A percentile approach to evaluate simulated groundwater levels and 1 frequencies in a Chalk catchment in Southwest England 2

9 Chalk aquifers are an important source of drinking water in the UK. Understanding and predicting groundwater levels is therefore 10 important for effective water management of this resource. Chalk is known for its high porosity and, due to its dissolvability, exposed 11 to karstification and strong subsurface heterogeneity. To cope with the karstic heterogeneity and limited data availability, specialised 12 modelling approaches are required that balance model complexity and data availability. In this study we present a novel approach 13 to simulate groundwater level frequency distributions with a semi-distributed karst model that represents subsurface heterogeneity 14 by distribution functions. Simulated groundwater storages are transferred into groundwater levels using evidence from different 15 observations wells. Using a newly developed percentile approach we can simulate the number of days exceeding or falling below 16 selected groundwater level percentiles. Firstly, we evaluate the performance of the model to simulate three groundwater time series 17 by a spilt sample test and parameter identifiability analysis. Secondly, we apply a split sample test on the simulated groundwater 18 level percentiles to explore the performance in predicting groundwater level exceedances. We show that the model provides robust 19 simulations of discharge and groundwater levels at 3 observation wells at a test site in chalk dominated catchment in Southwest 20 England. The second split sample test also indicates that percentile approach is able to reliably predict groundwater level 21 exceedances across all considered time scales up to their 75th percentile. However, when looking at the 90th percentile, it only 22 provides acceptable predictions for the longest available time scale and it fails when the 95th percentile of groundwater exceedance 23 levels is considered. Modifying the historic forcings of our model according to expected future climate changes, we create simple 24 climate scenarios and we show that the projected climate changes may lead to generally lower groundwater levels and a reduction 25 of exceedances of high groundwater level percentiles. 26


Introduction
The English Chalk aquifer region extends over large parts of south-east England and is an important water resource aquifer, providing about 55 % of all groundwater-abstracted drinking water in the UK (Lloyd, 1993).As a carbonate rock the English Chalk is exposed to karstification, i.e. the chemical weathering (Ford and Williams, 2013), resulting in particular surface and subsurface features such as dollies, river sinks, caves and conduits (Goldscheider and Drew, 2007).Consequently, karstification also produces strong hydrological subsurface heterogeneity (Bakalowicz, 2005).The interplay between diffuse and concentrated infiltration and recharge processes, as well as fast flow through karstic conduits and diffuse matrix flow, result in complex flow and storage dynamics (Hartmann et al., 2014a).Even though Chalk tends to less intense karstification, for instance compared to limestone, its karstic behaviour has increasingly been recognised (Fitzpatrick, 2011;Maurice et al., 2006Maurice et al., , 2012)).
Apart from the good water quality, favourable infiltration and storage dynamics which make chalk aquifers a preferred source of drinking water in the UK, their karstic behaviour also increases the risk of fast drainage of their storages by karstic conduit flow during dry years.This also increases the risk of groundwater flooding as a result of fast responses of groundwater levels to intense Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-386, 2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 22 December 2016 c Author(s) 2016.CC-BY 3.0 License.groundwater-dominated.During the summer months, discharge of the Frome typically is very low, hardly reaching 5 m³/s (Brunner et al., 2010).The geology is predominated by the Cretaceous Chalk outcrop which underlays around 65 % of the catchment.The headwaters of the Frome include outcrops of the Upper Greensand, often overlain by the rather impermeable Zig-Zag Chalk (Howden, 2006).The middle reaches of the Frome traverse the Cretaceous Chalk outcrop followed by Palaeogene strata in the lower reaches, eventually draining into Poole Harbour.The major aquifer Chalk appears mainly unconfined.However, in the lower reaches it is overlain by Palaeogene strata, resulting in confined aquifer conditions.The region around the Frome catchment is known for the highest density of solution features in the UK (Edmonds, 1983) which can be mainly observed in the interfluve between the Frome and Piddle (Adams et al., 2003).Loams over chalk, shallow silts, deep loamy, sandy and shallow clays constitute the primary types of soils occurring in the study area (Brunner et al., 2010).The soils of the upper parts of the catchment are mainly shallow and well drained (NRA, 1995).In the middle and lower reaches the soils are becoming more sandy and acidic due to waterlogged conditions caused by either groundwater or winter flooding (Brunner et al., 2010;NRA, 1995).Due to its geological setting, the area is prone to groundwater flooding.It has occurred several times at different locations, for example in Maiden Newton during winter 2000/2001(Environment Agency, 2012) and in Winterbourne Abbas during summer 2012 (Bennett, 2013).

