4. Discussion

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% [19]. 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 [34]. 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 [13]. The differences can be explained by the maximum leaf area index which strongly influences the evapotranspiration rate [3], 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 [21] 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., Salix caprea and Ligustrum vulgare) have a higher transpiration potential with ETa values of 600–700 mm year<sup>1</sup> and are more effective than grassland to minimise the leachate generation of landfill capping systems [13]. However, more deeprooted plants require thicker recultivation layers (2.0–3.0 m) to prevent shrinkage-induced crack formation in soil barriers due to desiccation and plant root penetration [9, 10]. Thus, the conflict of interest with regard to the choice of vegetation mainly depends on the local weather conditions, where robust grassland species should be preferred for locations with low precipitation [34], while more transpiring plant species are useful in more humid locations.

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 [2] at most 60 mm year<sup>1</sup> 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 [4]; between 2008 and 2017, the settlements of the waste body decreased from >20 to <4 cm year<sup>1</sup> , 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 [10], 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 [5]. 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 [14].
