1 Introduction
The presence of MP particles has been proven in a variety of different ecosystems
Currently, MP data collection from various environmental compartments is expensive and time-consuming; consequently, only small data sets are presently achievable. Here, numerical models, which are known and vigorously applied in sediment transport studies
Plastic denotes a wide range of different polymer types with different density ranges. Among the most widely produced are polyvinyl chloride (PVC), which has a density of 1275 , and polyethylene-terephthalate (PET), which has a density of 1400 ; these two plastics were used as model particles in the present study.
During cyclone “Xaver” in October 2017, mean horizontal bottom water currents exceeded 0.5 , e.g. in the Arkona Basin . We expect that significant transport and sorting of larger and denser plastic particles only takes place under such storm conditions. This assumption is justified in this study by a 1 month model run including storm and calm conditions. The interest of this study is the identification of potential areas of accumulation of MP particles to support the planning of measurement campaigns by identifying potential areas of interest, because we assume that a stock of high-density plastic particles exists in Baltic Sea sediments.
Extreme events have a strong impact on particle transport
compared the transport behaviour of amber with that of MPs and found dimensionless critical bottom shear stresses close to that represented by the Shields curve. They also found a variation depending on the plastic type and shape. Therefore, the Shields curve was adapted to calculate the critical shear stress.
A sediment transport model is applied in this study to simulate the transport of MP as suspended matter with sizes of the order of sand particles. Certain factors cannot be accounted for, such as the plastic type and shape, which can influence the critical bottom shear stress and the settling velocity of particles . Based on laboratory measurements using MPs down to 0.4 in size, calculated a sinking formula depending on the particle shape. For simplicity, the standard Stokes formula for spherical particles is used here.
Although the critical bottom shear stress and the settling velocity are assumed to strongly impact the uncertainty in the transport behaviour, this initial study focuses on a quantification of the metocean uncertainty in the transport behaviour. There are several other approaches to estimate the transport of MPs
A well-known method to quantify sensitivity to uncertainties in numerical models is the use of an ensemble approach. Ensemble forecasts have been used in operational weather prediction for more than 25 years and have also been successfully applied in different areas, such as aviation
Existing studies on the transport of MPs in the marine environment are mainly based on a particle tracking approach
2 Data and models
For our assessment, we applied a four-step model chain, as illustrated in Fig. . Firstly, ensemble data based on stochastic perturbations were produced with the WRF-ARW (Weather Research and Forecasting Model in the Advanced Research WRF variant) atmospheric model to account for uncertainties in the representation of storm events. Secondly, the atmospheric fields were passed to the WAVEWATCH III® wind wave model. Thirdly, atmospheric and wave ensemble data were then applied to drive the GETM (General Estuarine Transport Model) regional ocean model. Finally, a transport module in GETM simulated the transport of PET and PVC with particle sizes of 10 and 330 m. The WRF-ARW atmospheric model was applied here to produce an ensemble hindcast of a storm surge event in the Baltic Sea and to provide the necessary forcing fields for the wave and the ocean model. The simulation period covered 1–4 January 2019. This includes the storm Alfrida (the reader is referred to the ECMWF Severe Event Catalogue:
Figure 1
Schematic overview of the model chain used in this study.
[Figure omitted. See PDF]
2.1 The WRF-ARW atmospheric modelVersion 4.1.1 of the WRF-ARW atmospheric mesoscale model (
Figure 2
Bathymetry [] of the 1 nautical mile WAVEWATCH III® set-up. Black dots show stations for the validation of water level and significant wave height. The black rectangle shows the subregion for plots of the transport simulation results.
[Figure omitted. See PDF]
Sources of uncertainty in atmospheric model predictions originate from the initial conditions and from the model physics; for a regional model, they also originate from lateral boundary conditions. compared different ensemble generation methods and proposed the use of the ERA5 data from the Ensemble of Data Assimilations as initial conditions to allow for a spread from the start of the simulation. The initial conditions in the presented study are based on the high-resolution ERA5 reanalysis, and the model approach includes perturbations of the model physics and the lateral boundary conditions. In contrast, the desired spread needs to develop in the model ensemble in the method chosen here. We selected this method to keep our results comparable with a potential future application in forecast mode. While we ran the model for a storm event in the past, the same could be done for a predicted storm, possibly based on a deterministic forecast product.
