative criteria of landfills are legally fixed according to the  and define the vegetative and technical standards for engineered barriers .
In case of this study, semipermeable, temporary capping systems intend a specific shutdown of the bioreactor, containing heterogeneous wastes and different amounts of biodegradable material, through controlled infiltration of precipitation into the waste body  and also allow biogas extraction .
Temporary capping systems regularly consist of a recultivated layer, a drainage layer, and a sealing layer consisting of mineral substrates or in combination with polymers . The major aim of the recultivated layer is to restrain landfill gas migration and to minimise leachate generation (precipitation contaminated with heavy metals or polycyclic hydrocarbons) by a high water storage capacity in combination with a distinct evapotranspiration rate from the vegetation and soil surface [3, 7].
Therefore, the choice of a locally adapted vegetation type (grassland, shrubs, forest) is essential to ensure high evapotranspiration rates (grassland: 450–550 mm year−1), a quick vegetation establishment (erosion protection, slope stability), and avoid deep shrinkage-induced cracking (capillary rise from deeper horizons) and rooting to protect the sealing layer as last barrier above the waste body depending on the thickness of the recultivated layer [4, 8, 9, 10].
The functional requirements of the vegetation in the nutrient and water availability considering a proper air capacity and plant available water capacity , whereby the technical challenges in landfill construction, compacted installation versus loose installation of mineral substrates, can significantly influence the growth conditions of the vegetation .
The effectiveness of the vegetation can be assessed by the water balance or rather the leachate generation under the specific climate and soil conditions [4, 11, 12]. There are several modelling approaches of landfill capping systems, with and without polymers, combining water balance calculations with the predominant statistical-empirical Hydrologic Evaluation of Landfill Performance (HELP) model  or numerical models like Finite Element subsurface FLOW system (FEFLOW) . Such predictive models can be used to support the planning of a landfill and/or to optimise the particular system from an economic point of view  and to verify the long-term hydraulic stability of a final capping system.
This study presents modelled water balance data and in particular the annual leachate rate of the Rastorf landfill during an 8-year period in the context of (a) grassland vegetation and (b) local weather conditions.
2. Materials and methods
2.1. Study site and weather conditions
The Rastorf landfill (lat. 54° 16‘N, long. 10° 19′E) in Schleswig-Holstein (Northern Germany) was actively operated from February 1977 to May 2005 with a total area of 105,000 m2 and about 2.0 million tons of municipal domestic wastes were deposited in it (Figure 1).
The temporary capped area of nearly 75,000 m2 with three sections (I: 21,275 m2, II: 29,961 m2, III: 22,208 m2) consists of three mineral layers (boulder marl) with a partially permeable recultivated layer (humus topsoil: 40 cm, humus-poor subsoil: 30 cm) and, below this layer, is a low permeable, 30 cm thick mineral sealing layer, which serves as a water and root barrier to prevent leachate formation and the groundwater contamination. The bottom layer consists of hardly permeable up to 20 m thick clay. A high-density polymer of 2.5 mm thickness and a drainage system above the bottom layer collects the leachate before the treatment by inverse osmosis (Figure 2).
The maritime, semi-humid climate in Rastorf is characterised by an annual precipitation rate which is in the long-term average regularly between 6 and 9 months year-1 higher than the potential evapotranspiration rate . The local weather conditions also affect water balances of the landfill capping system with 10-year average precipitation rates of 728 mm and, between 2012 and 2015, an average annual temperature of 9.0°C. The slope gradient varies between 7 and 16° and the slope length between 48 and 99 m (Table 1).
|Average slope gradient (°)||7 ± 3||14 ± 3||16 ± 4|
|Average slope length (m)||99 ± 65||48 ± 23||69 ± 4|
2.2. Laboratory measurements
In 2012, more than 160 undisturbed soil cores (100 cm3) were sampled in the capping system in vertical (90°) and horizontal (0°) direction in area I (54°28′20”N, 10°32′60″E), II (54°28′11”N, 10°32′71″E) and III (54°28′08”N, 10°32′75″E) in depths of 0.2, 0.5 and 0.8 m. The saturated hydraulic conductivity (Ks) was measured under instationary conditions (n = 10 per depth) according to . The pore size distribution (n = 7 per depth) was determined by a combined pressure plate (saturated, −6, −30) and − 1500 kPa ceramic vacuum outflow method as well as oven-dried at 105°C, respectively .
