Learning from mistakes-Assessing the performance and uncertainty in process-based models.

Typical applications of process- or physically-based models aim to gain a better process understanding or provide the basis for a decision-making process. To adequately represent the physical system, models should include all essential processes. However, model errors can still occur. Other than large systematic observation errors, simplified, misrepresented, inadequately parametrised or missing processes are potential sources of errors. This study presents a set of methods and a proposed workflow for analysing errors of process-based models as a basis for relating them to process representations. The evaluated approach consists of three steps: (1) training a machine-learning (ML) error model using the input data of the process-based model and other available variables, (2) estimation of local explanations (i.e., contributions of each variable to an individual prediction) for each predicted model error using SHapley Additive exPlanations (SHAP) in combination with principal component analysis, (3) clustering of SHAP values of all predicted errors to derive groups with similar error generation characteristics. By analysing these groups of different error-variable association, hypotheses on error generation and corresponding processes can be formulated. That can ultimately lead to improvements in process understanding and prediction. The approach is applied to a process-based stream water temperature model HFLUX in a case study for modelling an alpine stream in the Canadian Rocky Mountains. By using available meteorological and hydrological variables as inputs, the applied ML model is able to predict model residuals. Clustering of SHAP values results in three distinct error groups that are mainly related to shading and vegetation-emitted long wave radiation. Model errors are rarely random and often contain valuable information. Assessing model error associations is ultimately a way of enhancing trust in implemented processes and of providing information on potential areas of improvement to the model.

Reply to STOTEN 802 (2022) 149713: The fallacy in the use of the "best-fit" solution in hydrologic modeling.

In this reply we respond to the short discussion contribution by Abbaspour (2022) in which a fallacy in the use of "best-fit" model solutions to be employed in hydrologic modeling studies is illustrated. Abbaspour (2022) advised to perform stochastic model calibration and proposed to employ the R- and P-Factor statistics for a model evaluation together with suggested thresholds for a model to be acceptable. In a minimal working example we followed the proposed stochastic approach for model evaluation and show that the proposed R- and P-Factor metrics and their thresholds accept implausible model ensemble simulations which would have been rejected in an individual assessment with the NSE metric. In this way, we want to raise the caution to rely on single performance metrics for model evaluation and the use of globally defined thresholds to define model acceptance.

Automatic Regionalization of Model Parameters for Hydrological Models.

Parameter estimation is one of the most challenging tasks in large-scale distributed modeling, because of the high dimensionality of the parameter space. Relating model parameters to catchment/landscape characteristics reduces the number of parameters, enhances physical realism, and allows the transfer of hydrological model parameters in time and space. This study presents the first large-scale application of automatic parameter transfer function (TF) estimation for a complex hydrological model. The Function Space Optimization (FSO) method can automatically estimate TF structures and coefficients for distributed models. We apply FSO to the mesoscale Hydrologic Model (mHM, mhm-ufz.org), which is the only available distributed model that includes a priori defined TFs for all its parameters. FSO is used to estimate new TFs for the parameters "saturated hydraulic conductivity" and "field capacity," which both influence a range of hydrological processes. The setup of mHM from a previous study serves as a benchmark. The estimated TFs resulted in predictions in 222 validation basins with a median NSE of 0.68, showing that even with 5 years of calibration data, high performance in ungauged basins can be achieved. The performance is similar to the benchmark results, showing that the automatic TFs can achieve comparable results to TFs that were developed over years using expert knowledge. In summary, the findings present a step toward automatic TF estimation of model parameters for distributed models.

The coupled socio-ecohydrological evolution of river systems: Towards an integrative perspective of river systems in the 21st century.