2.2The WAVEWATCH III® wind wave model
Wave-induced bottom shear stress is an important driver for the resuspension of bottom sediments and, potentially, of high-density MPs on the seafloor, as investigated in this study. To be able to prescribe wave parameters at high spatial and temporal resolution, the WAVEWATCH III v6.07® (
Figure 3
Significant wave height at five stations from the 1 nautical mile WAVEWATCH III® model run. Wind data are from UERRA/HARMONIE-v1, WRF-ARW is unperturbed, and the 30 WRF-ARW members are generated with stochastic perturbations.
[Figure omitted. See PDF]
Observation data from buoys available from the Copernicus Marine Environment Monitoring Service (http://marine.copernicus.eu/services-portfolio/access-to-products/, last access: 14 March 2020) (CMEMS) were used for validation and calibration. A comparison with station data in Fig. shows good agreement in the significant wave height as well as verification scores over January 2019 (Table ). The spread in the ensemble is visible at all stations and is expected to provoke differences in the bottom shear stress, leading to differences in the resuspension.
Table 1Verification scores – root mean square error (RMSE), scatter index
Station | Bias [m] | RMSE | SI [%] | COR |
---|---|---|---|---|
BrofjordenWR | 0.08 | 0.26 | 22.64 | 0.96 |
Knollsgrund | 0.02 | 0.20 | 15.25 | 0.98 |
Northern Baltic | 0.11 | 0.29 | 18.33 | 0.96 |
FinngrundetWR | 0.01 | 0.24 | 18.05 | 0.98 |
Tallinnamadal | 0.22 | 0.41 | 61.75 | 0.85 |
Waves affect the seafloor until a water depth of about half the wave length. The dominant wavelength in the Baltic Sea is between 20 and 70 and can reach up to 130 .
2.3 The GETM regional ocean modelGETM
A detailed validation of the model set-up can be found in and . For demonstration purposes, only the spread in sea surface elevation due to the different atmospheric forcing sets is shown here (Fig. ). A verification of the water level at different stations from EMODnet (
Figure 4
Water level at six stations with the 1 nautical mile GETM model; atmospheric data from UERRA/HARMONIE-v1, WRF-ARW is unperturbed, and the 30 WRF-ARW members are generated with stochastic perturbations.
[Figure omitted. See PDF]
The ensemble generation in the GETM model in this study is only based on the ensemble hindcasts of the atmospheric and wave parameters driving the model runs. showed that stochastic perturbations in the ocean model are also important for uncertainty estimation. The uncertainty in the ocean currents could therefore be underestimated.
2.4 Microplastic representationIn GETM and FABM, sediment and MPs are represented as Eulerian concentration fields. GETM simulated the 3-D transport of the pelagic concentrations, whereas the FABM model calculated the interaction with the corresponding bottom pools due to erosion and deposition and provided settling velocities to GETM. In FABM, a model for non-cohesive sediments
The simulations in this study started from homogenous bottom pools of 1 as a purely hypothetical reference value as well as zero suspended material in the water column. Rivers and open boundaries were assumed to not import material into the model domain. MP transport in the model is affected by wave activity and different types of currents. Tidal currents are represented, but they only play a role in the Danish straits, as the interior of the Baltic Sea is non-tidal. Turbidity currents cannot be represented in our model, as the concentration of suspended matter has no influence on seawater density in the model. Thermohaline circulation, in contrast, is fully taken into account.
3 Results and discussion
3.1 MP relocation and its uncertainty
After a 2 d storm surge event, a rearrangement of particles could be observed in the model with some locations dominated by erosion and others by deposition. This can be seen by the change in the amount of MP stored in the bottom pool (PET and PVC with a diameter of 330 m). To demonstrate the range of uncertainty in the transported amount of MP, two different grid cells in the Gotland Basin were selected (Fig. ): 57.69 N, 21.35 E (Fig. a–b) as a net erosion location, and 57.66 N, 21.32 E (Fig. c–d) as a net deposition location. Relative to the initial concentration, net erosion varied between 39 % and 72 % for PVC and between 16 % and 45 % for PET. Net accumulation varied between 13 % and 38 % for PVC and between 22 % and 34 % for PET. Thus, for PVC in the deposition grid cell (Fig. c), weak erosion is visible in some ensemble members, whereas the majority of the ensemble members show net deposition at this location. For the denser PET, the uncertainty range is smaller than for PVC, implying that its transport is less sensitive to uncertainties in the wind fields and more predictable. Still, the transported amount, even in this particle class, varies by around a factor of 2 between realizations, showing that a realistic quantitative estimation of MP transport is impossible in ocean circulation models, even if the precise sinking, settling, and resuspension properties of the MP particles were perfectly known.