2.3. Hydraulic Evaluation of Landfill Performance (HELP) model
The Hydraulic Evaluation of Landfill Performance (HELP) model is a quasi two-dimensional hydrologic model which combines one dimensional soil physical and hydrological processes in (a) vertical direction and (b) lateral direction according to . Thus, the model requires data of the landfill design, weather conditions, and material properties such as porosity, field capacity, wilting point and saturated hydraulic conductivity as input parameters . In addition, the evaporative zone corresponds to the root depth of the vegetative cover and was calculated to quantify the maximum soil depth from which water can be removed through evapotranspiration .
With respect to the landfill design data, the upper part of the recultivation layer (0–0.4 m) was classified as vertical percolation layer, the bottom part (0.4–0.7 m) was conducted as lateral drainage layer to take into account the lateral saturated hydraulic conductivity. The sealing layer was classified as barrier soil liner.
The HELP model was validated with actual landfill data with respect to field and laboratory measurements according to .
2.4. Estimation of the water balance components of the Rastorf landfill
The HELP model was validated with actual landfill data with respect to field and laboratory measurements according to . The leachate rate (L) was calculated as follows:
where: L = leachate rate, P = precipitation, ET = actual evapotranspiration (including interception), R = runoff, D = lateral drainage (interflow) and ∆S = change in soil moisture content in mm year-1 and m3 and it is the time step, performed from January 1, 2012 until December 31, 2015.
A separate water balance was modelled for each area (I–III) and a weather station located close to the landfill recorded the actual meteorological data such as precipitation (uncorrected), air temperature, wind speed, wind direction, air pressure, air moisture, and relative humidity on daily basis. The global solar radiation was calculated on the basis of .
In addition, the wind speed was measured in 10 m height and a logarithmic approximation was used to calculate the wind speed for 2 m height. The leaf area index (LAI) was calculated on the basis of the quarterly measured average vegetation height (h) in 8–10 repetitive transects (1 m2) per area with a folding ruler according to :
The average root intensity was determined annually on the basis of repetitive soil profile images in the three areas with the colour threshold method using ImageJ software  and classified according to .
2.5. HELP modules
The water balance calculations based on analytical and empirical equations, while a detailed description is shown in [19, 24]. With regard to the atmospheric boundary conditions, the method used in the HELP 3.95 D for calculating evapotranspiration was designed according to .
The potential evapotranspiration consists of (a) evaporation of surface water (primarily evaporation of intercepted water, besides this evaporation of snow), (b) soil evaporation, and (c) plant transpiration computed by a simplified approach of :
where: Eoi = potential evapotranspiration on day i (mm), PENRi = radiative component of the Penman equation on day i (langleys), PENAi = aerodynamic component of the Penman equation on day i (langleys), Lv = latent heat for vaporisation (for evaporating water) or latent heat of fusion (for evaporating snow) in langleys per mm and Ts = snow temperature (°C).
The actual evapotranspiration (ETa) was mainly calculated by an approach of  using a model of vegetation growth and decay by . Thus, the vegetative growth and decay sub-model included in HELP was taken from the model SWRRB . The ETa is limited by the water availability at the landfill surface and the maximum depth of the evaporative zone according to . Therefore, the plant available water capacity inside the evaporative zone (field capacity–wilting point) can only be removed by evapotranspiration, while the field capacity (US: −330 hPa) is the lowest soil water content to allow unsaturated vertical flow (drainage) within the evaporative zone . The capacity of the interception storage and the interception height were calculated following Hoyningen-Huene (1983), modified and adapted to German standards by .
The area factor v was implemented in the modelling approach and corresponds to the ratio of the monthly sums of the global solar radiation (Rs) on inclined and horizontal reception areas consider the exposure and the inclination angle (°) and a corrected albedo of 0.23 in the summer-half (05/01-10/31) and in the winter-half (11/01-04/30) under climatic conditions in Germany .