Figure 1: Overview on the Frome catchment 3 Methodology
In order to consider karstic process behaviour in our simulations we use the process-based karst model VarKarst introduced by Hartmann et al. (2013b).VarKarst includes the karstic heterogeneity and the complex behaviour of karst processes using distribution functions that represent the variability of soil, epikarst and groundwater and was applied successfully at different karst regions over Europe (Hartmann et al., 2013a(Hartmann et al., , 2014b(Hartmann et al., , 2016)).We use a simple linear relationship that takes into account effective porosities and base level of the groundwater wells (see Eq. 1) to enable the model to simulate groundwater levels based on the groundwater storage in VarKarst.Finally, a newly developed percentile approach is used to transfer simulated groundwater level time series into groundwater level frequency distributions to compare to observed behaviour at a number of monitored wells.

The model
The VarKarst model operates on a daily time step.Similar to other karst models, it distinguishes between three subroutines representing the soil system, the epikarst system and the groundwater system but it also includes their spatial variability , which is expressed by distribution functions that are applied to a set of N=15 model compartments (Figure 2).Pareto functions as distribution functions have shown to perform best in previous work (Hartmann et al., 2013a(Hartmann et al., , 2013b)), as well as the number of 15 model compartments (Hartmann et al., 2012).Including the spatial variability of subsurface properties in this manner, the VarKarst model can be seen as a hybrid or semi-distributed model.All relevant equations and model parameters are provided in Table 2 and Table    3, respectively.For a detailed description of VarKarst see Hartmann et al. (2013b).(1) The related parameters are hgw [m] and pgw [-].hgw is the difference of the base of the contributing groundwater storage (that is simulated by the model) and the base of the well that is used for calibration and evaluation.pgw represents the average porosity of the rock that is intersected by the well.

Data availability
The daily discharge data for gauge East Stoke was obtained from the Centre for Ecology & Hydrology (CEH, http://nrfa.ceh.ac.uk/ ) and dates back to the 1960s.The borehole data was provided by the Environment Agency (EA) and obtained via the University of Bristol.The total data used for modelling in this study can be seen in Table 1.The three boreholes (Ashton Farm, Ridgeway and Black House) comprised high resolution raw data which had been collected at a 15-minute interval.For further analysis, the data was aggregated to daily time averages.The potential evapotranspiration has a strong annual cycle.Since most recent data from years 2009-2012 was missing, representative PET-years were calculated on the basis of the last fifty years.Climate projections were obtained from the UK Climate Projections User Interface (UKCP09 UI, http://ukclimateprojections-ui.metoffice.gov.uk/ ).For more information about the UKCP see Murphy et al. (2010).

Model calibration and evaluation
The Kling-Gupta Efficiency (KGE) is used as a performance measure to calibrate against the discharge and the three boreholes.The KGE is a result of a decomposition of the NSE (and MSE), emphasizing the importance of the different components of the criterion (Gupta et al., 2009).We use the Shuffled Complex Evolution Method (SCEM) for our calibration.This method explores the parameter space using a Monte Carlo Markov Chain and searches for posterior distributions of the model parameters (Vrugt et al., 2003), including the regions with optimum performance.In addition, the posterior parameter distributions derived from SCEM provide information about the identifiability of the parameters.The more they differ from a uniform final posterior distribution the higher the identifiability of a model parameter.Parameter ranges were chosen following previous experience with the VarKarst model (Hartmann et al., 2013a(Hartmann et al., , 2013b(Hartmann et al., , 2014b(Hartmann et al., , 2016)).Besides the quantitative measure of efficiency, a split sample test (Klemeš, 1986) was carried out.Our data covered precipitation, evapotranspiration, discharge and groundwater levels from 2000 to the end of 2012.We calibrated the model on the period 2008-2012 and used the period 2003-2007 for validation.We chose this reversed order to be able including the information of 3 boreholes that was only available for 2008-2012.Three years were used as warmup, respectively.During calibration, the most appropriate of the N=15 groundwater compartments to represent each groundwater well was found by choosing the compartment with the best correlation to the groundwater dynamics of the well.This procedure was repeated for each well and each Monte Carlo run and finally provides the three model compartment numbers that produce the best simulations of groundwater levels at the three operation wells and the best catchment discharge according to our selected weighting scheme.During calibration we used a weighting scheme which was found by trial and error.Discharge and the borehole at Ashton Farm were both weighted as one third as Ashton farm is located in the lower parts within the catchment while the other two boreholes were located at higher elevation at the catchment's edge and weighted one sixth each.In order to explore to contribution of the different observed discharge and groundwater time series during the calibration, we use SCEM to derive the posterior parameter distributions using (1) the final weighting scheme, (2) only discharge, (3) only Ashton farm, and (4) only the other two boreholes