3.2 Erosion and deposition areas
Now we consider the spatial patterns where erosion and sedimentation take place. The spatial pattern in four selected ensemble members and the deterministic runs is shown in Fig. . We chose four members with a considerable spread in the simulated wave height (Fig. g). The overall spatial pattern is very similar between the different realizations. The main impact of the metocean uncertainty lies in the amount of the transported material. The perturbations of the atmospheric model also produce deviations in the track of the storm between ensemble members, which impacts the direction of ocean waves and currents and, in turn, the direction in which the bottom shear stresses are directed. These findings indicate that the bathymetry has a predominant impact on the region where erosion and deposition take place, as the locations are insensitive to changes in the track of the storm. For this specific storm surge event and selected region, net deposition took place on the south-western sides of ridges, and net erosion took place on the north-eastern sides. Model MP with a diameter of 330 m in deeper regions, below 50 , was completely unaffected. It is well known that water depth plays a major role in sediment erosion by waves, as deep-water waves (with wavelengths much shorter than the water depth) show an exponential attenuation in their velocity amplitude with depth
Figure 5
Bathymetry [m] of the subregion for which the model results are presented. Black dots indicate the locations of two selected grid cells for later reference.
[Figure omitted. See PDF]
Figure 6
Changing bottom concentration of PVC (a, c) and PET (b, d) particles with a 330 m diameter in the two grid cells indicated in Fig. , relative to the initial concentration. The different curves show 30 perturbed runs and 1 unperturbed run with WRF atmospheric forcing and another simulation with UERRA/HARMONIE-v1 forcing. Panels (a) and (b) show a grid cell predominated by processes of net erosion, whereas panels (c) and (d) show a cell with net sedimentation.
[Figure omitted. See PDF]
Figure 7
Seabed concentration of PVC with a 330 m diameter on 3 January 2019 at 12:00 UTC, i.e. after the storm surge event in the model, relative to the homogenous initial concentration. Individual panels show the unperturbed WRF run (a), the model driven by UERRA/HARMONIE-v1 (b), and four selected WRF ensemble members (c–f). Dots show the locations of the grid cells selected in Fig. . (g) Time series of the significant wave height [m] at the position of the dot in the other figures with net erosion.
[Figure omitted. See PDF]
The uncertainty ranges of the spatial pattern of the model results were further investigated by means of the ensemble statistics composed of the mean, minimum, and maximum of each individual grid cell of all ensemble members (Fig. ). The net effect – whether the location was characterized by deposition or erosion – appeared largely consistent for the entire uncertainty range. Only a few locations showed deviations from this finding where some ensemble members shifted between weak erosional and depositional net effects. The larger extent of the erosional areas was due to more severe representations of the storm event in some ensemble members. Overall, these findings suggest stability in spatial patterns of MP transport against changes in the wind forcing. Areas of erosion and deposition during a specific storm event are predictable.
Figure 8
Ensemble mean, minimum, and maximum of the seabed concentration of PVC with a 330 m diameter on 3 January 2019 at 12:00 UTC, i.e. after the storm surge event in the model, relative to the homogenous initial concentration. Dots show the locations of the grid cells selected in Fig. .
[Figure omitted. See PDF]
3.3 Effect of particle size on transport uncertaintyNext, we investigate the effect of particle size on the uncertainty in the transport by reducing the size of the particles to 10 m. The small PET particles show a net erosion across almost the whole model domain due to slower resettlement. That is, they are still found in the water column up to 1.5 d after the storm (at the end of the simulation). This partly explains the large difference between the ensemble minimum and maximum (Fig. b, c): When sedimentation takes longer, quantitative differences in erosion strength will result in larger transport deviations, as the material can be advected further. This finding is also supported by theory on sediment transport: smaller particles (if unconsolidated) are suspended under lower shear stress levels and also require calmer metocean conditions to deposit. Thus, the uncertainty in MP transport appears to strongly depend on the particle diameter and density.