The vertical percolation (drainage) is estimated using the equation for the unsaturated hydraulic conductivity (Eq. 4) which is based on . The saturated lateral drainage is modelled by a steady-state solution of the Boussinesq equation in combination with the Dupuit-Forchheimer (Forchheimer, 1930) assumptions, which take into account the Ks value of the drainage layer. The unsaturated conductivity for each soil layer was calculated as follows:
where: Ku = unsaturated hydraulic conductivity (cm s−1), Ks = saturated hydraulic conductivity (cm s−1), θ = actual volumetric water content (m3 m−3), θr = residual volumetric water content (m3 m−3), Φ = total porosity (m3 m−3) and λ = pore-size distribution index (−).
Therefore, θr is the amount of water remaining in a layer under infinite capillary suction and was estimated as follows :
where: WP = volumetric wilting point (m3 m−3).
The leakage rate depends upon the depth of the water-saturated soil (head) above the base of the layer, the liner thickness and the Ks value of the barrier soil. So, the leakage occurs whenever the moisture content of the layer above the liner is greater than the field capacity of the layer [19, 24].
In addition, the rainfall-runoff process is modelled using the SCS curve-number method with values above 0 up to 100, as presented in Section 4 of the National Engineering Handbook . The curve numbers for the areas I–III were obtained under the terms of the surface slope, the slope length, and the vegetation cover and also modified according to the previous sensitivity analysis. The SCS-CN method based on the following basic form :
where: R = runoff (m3), P = precipitation (m3), S = potential maximum soil moisture retention auf the runoff begins (m3) and Ia = initial abstractions (sum of interception + evapotranspiration + infiltration + depression storage) in m3. The retention parameter S is transformed into a curve number (CN) with following relationship :
The lateral drainage layer required information about the maximum drainage length as length of the horizontal projection of a representative flow path and the drain slope for the areas I–III . The lateral drainage equation can be described as follows :
where: x* = x/L (nondimensional horizontal distance), y* = y/L (nondimensional depth of saturation above liner), qD* = qD/KD (nondimensional lateral drainage rate) with KD = saturated hydraulic conductivity of the drain layer (cm/s) and α = inclination angle of the liner surface.
2.6. Model calibration and sensitivity analysis
The validity of the data used as input and output values for the comparison of observed and modelled data is of major importance . Therefore, the sensitivity analysis, calibration, and validation for the period from 2008 to 2015 were performed in a previous study on the basis of input and output values of the HELP model .
Therefore, an increasing evaporative zone depth from 10 to 100 cm can increase the actual evapotranspiration up to 100 mm year−1; an increasing LAI from 1 to 5 can increase the ETa values up to 85 mm year−1. Additionally, an increasing slope of the drainage layer from 2–30% can reduce the annual leachate rate of about 25%.
The associated calibration study made it necessary to implement a lateral drainage layer instead of a vertical percolation layer in 0.4–0.7 m depth to take into account the basic concept of the landfill capping system due to anisotropic Ks values of the compacted layer (see Section 2.4).
The correlation coefficient (r2) is an index of goodness of fit between the observed and modelled data according to .
3.1. Vegetation growth of the Rastorf landfill
The recultivated layer of the temporary capped area is used as pasture with a grass and clover mixture of flat-rooted, densely growing, and perennial grasses. The seed mixture used in 2008/2009 was composed as follows: 20% perennial ryegrass (
The species composition is significantly different from the initial seed mixture after several years of growth: 70–80% cocksfoot (
The white clover (
The landscape-ecological inventories and pedological excavations during 2013 and 2015 resulted in fine roots that were able to reach a maximum depth of 25–30 cm (flat rooting) and a weak to medium intensity (< 10 roots dm−2), mainly along smaller hair or shrinkage cracks in the upper part of the recultivated layer (Figure 4). The subsequently secured areas showed deeper and pronounced rooting with depths of 35–40 cm (medium rooting) and a medium to strong intensity (11–20 roots dm−2).