River systems have undergone a massive transformation since the Anthropocene. The natural properties of river systems have been drastically altered and reshaped, limiting the use of management frameworks, their scientific knowledge base and their ability to provide adequate solutions for current problems and those of the future, such as climate change, biodiversity crisis and increased demands for water resources. To address these challenges, a socioecologically driven research agenda for river systems that complements current approaches is needed and proposed. The implementation of the concepts of social metabolism and the colonisation of natural systems into existing concepts can provide a new basis to analyse the coevolutionary coupling of social systems with ecological and hydrological (i.e., 'socio-ecohydrological') systems within rivers. To operationalize this research agenda, we highlight four initial core topics defined as research clusters (RCs) to address specific system properties in an integrative manner. The colonisation of natural systems by social systems is seen as a significant driver of the transformation processes in river systems. These transformation processes are influenced by connectivity (RC 1), which primarily addresses biophysical aspects and governance (RC 2), which focuses on the changes in social systems. The metabolism (RC 3) and vulnerability (RC 4) of the social and natural systems are significant aspects of the coupling of social systems and ecohydrological systems with investments, energy, resources, services and associated risks and impacts. This socio-ecohydrological research agenda complements other recent approaches, such as 'socio-ecological', 'socio-hydrological' or 'socio-geomorphological' systems, by focusing on the coupling of social systems with natural systems in rivers and thus, by viewing the socioeconomic features of river systems as being just as important as their natural characteristics. The proposed research agenda builds on interdisciplinarity and transdisciplinarity and requires the implementation of such programmes into the education of a new generation of river system scientists, managers and engineers who are aware of the transformation processes and the coupling between systems.

Storm event impacts on in-stream nitrate concentration and discharge dynamics: A comparison of high resolution in-situ measured data with model simulations.

The relationship between nitrogen and discharge (N-Q) in a stream can be captured with high frequency nitrate nitrogen (NO3--N) samplers. In Austria, the Raab catchment (998 km2) has high frequency NO3--N data measured with a spectrometer probe. This study evaluated if the widely-used and typically calibrated eco-hydrological model Soil and Water Assessment Tool (SWAT) can reproduce the hysteresis loop direction and the dilution or accretion effects of NO3--N dynamics during storm events in this agricultural catchment. The daily aggregated NO3--N measurements were compared with the daily SWAT simulated discharge and NO3--N concentrations of 14 storm events by computing hysteresis indices - loop direction and area (h index), loop direction (HInew) and solute gradient (∆C). Overall, the SWAT model was able to replicate the predominant anticlockwise hysteresis and dilution effect of NO3--N in the Raab catchment. The loop direction was simulated correctly in 9 and 10 events, for the h and HInew indices, respectively. The hysteresis direction inferred from both indices did not always concur due to the differences in the calculation methods. The dilution or accretion effect was simulated correctly in 9 of the events. However, the SWAT model only correctly simulated the N-Q relationships for all three hysteresis criteria in 5 of the 14 events. Due to the aggregation of measured data to the daily time step, information pertaining to the hysteresis shape was sometimes lost, particularly if the storm event was <4 days in duration. Structural limitations of the SWAT as well as specific relevant basin parameters (parameters that have one value for the entire catchment) may restrict simulating N-Q dynamics. An enhanced calibrated and validated model would possibly improve the results, since the events during the better calibrated period more often reproduced the measured hysteresis indices.

Towards Improved Field Application of Using Distributed Temperature Sensing for Soil Moisture Estimation: A Laboratory Experiment.

The "dual probe heat pulse" (DPHP) method using actively heated fiber optic (AHFO) cables combined with distributed temperate sensing (DTS) technology has been developed for monitoring thermal properties and soil water content at the field scale. Field scale application, however, requires the use of robust and thicker fiber optic cables, corroborating the assumption of an infinite thin heat source in the evaluation process. We therefore included a semi-analytical solution of the heat transport equation into the evaluation procedure in order to consider the finite thermal properties of the heating cable without a calibration procedure to estimate effective thermal properties of the soil. To test this new evaluation procedure, we conducted a laboratory experiment and tested different heating scenarios to infer soil moisture from volumetric heat capacity. Estimates were made by analyzing the shift of the temperature amplitude at the sensing cable and the characteristics of the response heating curve. The results were compared with results from the calibrated infinite line source solution and in situ water content point measurements and showed a good approximation of thermal properties for strong and short heat pulses. Volumetric water content estimates are similarly accurate to the results of the calibrated infinite line source solution. Problems arose with the cable spacing and the resettlement process after burying the cable.