Figure 9
(a) Change in the seafloor concentration of PET particles with a 10 m diameter in one selected grid cell in 30 perturbed runs and 1 unperturbed run with WRF forcing and 1 run with UERRA/HARMONIE-v1 forcing. (b) Ensemble minimum and (c) ensemble maximum on 4 January 2019 at 00:00 UTC (at the end of the simulation). All concentrations are relative to the homogenous initial concentration. The black dots show the locations for the time series plots.
[Figure omitted. See PDF]
To find out whether this is a systematic effect, the uncertainties in the amount of transported material dependent on the particle properties size and density were investigated in more detail. These relationships were studied based on sensitivity runs with 30 ensemble members for (1) PVC with grain sizes of 200, 250, 300, and 350 m as well as (2) 330 m MP with different densities of 1100, 1200, 1300, and 1400 (Fig. a, b). The seafloor concentrations at the end of the model run deviate between the ensemble members. Relative deviations from the ensemble mean were calculated. Figure c and d show that the relative uncertainty increases with decreasing density and/or particle diameter, with the exception of the 1100 m MP class, which shows a smaller uncertainty as it is almost completely resuspended at the chosen location. We conclude that the uncertainty in the amount of transported material on the seafloor at a specific time depends strongly on the properties of the transported material. Thus, the application of an ensemble approach (using more than one model realization to predict transport pathways) is especially important if finer and lighter material is to be represented in future model applications.
Figure 10
Time series of 30 ensemble members at 57.69 N, 21.35 E for (a) different MP sizes and (b) different MP densities. (c, d) Box-and-whisker plots show the uncertainty in the concentration of material on the seabed, expressed as a relative deviation of the individual ensemble members from the ensemble mean.
[Figure omitted. See PDF]
Figure 11
Spread of runs with varying atmospheric forcing and/or varying wave forcing for PVC with a 330 m diameter (a, b, c) and PET with a 10 m diameter (d, e, f), for the bottom concentration at 57.69 N, 21.35 E (see Fig. ) relative to the initial value.
[Figure omitted. See PDF]
3.4 Pathways of atmospheric uncertainty propagationIn the following, the mechanism by which the atmospheric uncertainty affects the MP transport is identified. In our model, this can be caused (a) by influencing the wave height, which changes the bottom shear stress and, therefore, MP mobilization, or (b) by directly affecting the ocean circulation through factors such as momentum input, thereby influencing both mobilization and transport. We focused on these two major pathways and attempted to distinguish their influence. The possibility of interlinkage by wave–current interaction is neglected in the present model cascade. To estimate the respective uncertainties of MP transport of the two above-mentioned pathways, an ensemble driven with the wave data from the unperturbed WRF-ARW run with the perturbed WRF-ARW atmospheric forcing and vice versa (with perturbed wave data and unperturbed atmospheric data) has been conducted. By comparing (Fig. ) the outcome with the original ensemble, where both perturbed atmospheric and wave data were used, it can be seen that the impact of the wave field depends on the properties of the transported material. The lighter or smaller the MP, the more important the impact of the wave uncertainty on the amount of transported material. For denser and larger MP, the uncertainty in the direct effect of atmospheric uncertainty on hydrodynamics is predominant.
Figure 12
Evolution of the amount of PET and PVC with a 330 m diameter and sediment with a 64 m diameter on the seafloor during January 2019, starting from initial amount of 1 , at two grid cells, (a) with net deposition and (b) with net erosion.
[Figure omitted. See PDF]
Figure 13
(a) Pearson correlation between the time series of bottom concentrations of PVC with a 330 m diameter and sediment with a 64 m diameter for January 2019. (b) Scatter plot of bottom concentrations after the 1-month simulation. Concentrations are given relative to the homogenous initial concentration.