3.2. Weather data, vegetative period and leaf are index
The evapotranspiration parameters for the HELP model are summarised in Table 2. The average annual wind speed varied between 4.35 m s−1 in 2015 and 4.91 m s−1 in 2013 and the average relative humidity (%) between 70.6 and 87.3% in the spring and summer months and between 82.5 and 95.2% in the autumn and winter months (Table 2). Additionally, the maximum leaf area indices with values between 1.0 and 3.5 were chosen on the basis of average annual LAI measurements in March, May, and July and October, respectively.
|Average annual wind speed (m s−1)||4.76||4.56||4.73||4.75||4.78||4.91||4.58||4.35|
|Evaporative zone depth (cm)||20||20||30||50||50||50||50||50|
|Maximum leaf area index (−)||1.0||2.0||2.0||3.5||3.5||3.5||3.5||3.5|
|Vegetative period (days)||262||345||219||231||230||220||266||255|
|Average relative humidity (%)|
3.3. Landfill design and soil physical parameters
The porosities of the boulder marl differ between 0.292 and 0.307 m3 m−3 in the barrier soil layer and 0.317 and 0.356 m3 m−3 in the drainage layer as well as the percolation layer. The FC values range between 0.175 and 0.213 m3 m−3, while the WP values varied between 0.117 and 0.167 m3 m−3 (Table 3). The highest Ks values were identified in the drainage layer between 5.6e-04 and 6.3e-04 m s−1, lower values were determined in the percolation layer between 4.5e-06 and 5.9e-06 m s−1 and the barrier soil layer had values ≤6.1e-09 m s−1.
|Study area and layer||Porosity||FC*||WP**||Ks||WC***||Slope length and gradient|
|(m3 m−3)||(m3 m−3)||(m3 m−3)||(m s−1)||(m3 m−3)||(m)/(%)|
|Barrier soil layer||0.292||0.175||0.121||3.7E-09||0.292|
|Barrier soil layer||0.302||0.196||0.143||6.1E-09||0.302|
|Barrier soil layer||0.307||0.213||0.149||3.6E-09||0.307|
3.4. Modelled water balance components of the Rastorf landfill between 2008 and 2015
In the study period between 2008 and 2015, the climatic water balance was positive (precipitation > evapotranspiration) and with regard to the German weather conditions, the outflow (2008–2010) and the actual evapotranspiration (2011–2015) were the greatest output values of the water balance (Table 4). The years 2012 and 2013 showed lower annual precipitation rates with 655 and 669 mm, respectively, compared to the average annual precipitation rate of 728 mm. The winters of 2008–2015 were mostly mild and only had some snow.
|∆ soil moisture content||0||0.5||−0.5||1.5||0.2||−0.2||−0.3||−0.3|
The modelled average annual ETa values ranged between 33% in 2010 and 60% in 2012, and the outflow rates between 39% in 2009 and 54% in 2010 of the annual precipitation. The changes in soil moisture content with −0.3 and 1.5 mm year−1 were moderate and the modelled leachate rates ranged between 14 and 18% in 2008–2010, and between 11 and 15% in 2011–2015 of the annual precipitation (Table 4).
These drier phases are characterised by higher discrepancies between ETp and ETa up to 4.9 mm d−1, especially in the warmer months between June and September (Figure 5). On the other side, the early warming phase during March to May showed moderate discrepancies of 0.6–2.7 mm d−1, and the period October to February of the following year indicated mostly no discrepancies between the potential and actual evapotranspiration.
The ETa values ranged between 46 and 50%, and since 2011 between 60 and 69% of the ETp with the increasing depth of the evaporative zone (20, 30–50 cm) and the maximum leaf area indices (1, 2–3.5), respectively (Figure 5). The maximum depth complied with the part of the recultivation layer, in which the water content fluctuated intensely during the study period. The modelled water content in this evaporative zone appeared mostly above the field capacity of 95 mm, while longer phases during the vegetative period (July–September) nearly reached the wilting point of 65 mm, resulting in a decreased ETa capacity (Figure 6).
