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Introductory overview of identifiability analysis: A guide to evaluating whether you have the right type of data for your modeling purpose
Identifiability is a fundamental concept in parameter estimation, and therefore key to the large majority of environmental modeling applications. Parameter identifiability analysis assesses whether it is theoretically possible to estimate unique parameter values from data, given the quantities measured, conditions present in the forcing data, model structure (and objective function), and properties of errors in the model and observations. In other words, it tackles the problem of whether the right type of data is available to estimate the desired parameter values. Identifiability analysis is therefore an essential technique that should be adopted more routinely in practice, alongside complementary methods such as uncertainty analysis and evaluation of model performance. This article provides an introductory overview to the topic. We recommend that any modeling study should document whether a model is non-identifiable, the source of potential non-identifiability, and how this affects intended project outcomes.
The influence of model structure on groundwater recharge rates in climate-change impact studies
Numerous modeling approaches are available to provide insight into the relationship between climate change and groundwater recharge. However, several aspects of how hydrological model choice and structure affect recharge predictions have not been fully explored, unlike the well-established variability of climate model chains—combination of global climate models (GCM) and regional climate models (RCM). Furthermore, the influence on predictions related to subsoil parameterization and the variability of observation data employed during calibration remain unclear. This paper compares and quantifies these different sources of uncertainty in a systematic way. The described numerical experiment is based on a heterogeneous two-dimensional reference model. Four simpler models were calibrated against the output of the reference model, and recharge predictions of both reference and simpler models were compared to evaluate the effect of model structure on climate-change impact studies. The results highlight that model simplification leads to different recharge rates under climate change, especially under extreme conditions, although the different models performed similarly under historical climate conditions. Extreme weather conditions lead to model bias in the predictions and therefore must be considered. Consequently, the chosen calibration strategy is important and, if possible, the calibration data set should include climatic extremes in order to minimise model bias introduced by the calibration. The results strongly suggest that ensembles of climate projections should be coupled with ensembles of hydrogeological models to produce credible predictions of future recharge and with the associated uncertainties.
Infiltration under snow cover: Modeling approaches and predictive uncertainty
Groundwater recharge from snowmelt represents a temporal redistribution of precipitation. This is extremely important because the rate and timing of snowpack drainage has substantial consequences to aquifer recharge patterns, which in turn affect groundwater availability throughout the rest of the year. The modeling methods developed to estimate drainage from a snowpack, which typically rely on temporallydense point-measurements or temporally-limited spatially-dispersed calibration data, range in complexity from the simple degree-day method to more complex and physically-based energy balance approaches. While the gamut of snowmelt models are routinely used to aid in water resource management, a comparison of snowmelt models’ predictive uncertainties had previously not been done. Therefore, we established a snowmelt model calibration dataset that is both temporally dense and represents the integrated snowmelt infiltration signal for the Vers Chez le Brandt research catchment, which functions as a rather unique natural lysimeter. We then evaluated the uncertainty associated with the degree-day, a modified degree-day and energy balance snowmelt model predictions using the nullspace Monte Carlo approach. All three melt models underestimate total snowpack drainage, underestimate the rate of early and midwinter drainage and overestimate spring snowmelt rates. The actual rate of snowpack water loss is more constant over the course of the entire winter season than the snowmelt models would imply, indicating that mid-winter melt can contribute as significantly as springtime snowmelt to groundwater recharge in low alpine settings. Further, actual groundwater recharge could be between 2 and 31% greater than snowmelt models suggest, over the total winter season. This study shows that snowmelt model predictions can have considerable uncertainty, which may be reduced by the inclusion of more data that allows for the use of more complex approaches such as the energy balance method. Further, our study demonstrated that an uncertainty analysis of model predictions is easily accomplished due to the low computational demand of the models and efficient calibration software and is absolutely worth the additional investment. Lastly, development of a systematic instrumentation that evaluates the distributed, temporal evolution of snowpack drainage is vital for optimal understanding and management of cold-climate hydrologic systems.
Groundwater fluxes in a shallow seasonal wetland pond: The effect of bathymetric uncertainty on predicted water and solute balances
Summary The successful management of groundwater dependent shallow seasonal wetlands requires a sound understanding of groundwater fluxes. However, such fluxes are hard to quantify. Water volume and solute mass balance models can be used in order to derive an estimate of groundwater fluxes within such systems. This approach is particularly attractive, as it can be undertaken using measurable environmental variables, such as; rainfall, evaporation, pond level and salinity. Groundwater fluxes estimated from such an approach are subject to uncertainty in the measured variables as well as in the process representation and in parameters within the model. However, the shallow nature of seasonal wetland ponds means water volume and surface area can change rapidly and non-linearly with depth, requiring an accurate representation of the wetland pond bathymetry. Unfortunately, detailed bathymetry is rarely available and simplifying assumptions regarding the bathymetry have to be made. However, the implications of these assumptions are typically not quantified. We systematically quantify the uncertainty implications for eight different representations of wetland bathymetry for a shallow seasonal wetland pond in South Australia. The predictive uncertainty estimation methods provided in the Model-Independent Parameter Estimation and Uncertainty Analysis software (PEST) are used to quantify the effect of bathymetric uncertainty on the modelled fluxes. We demonstrate that bathymetry can be successfully represented within the model in a simple parametric form using a cubic Bézier curve, allowing an assessment of bathymetric uncertainty due to measurement error and survey detail on the derived groundwater fluxes compared with the fixed bathymetry models. Findings show that different bathymetry conceptualisations can result in very different mass balance components and hence process conceptualisations, despite equally good fits to observed data, potentially leading to poor management decisions for the wetlands. Model predictive uncertainty increases with the crudity of the bathymetry representation, however, approximations that capture the general shape of the wetland pond such as a power law or Bézier curve show only a small increase in prediction uncertainty compared to the full dGPS surveyed bathymetry, implying these may be sufficient for most modelling purposes.
Infiltration under snow cover: Modeling approaches and predictive uncertainty
Groundwater recharge from snowmelt represents a temporal redistribution of precipitation. This is extremely important because the rate and timing of snowpack drainage has substantial consequences to aquifer recharge patterns, which in turn affect groundwater availability throughout the rest of the year. The modeling methods developed to estimate drainage from a snowpack, which typically rely on temporally-dense point-measurements or temporally-limited spatially-dispersed calibration data, range in complexity from the simple degree-day method to more complex and physically-based energy balance approaches. While the gamut of snowmelt models are routinely used to aid in water resource management, a comparison of snowmelt models’ predictive uncertainties had previously not been done. Therefore, we established a snowmelt model calibration dataset that is both temporally dense and represents the integrated snowmelt infiltration signal for the Vers Chez le Brandt research catchment, which functions as a rather unique natural lysimeter. We then evaluated the uncertainty associated with the degree-day, a modified degree-day and energy balance snowmelt model predictions using the null-space Monte Carlo approach. All three melt models underestimate total snowpack drainage, underestimate the rate of early and midwinter drainage and overestimate spring snowmelt rates. The actual rate of snowpack water loss is more constant over the course of the entire winter season than the snowmelt models would imply, indicating that mid-winter melt can contribute as significantly as springtime snowmelt to groundwater recharge in low alpine settings. Further, actual groundwater recharge could be between 2 and 31% greater than snowmelt models suggest, over the total winter season. This study shows that snowmelt model predictions can have considerable uncertainty, which may be reduced by the inclusion of more data that allows for the use of more complex approaches such as the energy balance method. Further, our study demonstrated that an uncertainty analysis of model predictions is easily accomplished due to the low computational demand of the models and efficient calibration software and is absolutely worth the additional investment. Lastly, development of a systematic instrumentation that evaluates the distributed, temporal evolution of snowpack drainage is vital for optimal understanding and management of cold-climate hydrologic systems.