[Figure omitted. See PDF]
3.5 Importance of storms for MP transportHigher-density MPs of about 300 m diameter were only transported under severe storm conditions, as demonstrated in Fig. . The continuation of the simulation for the rest of January 2019 caused almost no further erosion or deposition. This confirms the assumption regarding the importance of extreme events for MP transport, which complicates its direct empirical determination. Budget methods will be required to empirically determine quantities of transported MP. A budget method relates (a) the input and (b) the output of a quantity to (c) changes in its mass, e.g. inside an area of interest. If two of the three values are known, the third one can be determined. That is, transport rates might be more reliably derived from observed amounts before and after storm events than by multiplying abundances of suspended MP by instantaneous volume transports, both of which might show strong temporal variation during extreme weather conditions.
3.6 Similarities between MP and sediment transport
The finding that spatial patterns of MP can be reliably predicted by ocean models, while the quantitative estimation of MP is prone to considerable uncertainties shows that additional approaches are required for a more reliable estimation of large-scale MP concentration levels. Here, the recently found MP–sediment proxy postulated by , which is based on correlations between certain high-density polymer size fractions ( 1000 , 500 m) and sediment grain size fractions, would be an achievable method. Estimations of MP levels can be based on a relatively small in situ data set and extrapolated to larger spatial scales by using the MP–sediment correlates. Lower densities of MP (1000–1600 ) compared with sediments (quartz: 2650 ) are offset by a larger size. This relationship was explained by comparable threshold bed shear stresses (and thus erosion rates) between these size fractions, which appeared to be the predominant mechanism determining the sorting in the described study area (Warnow Estuary, Baltic Sea, Germany; ). Although the MP size ranges covered in the present study were below those investigated by , it is assumed that similar patterns can be found for smaller size ranges. Indeed, in the present study, after the storm surge event, model PVC with a diameter of 330 m co-occurred with 64 m sediment grains, as apparent by the high correlation coefficient shown in Fig. . This correlation is found to be largely explained by similar erosion rates (Fig. b), whereas bottom concentrations, predominantly determined by deposition, are also influenced by the settling velocity of particles and, thus, differ slightly (higher amounts of PVC). Therefore, it is expected that areas largely influenced by the settling of MP show a larger difference in the expected MP–sediment size relation than described by the current MP–sediment proxy. For instance, larger (and/or heavier) MP particles than 330 m PVC (such as PET) would be closer to the deposition rate of sediment grains of 64 m (Fig. a). Existing maps of sediment substrate type, which typically differentiate between median grain sizes above and below 63 m
4 Conclusions
A storm surge event in the Baltic Sea in January 2019 has been hindcast by a four-step probabilistic model chain started from an homogeneous initial MP distribution. The model validation showed a good performance for water level and significant wave height compared with different station data.
A strong variation in the amount of transported MP between ensemble members was found. This illustrates that quantitative modelling of MP transport during storm events already exhibits substantial uncertainty due to uncertainties in meteorological forcing fields (e.g. wind speeds). A test with different particle sizes and densities showed a dependence of the uncertainty in the transport on the particle properties. The impact of the metocean uncertainty on sediment and MP transport increases with decreasing particle density and/or size.
The spatial distribution pattern where material was eroded or accumulated in the model runs was stable against the atmospheric perturbations, illustrating the capability of a numerical model to identify regions of interest where seafloor sampling of MP concentrations is promising.
The demonstrated procedure could also be applied in forecast mode, by exchanging the ERA5 reanalysis data used in this study for data such as the freely available GFS forecasts (
As a consequence of the insensitivity of the location of erosional and depositional areas to the uncertainty in the metocean forcing and a substantially smaller transport during moderate conditions, this study indicates that it would, in principle, be possible to construct a map of the spatial distribution of high-density MP particles in the Baltic Sea using long model runs containing several storm events. Differences between storm events might be larger than the uncertainty in a single event. To get a more general picture of erosional and depositional regions in the Baltic Sea, other storm events with different tracks also have to be taken into account.
The demonstrated ensemble approach can also be useful for other applications, such as implementation in the maritime transport sector. After a strong storm event, it could help to predict whether it would still be possible for large vessels to enter a harbour or whether the morphodynamic changes are so strong that dredging would be necessary.