The validity of the modelling results depends on the quality of the input data and related measurement methods that exhibit random errors depending on the site and weather conditions.
In this study, a weather station located close to the landfill recorded precipitation with a German Hellmann type gauge including wind-induced precipitation losses with an average underestimation of the actual annual precipitation of 10% . Additionally, snow or rather snowmelt were no water balance factors during the study period between 2008 and 2015 under the weather conditions in Northern Germany.
The average annual actual evapotranspiration in Central Europe with an uncorrected precipitation rate of 700–800 mm (i.e., Rastorf landfill) is valued of approx. 450–550 mm for grassland vegetation with a good stand . Therefore, the modelled annual ETa values, ranging between 277 and 390 mm are significantly lower than the mentioned ETa values for grassland vegetation. The modelled average annual ETa values ranged between 33 and 60% of the annual precipitation, but smaller than the ETa values of approx. Two-third of the annual precipitation in Hamburg (landfill Georgswerder) under approx. Comparable weather conditions as mentioned in . The differences can be explained by the maximum leaf area index which strongly influences the evapotranspiration rate , while the HELP model assumed a constant LAI of 1, 2 or 3.5 for the whole year, respectively. On the other side, the daily average values of the wind speed do not reflect the actual wind conditions of an entire day  and the evaporative capacity of the wind-exposed Rastorf landfill must also be regarded as underestimated.
Longer phases during the vegetative period (July–September) nearly reached the wilting point of 65 mm, so, the evaporative zone (0.5 m) dried out more strongly and the transpiration capacity and thereby the ETa values of the grassland were restricted by (a) the inadequate water availability in the evaporative zone and (b) the limited water storage capacity, and (c) the limited capillary rise from deeper soil layers due to the compacted construction of the temporary capping system [5, 6]. Thus, phases with water contents below the critical field capacity of 95 mm should be as short as possible to prevent desiccation in the deeper layer, thus, the modelled water content is a first indicator to describe the hydraulic stability of the capping system.
Tree species or shrub vegetation (i.e.,
The modelled leachate rates were at a consistent level of 11–18% of the annual precipitation rate without significant deviations but exceeded the requirements of  at most 60 mm year−1 5 years after construction at the latest.
Otherwise, the modelled leachate rates indicate a sufficient percolation of water into the waste body to support the microbial processes ; between 2008 and 2017, the settlements of the waste body decreased from >20 to <4 cm year−1, so, the temporary system fulfils its purpose.
The slightly varying annual leachate rates indicate the functionality of the temporary capping system; continuously rising leachate rates would be an indicator for shrinkage crack formation or root penetration in the sealing layer , thus, the capping system would be ineffective. So, the hydraulic stability of the temporary capping system and especially the barrier soil layer can be assumed as ensured.
In summary, the water balance model is not suitable to estimate more specific soil physical problems (i.e., preferential flow through cracks or root holes) of recultivation or sealing layers . For an approved process description due to the model limitations, the numerical-based FEFLOW could be a more precise two-dimensional process description of the water fluxes of the Rastorf landfill in the saturated and unsaturated soil .
The HELP model is one of the most commonly used statistical-empirical approaches and is an useful option to successfully determine the leachate quantity of landfill capping systems and to proof which final capping system could be installed under the given weather and site conditions due to the statutory requirements.
The grassland vegetation of the Rastorf landfill changed in its plant-specific composition but is still effective to ensure moderate to high evapotranspiration rates and slope stability, while avoiding shrinkage-induced cracking and deeper rooting to protect the barrier soil or rather sealing layer. The future development depends on the intensity of wetting/drying cycles and further studies are required to improve the understanding of the long-term hydraulic stability of a mineral temporary capping system under climate change.
In order to finally proof the detailed water fluxes in structured landfill capping systems the more physically-based models will give more detailed insights into the variations in the soil water characteristics and the risk of crack formation in soil barriers due to desiccation and plant root penetration that may influence the functionality of it.
This research was supported by the Innovation Foundation Schleswig-Holstein and the ZMD Rastorf GmbH, Germany.
Conflict of interest
The authors do not declare conflict of interest.