Estimation of evapotranspiration of temperate grassland based on high-resolution thermal and visible range imagery from unmanned aerial systems.

Spatially distributed high-resolution data of land surface temperature (LST) and evapotranspiration (ET) are important information for crop water management and other applications in the agricultural sector. While satellite data can provide LST high-resolution data of 100 m, the current development of unmanned aerial systems (UAS) and affordable low-weight thermal cameras allows LST and subsequent ET to be derived at resolutions down to centimetre scale. In this study, UAS-based images in the thermal infrared (TIR) and visible spectral range were collected over a managed temperate grassland in July 2016 at the Terrestrial Environmental Observatories Networks TERENO preAlpine observatory site at Fendt, Germany. The UAS set-up included a lightweight thermal camera (Optris Pi Lightweight) and a regular digital camera (Sony α 6000) that allowed for the acquisition of thermal and optical images with a ground resolution of 5 cm and 1 cm, respectively. Three TIR-based ET models of different complexity were applied and the resulting ET estimates were compared to the Eddy covariance (EC) observations of turbulent energy fluxes and also to the evaporative fraction. While the Deriving Atmosphere Turbulent Transport Useful To Dummies Using Temperature (DATTUTDUT) model and the Triangle Method belong to the group of simpler contextual models, the Two-Source Energy Balance (TSEB) model incorporates a more physically based formulation of the surface energy balance. In addition to the comparison of UAS-based estimates of latent heat fluxes to EC observations, the effect of the spatial resolution of the model imagery input on the modelled results was analysed by running the models with imagery from the native resolution of the acquired images to resolutions that were aggregated up to 30 m. The results show that both contextual models are sensitive to the input image resolution and that the agreement with the EC observations improves with increasing image resolution. The TSEB model assumes that LST pixels represent a mixed signal of the soil and canopy components, thus an image resolution coarse enough to ensure this assumption should be chosen. However, with the exception of the native image resolution of 5 cm, we found no effect of image resolution on the spatially weighted mean TSEB estimates. For the studied grassland, the comparison of model estimates with EC observations indicates that all three models are able to reproduce observed energy fluxes with comparable accuracy with mean absolute errors of ET between 20 and 40 W m-2. The TSEB model showed larger deviations from the reference observations under cloudy conditions with rapid fluctuations of LST within the 30 min averaging period for EC. The two contextual models yielded similar results for most of the flights. The good performance of the DATTUTDUT model, which had the lowest input requirements of the three models, is especially promising in view of the application of UAS for routine near-real-time ET monitoring.

Feasibility of Locating Leakages in Sewage Pressure Pipes Using the Distributed Temperature Sensing Technology.

The cost effective maintenance of underwater pressure pipes for sewage disposal in Austria requires the detection and localization of leakages. Extrusion of wastewater in lakes can heavily influence the water and bathing quality of surrounding waters. The Distributed Temperature Sensing (DTS) technology is a widely used technique for oil and gas pipeline leakage detection. While in pipeline leakage detection, fiber optic cables are installed permanently at the outside or within the protective sheathing of the pipe; this paper aims at testing the feasibility of detecting leakages with temporary introduced fiber optic cable inside the pipe. The detection and localization were tested in a laboratory experiment. The intrusion of water from leakages into the pipe, producing a local temperature drop, served as indicator for leakages. Measurements were taken under varying measurement conditions, including the number of leakages as well as the positioning of the fiber optic cable. Experiments showed that leakages could be detected accurately with the proposed methodology, when measuring resolution, temperature gradient and measurement time were properly selected. Despite the successful application of DTS for leakage detection in this lab environment, challenges in real system applications may arise from temperature gradients within the pipe system over longer distances and the placement of the cable into the real pipe system.