The percentile approach
Even though the VarKarst model includes spatial variability of system properties by its distribution functions, its semi-distributed structure does not allow for an explicit consideration of the locations of ground water wells.Its model structure allowed for an acceptable and stable simulation of groundwater level time series of the three wells (see subsection 4.1) but for groundwater management, frequency distributions of groundwater levels, calculated over the time scale of interest, are commonly preferred.For that reason we introduced a groundwater level percentile based approach.Other than Westerberg et al. ( 2016) that transferred discharge time series into signatures derived from flow duration curves, we calibrate directly with the discharge and groundwater time series in order to evaluate the performance of our approach for selected time periods (see evaluation below).Similar to the calculation of standardised precipitation or groundwater indices (e.g., Bloomfield and Marchant, 2013;Lloyd-Hughes and Saunders, 2002) we create cumulative frequency distributions of observed groundwater levels and the simulated groundwater levels from the previously evaluated model.Now, the exceedance probability or percentile for a selected observed groundwater level (for instance, the groundwater level above which groundwater flooding can be expected) can be used to define the corresponding simulated groundwater level and the number of days exceeding or falling below the chosen groundwater level can directly be extracted from the frequency distributions (Figure 3).Note that this procedure is performed after the model is calibrated and validated as described in the previous subsection.

Figure 3: schematic description of the percentile approach
As the approach is meant to be applied in combination with climate change scenarios, we perform an evaluation on multiple time scales and flow percentiles.We assess the 5 th , 10 th , 25 th , 50 th , 75 th , 90 th and 95 th percentiles on temporal resolutions of years, seasons, months, weeks and days.The deviation between modelled and observed number of exceedance days of these different percentiles is quantified by the mean absolute deviation (MAD) between simulated exceedances and observed exceedances: (2) Where x stands for the time scale (years, months, weeks, days) and p is the respective percentile.To better compare the deviation for different percentiles we normalize the MAD to a percentage of mean absolute deviation (PAD) with the total number of days of the chosen time scale: where dpx is a normalizing constant standing for total the number of days of the respective time scale and percentile.For example, if we take the time scale months and the 75 th percentile of exceedances we got a dpx of (100-75) % x (365.25 / 12) days.To evaluate the prediction performance of the approach, percentiles are calculated based on the calibration period and the applied on the validation period similar to the split sample test in subsection 3.3.That way we are able to evaluate our model over different thresholds and in terms of temporal resolution.

Establishment of simple climate scenarios and assessment of groundwater level frequency distributions
Given the model performance assessment above, we then use our approach to assess future changes of groundwater level frequencies at our study site.We derive projections of future precipitation and potential evapotranspiration by manipulating our observed 'baseline' climate data.We extract distributional samples of percentage changes of precipitation and evaporation from the UK probabilistic projections of climate change over land (UKCP09) for (1) a low emission scenario and (2) a high emission scenario for the time period of 2070-2099.This enables us to capture, in a pragmatic and computationally efficient approach, for the two emission scenarios the general range of changes for the most pertinent variables that we think will most impact changes to monthlyseasonal GW responses.We focus on projected median delta values for change in mean temperature (°C) and precipitation (%) as well as the respective 25 th and 75 th percentile from the probabilistic projections and apply them on our input data.For our model input we transfer projected temperatures into evapotranspiration via the Thornthwaite equation (Thornthwaite, 1948).In this way, we obtain 3 x 3 projections (3x precipitation and 3x evapotransration) for each of the emission scenarios that also address the uncertainty associated with the projections.The resulting simulations will provide an estimate of possible future changes of groundwater level frequencies for the two emission scenarios including an assessment of their uncertainty.

