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The climate modelling community has trialled a large number of metrics for evaluating the temporal performance of general circulation models (GCMs), while very little attention has been given to the assessment of their spatial performance, which is equally important. This study evaluated the performance of 36 Coupled Model Intercomparison Project 5 (CMIP5) GCMs in relation to their skills in simulating mean annual, monsoon, winter, pre-monsoon, and post-monsoon precipitation and maximum and minimum temperature over Pakistan using state-of-the-art spatial metrics, SPAtial EFficiency, fractions skill score, Goodman–Kruskal's lambda, Cramer's V, Mapcurves, and Kling–Gupta efficiency, for the period 1961–2005. The multi-model ensemble (MME) precipitation and maximum and minimum temperature data were generated through the intelligent merging of simulated precipitation and maximum and minimum temperature of selected GCMs employing random forest (RF) regression and simple mean (SM) techniques. The results indicated some differences in the ranks of GCMs for different spatial metrics. The overall ranks indicated NorESM1-M, MIROC5, BCC-CSM1-1, and ACCESS1-3 as the best GCMs in simulating the spatial patterns of mean annual, monsoon, winter, pre-monsoon, and post-monsoon precipitation and maximum and minimum temperature over Pakistan. MME precipitation and maximum and minimum temperature generated based on the best-performing GCMs showed more similarities with observed precipitation and maximum and minimum temperature compared to precipitation and maximum and minimum temperature simulated by individual GCMs. The MMEs developed using RF displayed better performance than the MMEs based on SM. Multiple spatial metrics have been used for the first time for selecting GCMs based on their capability to mimic the spatial patterns of annual and seasonal precipitation and maximum and minimum temperature. The approach proposed in the present study can be extended to any number of GCMs and climate variables and applicable to any region for the suitable selection of an ensemble of GCMs to reduce uncertainties in climate projections.

Satellite-based earth observations offer great opportunities to improve spatial model predictions by means of spatial-pattern-oriented model evaluations. In this study, observed spatial patterns of actual evapotranspiration (AET) are utilised for spatial model calibration tailored to target the pattern performance of the model. The proposed calibration framework combines temporally aggregated observed spatial patterns with a new spatial performance metric and a flexible spatial parameterisation scheme. The mesoscale hydrologic model (mHM) is used to simulate streamflow and AET and has been selected due to its soil parameter distribution approach based on pedo-transfer functions and the build in multi-scale parameter regionalisation. In addition two new spatial parameter distribution options have been incorporated in the model in order to increase the flexibility of root fraction coefficient and potential evapotranspiration correction parameterisations, based on soil type and vegetation density. These parameterisations are utilised as they are most relevant for simulated AET patterns from the hydrologic model. Due to the fundamental challenges encountered when evaluating spatial pattern performance using standard metrics, we developed a simple but highly discriminative spatial metric, i.e. one comprised of three easily interpretable components measuring co-location, variation and distribution of the spatial data. The study shows that with flexible spatial model parameterisation used in combination with the appropriate objective functions, the simulated spatial patterns of actual evapotranspiration become substantially more similar to the satellite-based estimates. Overall 26 parameters are identified for calibration through a sequential screening approach based on a combination of streamflow and spatial pattern metrics. The robustness of the calibrations is tested using an ensemble of nine calibrations based on different seed numbers using the shuffled complex evolution optimiser. The calibration results reveal a limited trade-off between streamflow dynamics and spatial patterns illustrating the benefit of combining separate observation types and objective functions. At the same time, the simulated spatial patterns of AET significantly improved when an objective function based on observed AET patterns and a novel spatial performance metric compared to traditional streamflow-only calibration were included. Since the overall water balance is usually a crucial goal in hydrologic modelling, spatial-pattern-oriented optimisation should always be accompanied by traditional discharge measurements. In such a multi-objective framework, the current study promotes the use of a novel bias-insensitive spatial pattern metric, which exploits the key information contained in the observed patterns while allowing the water balance to be informed by discharge observations.

This paper investigates the effect of a Bayesian Model Averaging (BMA) method on simulated precipitation over the Columbia River Basin using two statistically downscaled climate datasets, i.e., Bias-Correction Spatial Disaggregation (BCSD) and Multivariate Adaptive Constructed Analogs (MACA). To this end daily observed and simulated precipitation are used to calculate different indices focusing solely on seasonality, event-timing, and variability in timing (persistence) of the precipitation. The climate model weights are estimated for each cell (6 × 6 km) of the Columbia River Basin using daily time series for the historical period 1970–1999 from the ten Global Climate Models (GCMs) participating to the Coupled Model Intercomparison Project platform, Phase 5. The results show that BMA results in more than 15 % improvement/reduction in mean absolute error as compared to the individual GCMs. The improvement is, in general, higher for the MACA models than for the BCSD models. The results of variability in precipitation timing show that extreme precipitation events are mostly not persistent (i.e., occurring in different periods throughout the year), i.e., more than 75 % of the grid cells with an elevation above 900 m indicate persistence values less than 0.2 whereas nearly 70 % of the high elevation cells indicate such low persistence. Further we find that the variability in persistence is higher in high elevation cells than those with low elevation. The picture is different for MACA ensembles as the simulated persistence of extreme precipitation events is higher than that for the observed and BCSD datasets.