Estimating spatially distributed turbulent heat fluxes from high-resolution thermal imagery acquired with a UAV system.

In this study, high-resolution thermal imagery acquired with a small unmanned aerial vehicle (UAV) is used to map evapotranspiration (ET) at a grassland site in Luxembourg. The land surface temperature (LST) information from the thermal imagery is the key input to a one-source and two-source energy balance model. While the one-source model treats the surface as a single uniform layer, the two-source model partitions the surface temperature and fluxes into soil and vegetation components. It thus explicitly accounts for the different contributions of both components to surface temperature as well as turbulent flux exchange with the atmosphere. Contrary to the two-source model, the one-source model requires an empirical adjustment parameter in order to account for the effect of the two components. Turbulent heat flux estimates of both modelling approaches are compared to eddy covariance (EC) measurements using the high-resolution input imagery UAVs provide. In this comparison, the effect of different methods for energy balance closure of the EC data on the agreement between modelled and measured fluxes is also analysed. Additionally, the sensitivity of the one-source model to the derivation of the empirical adjustment parameter is tested. Due to the very dry and hot conditions during the experiment, pronounced thermal patterns developed over the grassland site. These patterns result in spatially variable turbulent heat fluxes. The model comparison indicates that both models are able to derive ET estimates that compare well with EC measurements under these conditions. However, the two-source model, with a more complex treatment of the energy and surface temperature partitioning between the soil and vegetation, outperformed the simpler one-source model in estimating sensible and latent heat fluxes. This is consistent with findings from prior studies. For the one-source model, a time-variant expression of the adjustment parameter (to account for the difference between aerodynamic and radiometric temperature) that depends on the surface-to-air temperature gradient yielded the best agreement with EC measurements. This study showed that the applied UAV system equipped with a dual-camera set-up allows for the acquisition of thermal imagery with high spatial and temporal resolution that illustrates the small-scale heterogeneity of thermal surface properties. The UAV-based thermal imagery therefore provides the means for analysing patterns of LST and other surface properties with a high level of detail that cannot be obtained by traditional remote sensing methods.

Monitoring and assessing of landscape heterogeneity at different scales.

In numerous studies, spatial and spectral aggregations of pixel information using average values from imaging spectrometer data are suggested to derive spectral indices and the subsequent vegetation parameters that are derived from these. Currently, there are very few empirical studies that use hyperspectral data, to support the hypothesis for deriving land surface variables from different spectral and spatial scales. In the study at hand, for the first time ever, investigations were carried out on fundamental scaling issues using specific experimental test flights with a hyperspectral sensor to investigate how vegetation patterns change as an effect of (1) different spatial resolutions, (2) different spectral resolutions, (3) different spatial and spectral resolutions as well as (4) different spatial and spectral resolutions of originally recorded hyperspectral image data compared to spatial and spectral up- and downscaled image data. For these experiments, the hyperspectral sensor AISA-EAGLE/HAWK (DUAL) was mounted on an aircraft to collect spectral signatures over a very short time sequence of a particular day. In the first experiment, reflectance measurements were collected at three different spatial resolutions ranging from 1 to 3 m over a 2-h period in 1 day. In the second experiment, different spectral image data and different additional spatial data were collected over a 1-h period on a particular day from the same test area. The differently recorded hyperspectral data were then spatially and spectrally rescaled to synthesize different up- and down-rescaled images. The normalised difference vegetation index (NDVI) was determined from all image data. The NDVI heterogeneity of all images was compared based on methods of variography. The results showed that (a) the spatial NDVI patterns of up- and downscaled data do not correspond with the un-scaled image data, (b) only small differences were found between NDVI patterns determined from data recorded and resampled at different spectral resolutions and (c) the overall conclusion from the tests carried out is that the spatial resolution is more important in determining heterogeneity by means of NDVI than the depth of the spectral data. The implications behind these findings are that we need to exercise caution when interpreting and combining spatial structures and spectral indices derived from satellite images with differently recorded geometric resolutions.