Appendix A Mathematical description of the particle sinking and erosion model
Sinking velocity of the particles is initially calculated using the Stokes formula: A1 where is the gravitational acceleration, is the particle diameter, is the kinematic viscosity of water, and and are the densities of the particle and the water respectively. To correct for larger particles whose sinking velocity would be overestimated by the Stokes formula, a Newtonian correction is applied by an iterative algorithm:
-
a Reynolds number is calculated as ;
-
a relative drag coefficient is derived from this Reynolds number as following Perry and Chilton, as cited by ;
-
the updated velocity is calculated as , which can be understood as a weighted geometric mean between the two velocities and .
Erosion takes place when the actual shear stress exceeds the critical shear stress. To determine the critical shear stress, we follow the Shields curve, using the version that was corrected by . First, we calculate the dimensionless particle diameter , which relates the particle diameter to a viscosity-determined length scale, following : A2 where is the kinematic viscosity of water, is the particle density, and is the water density. Then, we calculate the critical Shields parameter for non-cohesive grains, (also dimensionless), following as cited by : A3 The critical shear stress can then be calculated as A4
The actual shear stress is calculated from the wave-induced and the current-induced shear stress, and respectively. The current-induced shear stress itself, however, is also modified by the wave field, as it changes the bottom drag coefficient according to the DATA2 formula given by : A5 where is the shear stress induced by the current in the absence of waves. The shear stresses induced by currents and waves are combined depending on the angle between currents and waves: A6 If the actual shear stress exceeds the critical one, the deposited material becomes resuspended with first-order kinetics, i.e. proportional to its mass in the sediment pool.
The actual values for sinking velocities and critical stresses depend on temperature, as it influences sea water viscosity. Values for 10 C are presented in Table .
Table A1Sinking velocities and critical shear stress in the model at 10 C.
Diameter | Density | Sinking | Critical |
---|---|---|---|
velocity | shear stress | ||
(m) | (kg m) | (mm s) | (N m) |
10 | 1275 | 0.15 | 0.006210895 |
330 | 1275 | 8.14 | 0.045142586 |
10 | 1400 | 0.20 | 0.009277999 |
330 | 1400 | 10.98 | 0.062337737 |
Code and data availability
The WRF source code is available from
Sample availability
The demonstrated model results can be obtained upon request from the corresponding author.
Author contributions
RO developed the concept of the ensemble approach, set up the wave and atmospheric model, and carried out the model runs. KE planned the sediment–MP proxy study. UG and KK created the ocean model set-up and provided technical assistance. HR planned the MP transport study and provided assistance with the ocean model set-up. All authors contributed to writing the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This study was financed by the BONUS MICROPOLL project; BONUS MICROPOLL received funding from BONUS (article 185), which was jointly funded by the EU and Baltic Sea national funding institutions. Knut Klingbeil acknowledges sub-project M5 “Reducing spurious diapycnal mixing in ocean models” of the Collaborative Research Centre TRR 181 “Energy Transfers in Atmosphere and Ocean” (project no. 274762653), funded by the German Research Foundation (DFG). The simulations run in this study consumed computing resources at the North German Supercomputing Alliance (HLRN). Observational data originate from the EU Copernicus Marine Environment Monitoring Service. The simulations in this study were generated using Copernicus Climate Change Service information (2018/2019). The research and work leading to the UERRA data set used in this work has received funding from the European Union Seventh Framework Programme (FP7/2007–2013; under grant agreement no. 607193). We would like to thank the WRF and WAVEWATCH III® developers for providing their models via GitHub, the editor Erik van Sebille, and the two reviewers Andrei Bagaev and Florian Pohl.
Financial support
This study was financed by the BONUS MICROPOLL project. The publication of this article was funded by the Open Access Publishing Fund of the Leibniz Association.
Review statement
This paper was edited by Erik van Sebille and reviewed by Andrei Bagaev and Florian Pohl.
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Abstract
Microplastics (MPs) are omnipresent in the aquatic environment where they pose a risk to ecosystem health and functioning. However, little is known about the concentration and transport patterns of this particulate contaminant. Measurement campaigns remain expensive, and assessments of regional MP distributions need to rely on a limited number of samples. Thus, the prediction of potential MP sink regions in the sea would be beneficial for a better estimation of MP concentration levels and a better sampling design. Based on a sediment transport model, this study investigates the transport of different MP model particles, polyethylene-terephthalate (PET) and polyvinyl chloride (PVC) particles with simplified spherical sizes of 10 and 330
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Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer