Abstract. Karst groundwater systems exhibit heterogeneity in recharge, circulation, and discharge, occupying a unique position within groundwater systems. This complexity facilitates rapid responses via the preferential flow routes, making karst systems vulnerable to climatic and anthropogenic pressures. High-altitude karst aquifers are particularly susceptible to shifting climate patterns – specifically rising temperatures, declining snow cover, and increasingly less and inconsistent precipitation – within the Mediterranean climate hotspot. Effective sustainable management of these groundwater systems require robust hydrological modelling; however, the application of such models is often constrained by the availability of high-quality, reliable datasets. This study presents a comprehensive collection of high-resolution karst spring discharge data from major Euro-Mediterranean mountain belts, including the Atlas, Betics, Pyrenees, Jura, Alps, Carpathians, Apennines, Dinarides, Hellenides, Balkans, Taurus, Levant, and Zagros. We compiled a total of 118 discharge time series specifically curated for hydrological modelling. Geographically, the dataset is led by the Alps (approx. 42%), followed by the Dinarides (approx. 10%), with the Apennines, Carpathians, and Zagros each contributing approx. 7%. The Levant and Taurus account for approx. 5% each, while the remaining regions (Atlas, Balkans, Betics, Hellenides, Jura, and Pyrenees) represent less than 5% each. In terms of temporal resolution, 92% of the records are daily, while hourly and monthly data each comprise 4%. The average record length is 19 years, which is led by a 99-year series from Unica Spring, Slovenia (1926–2025). Regional analysis indicates that the Alps, Apennines, Balkans, Betics, Dinarides, Jura, and Levant maintain average record lengths exceeding 20 years, whereas the Atlas, Carpathians, Taurus, and Zagros range between 10 and 20 years. The shortest average records were observed in the Hellenides and Pyrenees (7 and 8 years, respectively), which is still adequate for hydrological modelling applications.

Karst aquifers are a crucial source of water, supplying approximately 10% of the global population and often serving as the sole water resource in certain regions. These aquifers are characterized by highly heterogeneous flow dynamics and exhibit significant temporal variability in both hydrodynamic and physico-chemical conditions. Continuous monitoring of these parameters is essential for advancing our understanding of karst aquifer functioning; however, comprehensive, high-frequency datasets remain limited. We present a comprehensive dataset covering 13 karst springs monitored across nine observatories of the French Karst National Observatory Service (SNO KARST), spanning various hydroclimatic regions (oceanic, mountainous, Mediterranean). The SNO KARST aims to strengthen knowledge-sharing and to promote cross-disciplinary research on karst systems at the national scale. The dataset includes: (1) hydrodynamic data (water level, discharge), and (2) physico-chemical data (water temperature, electric conductivity, pH, dissolved oxygen, turbidity, Total Organic Carbon (TOC), Dissolved Organic Carbon (DOC), nitrate, and organic matter fluorescence). Spanning over a decade of continuous monitoring, such a dataset is required for the analysis of the hydrological and physico-chemical dynamics of karst aquifers, the assessment of their vulnerability to pollution and climate change, and the modeling of hydrodynamic and hydrochemical variables, ultimately aiming to improve the management and preservation of these critical water resources in contrasted contexts.

High concentrations of ammonia nitrogen (NH4+-N) are a dominant water pollutant in ionic rare earth mining basins, threatening aquatic ecosystems and drinking-water safety. To quantify these dynamics, this study developed a coupled SWAT-WASP model for the upper Dongjiang River Basin (UDRB), integrating remote sensing and long-term monitoring data; the model was calibrated and validated with 2016-2018 monthly observations, and quantitative evaluation via Nash-Sutcliffe Efficiency (NSE) and Percent Bias (PBIAS) showed good performance (runoff: NSE = 0.77-0.80; NH4+-N: SWAT NSE = 0.56-0.61, SWAT-WASP NSE = 0.65-0.87), confirming its reliability. 2022 simulations revealed strong NH4+-N spatial heterogeneity, with concentrations >1.8 mg L-1 near mining zones versus <0.5 mg L-1 in upstream natural areas; geodetector analysis identified population density combined with industrial-agricultural activity as the top driver of spatial differentiation (q > 0.40), while interactions between precipitation, temperature, and land use further amplified variability. Overall, the SWAT-WASP framework provides a robust tool for evaluating NH4+-N dynamics and supports targeted pollution control and ecological restoration in rare earth mining watersheds.

This study explores the complex interactions among eco-hydro-meteorological (EHM) variables, such as soil moisture (SM), precipitation (P), vapor pressure deficit (VPD), and sap flow velocity (SF), in the Mediterranean climate, where water scarcity and the effects of climate change are becoming increasingly pronounced. While previous studies have identified thresholds controlling runoff generation in Mediterranean catchments, it remains unclear how lead-lag dynamics among EHM variables govern ecological responses. This study addresses this gap by using wavelet analysis to explore the controls and dynamics of FSM-P and FSM-VPD feedbacks across different time and frequency scales, investigating whether EHM interactions exhibit evident thresholds that trigger feedback switches in response to SM availability and atmospheric demand. These dynamics were studied during the 2021 growing season at two topographic positions (riparian and hillslope) on an experimental hillslope in a Mediterranean forested catchment, central Italy. Our results revealed that SM in the hillslope position showed rapid, event-driven responses to P, with soil water recharge processes that differed significantly between the wet and dry seasons. This sensitivity to climatic forcings was greater in the hillslope SM than in the riparian one, which was characterized by more uniform and smoothed responses. Furthermore, the results highlighted the activation of proactive water-saving strategies adopted by trees located in the hillslope position, as evidenced by a critical SM threshold of 0.15 m3/m3 below which not only was P ineffective, but also SF was severely limited. In contrast, the constant availability of soil water in riparian areas allowed trees to maintain higher transpiration rates, showing a more passive response to atmospheric demand. In conclusion, although P is the main source of soil water recharge, its effectiveness on water availability and tree transpiration depends on complex interactions within the soil-plant-atmosphere continuum, with topography acting as the dominant controlling factor. These insights are critical for improving our understanding of the resilience of forest ecosystems and for guiding more effective water and forest management strategies.

Mountain ecosystems have experienced significant anthropogenic disturbances, resulting in severe degradation. Due to their intricate topography, climatic zonation, and spatial heterogeneity, the spatial and temporal evolution of net productivity in mountain ecosystems and the underlying driving factors remain unclear. This study focuses on the Southern Hilly Mountainous Belt of China (SHMB) to investigate the trends in net primary productivity (NPP) and its response mechanism from 2001 to 2020. The study employs Mann-Kendall trend test, Convergent Cross Mapping analysis, Pearson correlation analysis, and Geographical Detectors. The findings of this study are as follows: (1) The spatial distribution of NPP in the entire SHMB is significantly influenced by LULC (0.43 > q > 0.14, p < 0.005). (2) Human activities have significantly enhanced the carbon sequestration capacity in low-altitude areas (< 650 m) and gentle slope areas (< 16°). (3) Temperature, as the primary driving factor, has influenced the changes in NPP in the SHMB region over the 20 years. However, in the steep slope areas of the eastern and central regions of the SHMB, precipitation has significantly hindered the increase in NPP (-0.17 > q > -0.32, p < 0.05). In summary, human activities have significantly and positively driven the increase in NPP. However, in the central and eastern regions of SHMB, it is also necessary to guard against the ecological degradation caused by increased precipitation. These findings contribute to an enhanced understanding of the carbon cycle process crucial for achieving carbon neutrality, enhancing ecological functions, and studying global change.

Analysis of temporal variability of Okavango River discharge time series is important in revealing the hydrological processes and processes in a semi-arid system. The aim of analyzing the discharge patterns was to determine periodicities and temporal evolution of stream flow regime of the transboundary Okavango River system over a 90-year time series (1930 – 2020). Using the Daubechies wavelet transform for multiresolution decomposition, several significant periodicities at multiple temporal scales were identified. The analysis revealed dominant cycles across varying timescales; semi-annual (0.5 years), annual (1-year) and multiyear (8 and 10 years) cyclic patterns suggesting complex hydroclimatic influences from the upstream Angolan highlands. Cross-wavelet analysis between the river discharge and precipitation in the headwaters highlighted the evolution of the identified periodicities and their spatial coherence across the transboundary basin. Of particular significance was the discharge patterns which showed declining flows over time due to the absence of historically prevalent peak flows in recent decades. The findings provide vital insights which would enable better prediction of flow patterns to inform adaptive management strategies and sustainable use of the available water resources. With the growing hydroclimatic uncertainty in the region, the periodicities and temporal patterns provide a basis for improving resilience of water management systems.

Karst water resources play a vital role in global water supply, providing drinking water to 10–25% of the world´s population. Karst systems exhibit complex hydrological behavior, with fast-flow pathways and highly variable storage capacities. Hydrological models are essential for effective water resource management. However, modelling of karst systems is still a difficult task due to the heterogeneity of these systems and the uncertainties in karst structure.LuKARS, a semi-distributed hydrological model for karst systems, addresses some of these challenges by allowing the consideration of multiple hydrotopes (i.e. distinct landscape units characterized by similar land use and soil types and thus by homogeneous hydrological properties) within a catchment. Despite its low computational cost, LuKARS faces challenges in the context of sensitivity analysis and uncertainty quantification due to its large number of parameters. Compared to the original LuKARS version developed by Bittner et al., (2018), the newly developed version of LuKARS 3.0 presented in this study allows much faster computational times with reduction in runtime of approximately 99.39% (from 1.14 seconds per test run down to 7 milliseconds), for the same model structure. In addition, LuKARS 3.0 allows an easy implementation of the model on clusters and a flexible model structure characterized by an arbitrary number of hydrotopes as well as by the possibility of activating/deactivating different model compartments, i.e., epikarst, matrix and conduit. In this study, we leverage the low computation time of LuKARS 3.0 to apply Morris’ sensitivity analysis method, demonstrating its comparability to dimensional reduction techniques like the active subspace method. The efficient runtime also facilitates the investigation of combined parameter and structural uncertainties. We calibrate different model structures for the Kershbaum spring in Austria, with parameter estimation and uncertainty quantified via the GLUE method. The best-performing model structure is then coupled with PHREEQC to create an initial solute transport model based on the complete mixing assumption accounting for the posterior distributions of the parameter of the selected model structure of LuKARS 3.0. ReferenceBittner, D., Narany, T.S., Kohl, B., Disse, M., and Chiogna, G. (2018). Modeling the hydrological impact of land use change in a dolomite-dominated karst system. Journal of Hydrology 567:267–279.

Hydrological models are fundamental tools for the characterization and management of karst systems. We propose an updated version of KarstMod, software dedicated to lumped-parameter rainfall–discharge modelling of karst aquifers. KarstMod provides a modular, user-friendly modelling environment for educational, research, and operational purposes. It also includes numerical tools for time series analysis, model evaluation, and sensitivity analysis. The modularity of the platform facilitates common operations related to lumped-parameter rainfall–discharge modelling, such as (i) setup and parameter estimation of a relevant model structure and (ii) evaluation of internal consistency, parameter sensitivity, and hydrograph characteristics. The updated version now includes (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation; (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions and observation type; and (iii) additional tools for model performance evaluation, including further performance criteria and tools for model error representation.

Karst water resources are valuable freshwater sources for around 10 % of the world population. Nonetheless, anthropogenic factors and global changes have been seriously deteriorating the karst water quality and dependent ecosystems. Solute transport models are powerful tools to monitor, control, and manage the water quality and dependent ecosystem functioning. By representing and predicting the spatiotemporal behavior of solute migration in karst systems, the transport models enhance our understanding about the karst transport processes, thus enabling us to explore contamination risks and potential outcomes. This paper reviews the current state of knowledge on the modelling of solute transport processes in karst aquifers, thereby unveiling the fundamental challenges underlying a successful karst transport modelling. We discuss to what extent and in what ways we can handle these challenges and derive the key challenges and directions for reliable modelling of transport processes in karst systems in the present context of global changes.

The interaction between surface water and groundwater has been extensively studied due to its water management implications and the potential environmental impacts arising from it. Experimental studies and numerical modeling have supported analytical solutions; these solutions have been proposed for specific cases in which the aim has been to understand discharge/recharge and aquifer characterization. In this study, new graphical solutions or type curves are provided to estimate the subsurface flow and thermal–mechanical parameters in anisotropic porous media. Using the non-dimensionalization technique of the governing equations, new dimensionless groups (lumped parameters) that govern the solution of both the mechanical problem (uncoupled) and the thermal problem are obtained. From these groups, and by applying the pi theorem and examining numerical simulations of numerous cases, user-friendly type curves are obtained. The recharge flow and hydraulic conductivity are calculated when the thermal properties, geometrical parameters, and temperature variables are known. To evaluate the reliability of the type curves, two real case studies are presented: the interaction between the Guadalfeo River and the Motril-Salobreña coastal aquifer, and the artificial recharge program in the coastal aquifer of Agua Amarga in southern Spain. For verification, the groundwater flow obtained from the type curves is compared with the recharge data. In the case of the river–aquifer interaction, the recharge flow obtained is 13% less than that estimated in previous studies. Regarding the artificial recharge of the coastal aquifer, the flow obtained is 21% less than the volume irrigated over the salt marsh. The uncertainties related to hydrogeological features are considered to have the greatest influence on the error.

We introduce LuKARS 3.0, an optimized and flexible version of the LuKARS semi-distributed karst simulation model, designed for improved computational efficiency in discharge and reactive transport simulations. Code optimization and a flexible model structure enabled extensive sensitivity and uncertainty analyses. We demonstrate it with three applications. First, we tested the reduction in runtime, achieving a 420-fold decrease. Second, we implemented the Morris sensitivity analysis, producing results comparable to the active subspace method. Third, we performed combined structural and parametric uncertainty analyses revealing that increasing hydrotopes does not necessarily enhance model performance. Additionally, we couple LuKARS 3.0 with IPhreeqc to implement a solute transport model based on complete mixing. Results show that discharge performance metrics alone may not fully capture solute transport dynamics, highlighting the need for a multi-objective approach. These advancements make LuKARS 3.0 a powerful tool for large-scale karst hydrology studies, with future applications aimed at integrating chemical reactions and enhancing uncertainty analyses for water resource management.

Abstract Mountain ecosystems (ME) have experienced significant anthropogenic disturbances, resulting in severe degradation. Due to their intricate topography, climatic zonation, and spatial heterogeneity, the spatial and temporal evolution of net productivity in ME, and the underlying driving mechanisms remain unclear. This study focuses on the Southern Hilly Mountainous Belt of China (SHMB) to investigate the trends in net primary productivity (NPP) and its response mechanism from 2001 to 2020. The study employs various quantitative methods such as Theil-Sen slope estimator, Mann-Kendall trend test, Convergent Cross Mapping (CCM) analysis, Granger Causality analysis, and Geographical Detectors. The findings of this study are as follows: (1) CCM analysis is deemed suitable for monitoring the causal relationship between climate factors and NPP. (2) NPP exhibits a significant decreasing trend in the eastern and central regions of SHMB while showing a notable increase in the northwestern region. The southwestern region demonstrates a declining trend due to warming and drying effects. (3) NPP is slightly lower on sunny slopes compared to shady slopes. Human activities significantly impact vegetation at lower altitudes by altering forest stand structures which affects carbon sequestration capacity. Vegetation at higher altitudes is primarily influenced by precipitation with temperature playing a lesser direct role. In conclusion, climatic factors exert limited influence on NPP at lower altitudes underscoring the importance of regional governments' efforts towards improving ecological environment through effective forest management practices. These findings contribute to an enhanced understanding of the carbon cycle process crucial for achieving carbon neutrality, enhancing ecological functions, and studying global change.

Continuous hourly time series of hydrochemical data can provide insights into the subsurface dynamics and main hydrological processes of karst systems. This study investigates how high-resolution hydrochemical data can be used for the verification of robust conceptual event-based karst models. To match the high temporal variability of hydrochemical data, the LuKARS 2.0 model was developed on an hourly scale. The model concept considers the interaction between the matrix and conduit components to allow a flexible conceptualization of binary karst systems characterized by a perennial spring and intermittent overflow as well as possible surface water bypassing the spring. The model was tested on the Baget karst system, France, featuring a recharge area defined by the coexistence of karst and nonkarst areas. The Morris screening method was used to investigate parameter sensitivity, and to calibrate the model according to the Kling-Gupta Efficiency (KGE). Model verification was performed by considering additional hydrochemical constraints with the aim of representing the internal dynamics of the systems, i.e., water contributions from the various compartments of the conceptual model. The hydrochemical constraints were defined based on high-temporal resolution time series of SO42− and HCO3−. The results of this study show that the simulation with the highest KGE among 9,000 model realizations well represents the dynamics of the spring discharge but not the variability of the internal fluxes. The implementation of hydrochemical constraints facilitates the identification of realizations reproducing the observed relative increase in the flow contribution from the nonkarst area.

The accuracy of gauge-based, satellite-based and reanalysis precipitation products for streamflow simulation has rarely been investigated in data-scarce and meso-scale karst catchments characterized by infra-daily response time due to the predominance of quick flow processes. This study evaluates and compares the reliability of gauge- and satellite-based precipitation products (CPC, E-OBS, PERSIANN-CDR, IMERG-LR, SM2RAIN-ASCAT, CHIRPS) and reanalysis products (SAFRAN, COMEPHORE, ERA5-Land) in simulating the daily flow of the Baget karst catchment (13.25 km2), located in the Southwestern French Pyrenees. The assessment was conducted over the 2006-2018 period using the semi-distributed karst hydrogeological model ISPEEKH, integrated with a PEST framework for model calibration, global sensitivity analysis using the Morris method, and parameter estimation using an iterative ensemble smoother form of the Gauss-Levenberg-Marquardt algorithm. The discharge coefficients and emptying exponents of the epikarst-to-conduit and conduit-to-spring quick flows were the most sensitive model parameters irrespective of the input precipitation, and ISPEEKH successfully reproduced the non-linear conduit flow dynamics in the catchment. Yet, simulated streamflow was significantly underestimated under the ensemble of precipitation products (up to 32-79 % in the calibration period and up to 28-70 % in the validation period), and the reanalysis products outperformed the gauge- and satellite-based products. Downscaling of the CPC, IMERG-LR, ERA5-Land and E-OBS products, and merging of the CPC and IMERG-LR datasets at 1-km spatial resolution did not improve the model predictive performance. Finally, the study showed that watershed-scale precipitation correction can effectively improve the hydrological simulation performance in the catchment, particularly under the French reanalysis precipitation product COMEPHORE. This result emphasizes the need to install representative rain gauge stations at different altitudes in studied karst catchments of similar scale and hydrodynamics characteristics, and apply observation-based correction methods in order to reduce the errors in regional reanalysis precipitation database and optimize the karst discharge simulation.

Abstract Climate change and human activity are leading to water scarcity in southwestern Europe. Groundwater use is thought to be unsustainable in the region, yet regional assessments using measured data are missing. Here, we evaluate long-term trends and drivers of groundwater levels and found a more complex situation. Historical data (1960–2020) from 12,398 wells in Portugal, Spain, France, and Italy showed 20% with rising groundwater levels, 68% were stable, and only 12% were declining. Rising wells in temperate climates were due to increased precipitation. Recovering wells in semi-arid regions were attributed to improved groundwater management. Stable wells are concentrated in temperate climates with year-round high precipitation. Declining wells in semi-arid regions are primarily located near agricultural areas and experience prolonged summer soil moisture loss, whereas in temperate regions, the decline is associated with large urban areas. Systematic groundwater monitoring and data sharing are essential for sustainable and science-based water resources management.

Karstic aquifers, because of their conduit system, are susceptible to climate change. Ten karst springs in the Zagros region were selected to investigate the impact of climate change under three CMIP6 scenarios: SSP1-1.9, SSP2-4.5, and SSP5-8.5. This study was conducted in three steps: downscaling climate projection, analyzing spring discharge time series, and introducing a new index to assess the impact of climate change on spring flow rate. Applying LARS-WG6, precipitation was downscaled at 14 stations in the study area. Moreover, time series and trend analysis showed that the selected springs have experienced a decrease in their flow rate. Assuming the covariance function between precipitation and spring discharge is constant, new indices (i.e., IQd, IdQd, and Icc) were introduced to highlight the effect of climate change according to the three scenarios. dQd is the variability of spring discharge from past to future, IdQd is spring discharge variability over the historical data, and Icc is the effect of precipitation and spring discharge change together. Icc has a range from −0.25 to 0.25 below and above, which is indicative that two extreme conditions including the spring dryness and overflow are in effect, respectively. The main results revealed that the degree of impact at each spring is a function of climate change scenarios and hydrogeological characteristics of the karstic systems. A more noticeable negative trend in spring flow rate is observed for the karst springs characterized by a dominant conduit flow regime and low matrix storage, located in the areas with low cumulative rainfall, and has a stronger relationship with precipitation. Based on the results, decisions on the management of karst water resources should be made considering where the springs bear free surface and pressurized flow conditions.

The evaluation of saturated hydraulic conductivity (Ks) constitutes an invaluable tool for the management and protection of groundwater resources. This study attempted to estimate Ks in the shallow aquifer of Kabul City, Afghanistan, in response to the occurring groundwater crisis caused by overexploitation and a lack of an appropriate monitoring system on pumping wells, based on datasets from well drilling logs, various analytical methods for pumping test analyses, and laboratory-based methodologies. The selection of Ks estimation methods was influenced by data availability and various established equations, including Theis, developed by Cooper–Jacob, Kruger, Zamarin, Zunker, Sauerbrei, and Chapuis, and pre-determined Ks values dedicated to well log segments exhibited the highest correlation coefficients, ranging between 60% and 75%, with the real conditions of the phreatic aquifer system with respect to the drawdown rate map. The results successfully obtained local-specific quantitative Ks value ranges for gravel, sand, silt, clay, and conglomerate. The obtained results fall within the high range of Ks classification, ranging from 30.0 to 139.8 m per day (m/d) on average across various calculation methods. This study proved that the combination of pumping test results, predetermined values derived from empirical and laboratory approaches, geological description, and classified soil materials and analyses constitutes reliable Ks values through cost-effective and accessible results compared with conducting expensive tests in arid and semi-arid areas.

Hydrochemical data of karst springs provide valuable insights into the internal hydrodynamical functioning of karst systems and support model structure identification. However, the collection of high-frequency time series of major solute species is limited by analysis costs. In this study, we develop a method to retrieve the individual solute concentration time series and their uncertainty at high temporal resolution for karst springs by using continuous observations of electrical conductivity (EC$$ \mathrm{EC} $$) and low-frequency ionic measurements. Due to the large ion content and non-negligible concentrations of aqueous complexes in karst systems, the concentration of each solute species occurring as free ion and as part of aqueous complexes are computed separately. The concentration of species occurring as free ions are computed considering their contributions to the total EC$$ \mathrm{EC} $$, whereas the concentration of the species as part of complexes are obtained from speciation calculations. The pivotal role of the complexation processes for the reconstruction of solute concentration time series starting from the EC$$ \mathrm{EC} $$ signal is investigated in two karstic catchments with different geologies and temporal resolution of the available hydrochemical datasets, that is the Kerschbaum dolostone system in Austria and the Baget limestone system in France. The results show that complexation processes are significant and should be considered for the estimation of the total solute concentration in case of SO4, Ca, Mg and HCO3. The EC$$ \mathrm{EC} $$ signal of a karst spring can be used to interpolate and quantify the dynamics of those solutes characterized by large contribution (approximately >6%) to the total EC$$ \mathrm{EC} $$ and low relative variability, that is HCO3, Ca and Mg. Moreover, the presented method can be used to estimate concentrations of solutes when applied to karst systems with stationary and hydrogeochemical homogeneous contributing area. On the contrary, the method is affected by large uncertainty in case of dynamic systems characterized by varying contributions of water from different geological areas. This study aims to contribute to the problem of hydrogeochemical data availability and to support future works on karst systems conceptualization.

Abstract. We propose an updated version of KarstMod, an adjustable platform dedicated to lumped parameter rainfall-discharge modeling of karst aquifers. KarstMod provides a modular, user-friendly modeling environment for educational, research and operational purposes. It also includes numerical tools for time series analysis, model evaluation and sensitivity analysis. The modularity of the platform facilitates common operations related to lumped parameter rainfall-discharge modeling, such as (i) set up and parameter estimation of a relevant model structure, and (ii) evaluation of internal consistency, parameter sensitivity and hydrograph characteristics. The updated version now includes (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation, (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions as well as observation type and (iii) additional tools for model performance evaluation including further performance criteria and tools for model errors representation.