Model calibration and evaluation
Table 3 shows the optimised parameter values as well as the model performance.The simulation of the discharge shows KGE values of 0.73 and 0.58 in the calibration and validation period, respectively.The borehole simulations show high KGE values and only slight deteriorations in the validation period.The parameters are located well within their pre-defined ranges.Mean soil storage Vmean,S and mean epikarst storage Vmean,E are 2015.6mm and 1011.7 mm, respectively.The porosity parameter at Ashton Farm is the highest, followed by the borehole at Black House.Ridgeway shows the smallest porosity value.For Ashton Farm and Blackhouse the calibration chose the groundwater storage compartment 7, for Ridgeway it chose the compartment number 8.
Figure 4 plots the observations against simulations for the calibration and validation period.Modelled discharge generally matches the seasonal behaviour of the observations.However, some low-flow peaks are not depicted well in the simulation.When looking at the groundwater levels, the simulation of Ashton Farm appears to be most adequate.However, there are considerable periods when differences from the observations can be found for all wells.Simulations at Ridgeway and Black House show moderate performance in capturing peak groundwater levels.Notably the simulation at Black House is slightly better in the validation period.
The cumulative parameter distributions derived by SCEM indicate that the model parameters were well identifiable when we use all available data (Figure 5), while some parameters remain hardly identifiable when only parts of the available data were used for calibration.For instance, non-identifiable groundwater porosity and base level parameters if only discharge was used for calibration.

The percentile approach
When simulated peak values of groundwater levels are compared to the observations, we find a rather moderate agreement.Using the percentile approach we find different thresholds to exceed our selected groundwater level percentiles.This is elaborated for 90 th percentile of simulated and observed groundwater levels of Ashton farm (Figure 6).  4 shows the mean observed and modelled exceedances of all selected thresholds (the 5 th , 10 th , 25 th , 50 th , 75 th , 90 th , and 95 th percentiles) at all temporal resolutions in the validation period.By comparing matches in the number days of exceedance we evaluate our model at different percentiles and time scales.The left value is the mean absolute deviation (MAD) and the right value is the percentage of absolute deviation (PAD).We can see that the higher the percentile the larger is the deviation between observed and modelled exceedances.The same is true for the PAD when moving from lower to higher temporal resolutions.The MAD gets lower the higher the temporal resolution is.

Impact of simulated climate changes on groundwater level distributions
The results of applying the two climate projections to the model can be found at Table 5 and in Figure 7.Both emission scenarios (low & high) lead to an increased modelled actual evapotranspiration and to decreased discharge simulations.In addition, both emission scenarios show a substantial reduction in exceedances of high percentiles.We also find that the standard error of the exceedances and non-exceedances of high emission scenario tends to be higher than the standard error of the low emission scenario.

Reliability of the simulations
The low decrease in model performance during the validation period for the discharge and groundwater time series indicates acceptable robustness of the calibrated parameters, which is corroborated by their generally mainly high identifiability derived by SCEM for the final calibration scheme the used all 4 available observed discharge and ground water level time series.Using the different weighting schemes we also see that only the combined calibration with all 4 time series allowed for identifying all model parameters, while using the discharge or the groundwater observations alone would have produced posterior distributions that indicate low sensitivity of some of the model parameters.A look at the parameter values reveals an adequate reflection of the reality.However, Vmean,S and Vmean,E are quite high considering that initial ranges for these parameters were 0-250/0-500 mm (Hartmann et al., 2013a(Hartmann et al., , 2013c)).As previous studies took place in fairly dry catchments, the ranges were extended substantially to deal with the wetter climate in southern England.A high aSE indicates a high variability of soil and epikarst thicknesses favouring lateral karstic flow concentration (Ford and Williams, 2007).Butler et al. (2012) notes that the unsaturated zone of the Chalk is highly variable, ranging from almost zero near the rivers to over 100 m in interfluves.
Additionally, the mean epikarst storage coefficient Kmean,E is quite low, indicating fast water transport from the epikarst to the groundwater storage which is in accordance to other studies (e.g., Aquilina et al., 2006).The value of parameter afsep indicates that a significant part of the recharge is diffuse.A moderately high conduit storage coefficient KC and a high aGW indicate that there is a significant contribution of slow pathways by the matrix system.This is in accordance with the findings of Jones and Cooper (1998) as well as Reeves (1979) who reported 30 % and 10-20 % of the recharge occurring through (macro-) fissures in Chalk catchments, respectively.Although groundwater flow in the chalk is dominated by the matrix, given antecedent wet conditions, fracture flow can increase significantly (Butler et al., 2012;Ireson and Butler, 2011;Lee et al., 2006).Overall, split-sample test, parameter identifiability analysis, realistic values of parameters and plausible simulation results provide strong indication for a reliable model functioning.

