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Models of environmental systems are simplified representations of the reality. For this reason, their results are affected by systematic errors. This bias makes it difficult to get reliable uncertainty estimates of model parameters and predictions. A relatively simple way of considering this bias when using deterministic models is to add a statistical representation of the bias to the model output in addition to observation error and to jointly estimate model parameters, bias and observation error. When assuming Normal distributions for bias and observation error, this leads to a relatively simple likelihood function that can easily be evaluated. Nevertheless, the sampling from the posterior distribution still requires long Markov chains to be calculated which can be prohibitive for computationally demanding models. In order to extend the range of applicability of this technique to computationally demanding models, we suggest to replace Markov chain sampling by a Normal approximation to the posterior of the parameters and to estimate prediction uncertainty by linearized error propagation. We tested this procedure for a didactical example and for an application of the biogeochemical-ecological lake model BELAMO to long-term data from Lake Zurich. This is a good test application because the strong coupling of output variables makes it difficult to avoid bias in the results of this model. These tests demonstrate the applicability of the suggested procedure, the approximate reproduction of the results of the full procedure for the didactical example, and meaningful results for the lake model. For the latter, the results demonstrate that the assumption of a realistic likelihood function leads to the conclusion that prediction uncertainty may be high.

Aquatic pesticide pollution from both agricultural and urban pest control is a concern in many parts of the world. Making an accurate assessment of pesticide exposure is the starting point to protecting aquatic ecosystems. This in turn requires the design of an effective monitoring program. Monitoring is also essential to evaluate the efficacy of mitigation measures aimed to curb pesticide pollution. However, empirical evidence for their efficacy can be confounded by additional influencing factors, most prominently variable weather conditions. This review summarizes the experiences gained from long-term (>5 years) pesticide monitoring studies for detecting trends and provides recommendations for their improvement. We reviewed articles published in the scientific literature, with a few complements from selected grey literature, for a total of 20 studies which fulfill our search criteria. Overall, temporal trends of pesticide use and hydrological conditions were the two most common factors influencing aquatic pesticide pollution. Eighteen studies demonstrated observable effects to surface water concentrations from changes in pesticide application rates (e.g., use restriction) and sixteen studies from interannual variability in hydrological conditions during the application period. Accounting for seasonal- and streamflow-related variability in trend analysis is important because the two factors can obscure trends caused by changes in pesticide use or management practices. Other mitigation measures (e.g., buffer strips) were only detectable in four studies where concentrations or loads were reduced by > 45%. Collecting additional agricultural (e.g., pesticide use, mitigation measures) and environmental (e.g., precipitation, stream flow) data, as well as establishing a baseline before the implementation of mitigation measures have been consistently reported as prerequisites to interpret water quality trends from long-term monitoring studies, but have rarely been implemented in the past.

Summary1. The community assembly of macroinvertebrates in streams depends on the regional taxon pool, dispersal limitations, local habitat conditions and biotic interactions. By integrating existing knowledge about these processes from theoretical ecology in a mechanistic model, we can test our mechanistic understanding and disentangle multiple stressor effects on community assembly. 2. To assess to which degree we can predict the community composition of macroinvertebrates, we integrated these processes in the mechanistic food web model Streambugs and tested it on 36 sites in the Glatt catchment on the Swiss plateau. The model predicts the observation probability of taxa from a regional taxon pool at each site taking into account uncertain knowledge on parameters, environmental conditions at the sites and sampling errors. 3. We use allometric scaling according to the metabolic theory of ecology, ecological stoichiometry and autecological data from trait databases that include the current knowledge on habitat requirements of the different taxa to parameterize their growth, respiration and death. 4. Without any calibration, for the majority of taxa at the 36 sites, the difference between the observed and predicted relative frequency of occurrence is <50% when taking prior parameter uncertainty and the uncertainty of environmental conditions into account (79% compared to 61% for the random model). By calibrating taxon-specific modification factors for the growth rate, we can increase the model compliance with data. 5. Analysing the influence of different ecological traits and their corresponding environmental influence factors reveals that feeding types and sensitivity to organic toxicants contribute most to the predictive capabilities of the model in this catchment. The influence of temperature stress and oxygen depletion due to pollution with organic matter on the community composition is negligible. These results confirm our expectations regarding the most important water quality issues of streams on the Swiss plateau. Current velocity plays an intermediate role in this model application. 6. The contribution of the feeding types to model performance highlights the importance of taking biotic interactions (competition for food sources and predator-prey interactions) into account to predict the coexistence of taxa. Better knowledge of the actual feeding links in the food web (e.g. from gut content or stable isotope data) that are currently inferred from feeding types, body size and food availability could further improve this approach.

Summary 1. With a modified version of the lake model BELAMO, we were able to describe the essential features of the dynamics of nutrients, dissolved oxygen, phyto‐ and zooplankton in three lakes of different trophic status over periods of 19–30 years, with essentially the same model parameters for all three lakes. This is remarkable, as the measured nutrient inputs decreased considerably during the simulated time period. 2. Despite having done this before for a period of 4 years with an earlier version of the model, a considerable effort was required that led to a series of model modifications without which the data could not be matched. This demonstrates that long‐term calibration of a model that combines processes in the water column with mineralisation in the sediment can be difficult. 3. Due to the necessarily simplified processes within the model, there is a bias in its output. We applied a recently developed technique for model calibration and uncertainty analysis to address bias and multiple calibration criteria. To account for the demanding long‐term simulations, a simplified numerical implementation of this technique was used. 4. Our results demonstrate good understanding of the chemical state of the lake during the calibration period but less of the biological variables. The credibility intervals used to visualise this knowledge widen substantially during the prediction period (consisting of the last 10 years of the simulation). 5. The joint calibration of the model with long‐term data from lakes of different trophic status is possible but only with considerable prediction uncertainty. Due to the explicit consideration of bias in our calibration technique, we are able to estimate quantitatively the uncertainty of our knowledge about chemical and biological variables in the lake.

We use a Gaussian stochastic process emulator to interpolate the posterior probability density of a computationally demanding application of the biogeochemical-ecological lake model BELAMO to accelerate statistical inference of deterministic model and error model parameters. The deterministic model consists of a mechanistic description of key processes influencing the mass balance of nutrients, dissolved oxygen, organic particles, and phytoplankton and zooplankton in the lake. This model is complemented by a Gaussian stochastic process to describe the remaining model bias and by Normal, independent observation errors. A small subsample of the Markov chain representing the posterior of the model parameters is propagated through the full model to get model predictions and uncertainty estimates. We expect this approximation to be more accurate at only slightly higher computational costs compared to using a Normal approximation to the posterior probability density and linear error propagation to the results as we did in an earlier paper. The performance of the two techniques is compared for a didactical example as well as for the lake model. As expected, for the didactical example, the use of the emulator led to posterior marginals of the model parameters that are closer to those calculated by Markov chain simulation using the full model than those based on the Normal approximation. For the lake model, the new technique proved applicable without an excessive increase in computational requirements, but we faced challenges in the choice of the design data set for emulator calibration. As the posterior is a scalar function of the parameters, the suggested technique is an alternative to the emulation of a potentially more complex, structured output of the simulation model that allows for the use of a less case-specific emulator. This is at the cost that still the full model has to be used for prediction (which can be done with a smaller, approximately independent subsample of the Markov chain).

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