Performance of the percentile approach
Based on the idea of the standardised precipitation or groundwater indices (Bloomfield and Marchant, 2013;Lloyd-Hughes and Saunders, 2002) our new percentile approach permits to improve the performance of the model to reflect observed groundwater level exceedances.It yields acceptable performance for years to days up to the 90 th percentile.A reduction of precision with the time scale is obvious but in an acceptable order of magnitude when the validation period is considered.Although deviations are considerable both in the calibration and validation period, they are stable demonstrating certain robustness but also the limitations of our approach.Although the variable model structure of the VarKarst model was shown to provide more realistic results than commonly used lumped models (Hartmann et al., 2013b) it still simplifies a karst system's natural complexity.This is obvious in the simulated time series at Ashton Farm and Black House indicate, which also an over-estimation of high levels and underestimation of low levels.The reason for this behaviour might be due to the modelling assumption of a constant vertical porosity, despite the knowledge that there can be a strongly non-linear relation between chalk transmissivity and depth.Several studies acknowledge that hydraulic conductivity in the Chalk follows a non-linear decreasing trend with depth (Allen et al., 1997;Butler et al., 2009;Wheater et al., 2007).This is mainly attributed to the decrease of fractures because of the increasing overburden and absence of water level fluctuations (Butler et al., 2012;Williams et al., 2006).Hydraulic conductivities in the Chalk can span several orders of magnitude (Butler et al., 2009) and are particularly enhanced at the zone of water table fluctuations (Williams et al., 2006).
In addition, cross-flows occurring in the aquifer can lead to complicated system responses in the Chalk (Butler et al., 2009).For the sake of a parsimonious model structure, these characteristics were omitted in this study but their future consideration could help to improve the simulations if information about the depth profile of permeability is available.Such decrease of performance was also found for standardised indices that use probability distributions instead of a simulation model (Van Lanen et al., 2016;Núñez et al., 2014;Vicente-Serrano et al., 2012).To improve the approach's reliability for higher groundwater level percentiles, a model calibration that is more focussed on the high groundwater level percentiles may be a promising direction.A consideration of the time spans above the 90 th percentile will allow for a better simulation quality.However, longer time series than available for this study would be needed for a proper evaluation of this idea.

Applicability and transferability of our approach
We prepared two scenarios by manipulating our input data using probabilistic projections of annual changes of precipitation and potential evaporation at 2070-2099 for a low and a high emission scenario.This might neglect some of the changes on climate patterns predicted by climate projections but it is based on local and real meteorological values of the reference period therefore avoiding problems that arise when historic and climate projection data show pronounced mismatches during their overlapping periods.Our results revealed that both scenarios lead to less exceedances over higher percentiles and more non-exceedances of lower percentiles indicating a higher risk of groundwater drought at our study site.However, one problem that arises from our approach is that we do not consider changes in the seasonal patterns of our input variable, for example the increase of winter precipitation.If this increase was considered the results would probably yield more exceedances of higher percentiles, as for instance found by Jimenez-Martinez et al. (2015).Although quite simplistic our results are qualitatively in accordance with previous studies indicating increased occurrence of droughts in the UK (Burke et al., 2010;Prudhomme et al., 2014).The risk of drought occurrences might increase depending on the magnitude of change in evapotranspiration.However, more research and the application of more elaborated scenarios is necessary to completely understand the consequences of the change in groundwater frequency patterns in the UK chalk regions.
As the VarKarst model is a process-based model that includes the relevant characteristics of karst systems over range of climatic settings (Hartmann et al., 2013b) our approach can to some extent be used to assess future changes of groundwater level distributions and also be applied in other regions.This may bring some advantage concerning approaches that used transfer functions (Jimenez-Martinez et al., 2015) or regression models (Adams et al., 2010) for estimating groundwater levels, if enough data for model calibration and evaluation is available.
As has been noted by Cobby et al. (2009), the likelihood and depth of groundwater inundations is one of the major challenges for future research of groundwater flooding.Since it is a lumped approach it may provide, after Butler et al. (2012), "a good indication of the likelihood of groundwater flooding, but do[es] not indicate where the flooding will take place".A spatial determination of the groundwater table as in Upton and Jackson (2011) would be possible but only in catchments where the borehole network is extensive.Thereby, the possibility to model several boreholes with one single calibration, due to compartment structure in VarKarst, might be also an advantage.Butler et al. (2012) noted that the parameterization of the unsaturated zone is a major difficulty in the Chalk.Since this study struggles also with the porosity, future work should take a closer look at this subject.

Conclusions
We used an existing process-based lumped karst model to simulate groundwater levels in a chalk catchment in South England.
Groundwater levels were simulated by translating the modelled groundwater storage into groundwater levels with a simple linear relationship.To evaluate our approach we analysed the agreement of observed and simulated groundwater level exceedances for different percentiles.Finally, a simple scenario analysis was undertaken to investigate the potential future changes of groundwater level frequencies that affect the risk of groundwater flooding as well as the risk of groundwater droughts.The model performance for discharge and the groundwater levels was satisfying showing the general adequacy of the model to simulate groundwater levels in the chalk.It also revealed shortcomings concerning higher groundwater levels.This was corroborated by the percentile approach that showed a robust performance up to the 90 th percentile.A scenario analysis using UKCP projections on expected regional climate changes showed that expected changes may lead to an increased occurrence of low groundwater levels due to increasing actual evaporation.In order to obtain more reliable results we recommend collecting more data about the hydrogeological properties of our study site to improve the structure of our model regarding the porosity and the unsaturated zone.In addition, longer time series and an adapted calibration approach which, in particular, emphasizes on the >90 th percentiles of groundwater levels could significantly improve our simulations.In addition we propose to apply the method on other catchments to test the transferability of our approach and to quantify the variability of climate change impacts over a wide range of Chalk catchments across the UK.

Figure 2 :
Figure 2: The VarKarst model structure Earth Syst.Sci.Discuss., doi:10.5194/nhess-2016-386,2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 22 December 2016 c Author(s) 2016.CC-BY 3.0 License.(equally weighted).Posterior parameter distributions are plotted as cumulative distributions.Deviations of the posterior distribution (diagonal) indicate a sensitive parameter.The more parameters that show sensitivity, the more information is contained in the selected calibration scheme.

Figure 4 :Figure 5 :
Figure 4: Modelled discharge [m³/s] of the Frome at East Stoke and groundwater levels [m a.s.l.] at the boreholes Ashton Farm, Ridgeway and Black House

Figure 6 :
Figure 6: Illustration of the percentile approach.Time series of the observed (grey dots) and modelled (green line) groundwater level at Ashton Farm.The dotted lines represent the respective 90th percentile

Figure 5 :Figure 6 :
Figure 5: Cumulative parameter distributions (blue) of all model parameters; strong deviation from the 1:1 (dark grey) indicate good identifiability

Figure 7 :
Figure 7: Mean (manipulated) input (mm/a), mean modelled output (mm/a) and mean (non-)exceeded percentiles (number/a) in the reference period and both scenarios (borehole: Ashton Farm; future period: 2070-2099).The circles indicate the spread among the 9 realisations for each of the two scenarios Earth Syst.Sci.Discuss., doi:10.5194/nhess-2016-386,2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 22 December 2016 c Author(s) 2016.CC-BY 3.0 License.Earth Syst.Sci.Discuss., doi:10.5194/nhess-2016-386,2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 22 December 2016 c Author(s) 2016.CC-BY 3.0 License.Table 4: Deviations of simulated to observed exceedances of different percentiles in the validation period (borehole: Ashton Farm).The left value is the mean absolute deviation MAD [d], the right value is the deviation percentage PAD [