Low flow forecasting is crucial for sustainable cooling water supply and planning of river navigation in the Rhine River. The first step in reliable low flow forecasting is to understand the characteristics of low flow. In this study, several methods are applied to understand the low flow characteristics of Rhine River basin. In 108 catchments of the Rhine River, winter and summer low flow regions are determined with the seasonality ratio (SR) index. To understand whether different numbers of processes are acting in generating different low flow regimes in seven major sub-basins (namely, East Alpine, West Alpine, Middle Rhine, Neckar, Main, Mosel and Lower Rhine) aggregated from the 108 catchments, the dominant variable concept is adopted from chaos theory. The number of dominant processes within the seven major sub-basins is determined with the correlation dimension analysis. Results of the correlation dimension analysis show that the minimum and maximum required number of variables to represent the low flow dynamics of the seven major sub-basins, except the Middle Rhine and Mosel, is 4 and 9, respectively. For the Mosel and Middle Rhine, the required minimum number of variables is 2 and 6, and the maximum number of variables is 5 and 13, respectively. These results show that the low flow processes of the major sub-basins of the Rhine could be considered as non-stochastic or chaotic processes. To confirm this conclusion, the rescaled range analysis is applied to verify persistency (i.e. non-randomness) in the processes. The estimated rescaled range statistics (i.e. Hurst exponents) are all above 0.5, indicating that persistent long-term memory characteristics exist in the runoff processes. Finally, the mean values of SR indices are compared with the nonlinear analyses results to find significant relationships. The results show that the minimum and maximum numbers of required variables (i.e. processes) to model the dynamic characteristics for five out of the seven major sub-basins are the same, but the observed low flow regimes are different (winter low flow regime and summer low flow regime). These results support the conclusion that a few interrelated nonlinear variables could yield completely different behaviour (i.e. dominant low flow regime).

Cluster analysis of gauged streamflow records into homogeneous and robust regions is an important tool for the characterization of hydrologic systems. In this paper we applied the hierarchical cluster analysis to the task of objectively classifying streamflow data into regions encompassing similar streamflow patterns over Turkey. The performance of three standardization techniques was also tested, and standardizing by range was found better than standardizing with zero mean and unit variance. Clustering was carried out using Ward's minimum variance method which became prominent in managing water resources with squared Euclidean dissimilarity measures on 80 streamflow stations. The stations have natural flow regimes where no intensive river regulation had occurred. A general conclusion drawn is that the zones having similar streamflow pattern were not be overlapped well with the conventional climate zones of Turkey; however, they are coherent with the climate zones of Turkey recently redefined by the cluster analysis to total precipitation data as well as homogenous streamflow zones of Turkey determined by the rotated principal component analysis. The regional streamflow information in this study can significantly improve the accuracy of flow predictions in ungauged watersheds.

Missing rainfall data are a major limitation for distributed hydrological modeling and climate studies. Practitioners need reliable approaches that can be employed on a daily basis, often with too limited data in space to feed complex predictive models. In this study we compare different automatic approaches for missing data imputation, including geostatistical interpolation and pattern-based estimation algorithms. We introduce two pattern-based approaches based on the analysis of historical data patterns: (i) an iterative version of K-nearest neighbor (IKNN) and (ii) a new algorithm called vector sampling (VS) that combines concepts of multiple-point statistics and resampling. Both algorithms can draw estimations from variably incomplete data patterns, allowing the target dataset to be at the same time the training dataset. Tested on five case studies from Denmark, Australia, and Switzerland, the algorithms show a different performance that seems to be related to the terrain type: on flat terrains with spatially homogeneous rain events, geostatistical interpolation tends to minimize the average error, while in mountainous regions with nonstationary rainfall statistics, data mining can recover better the rainfall patterns. The VS algorithm, requiring minimal parameterization, turns out to be a convenient option for routine application on complex and poorly gauged terrains.

The authors are to be congratulated for a systematic investigationof the accurate and non subjective classifying approach in seismic research. The authors have conducted several clustering algorithms to the seismic event records from Volcanological and SeismologicalObservatory at Manizales. Their objective was to improve the grouping of seismic data (i.e., volcano-tectonic earthquakes, long-period earthquakes and icequakes) digitized at 100.16 Hz sampling frequency.Their study seems adding new approach to their previous work of Langer et al. (2006) who applied different classification techniques to seismic data.

The process of model evaluation is not only an integral part of model development and calibration but also of paramount importance when communicating modelling results to the scientific community and stakeholders. The modelling community has a large and well-tested toolbox of metrics to evaluate temporal model performance. In contrast, spatial performance evaluation does not correspond to the grand availability of spatial observations readily available and to the sophisticate model codes simulating the spatial variability of complex hydrological processes. This study makes a contribution towards advancing spatial-pattern-oriented model calibration by rigorously testing a multiple-component performance metric. The promoted SPAtial EFficiency (SPAEF) metric reflects three equally weighted components: correlation, coefficient of variation and histogram overlap. This multiple-component approach is found to be advantageous in order to achieve the complex task of comparing spatial patterns. SPAEF, its three components individually and two alternative spatial performance metrics, i.e. connectivity analysis and fractions skill score, are applied in a spatial-pattern-oriented model calibration of a catchment model in Denmark. Results suggest the importance of multiple-component metrics because stand-alone metrics tend to fail to provide holistic pattern information. The three SPAEF components are found to be independent, which allows them to complement each other in a meaningful way. In order to optimally exploit spatial observations made available by remote sensing platforms, this study suggests applying bias insensitive metrics which further allow for a comparison of variables which are related but may differ in unit. This study applies SPAEF in the hydrological context using the mesoscale Hydrologic Model (mHM; version 5.8), but we see great potential across disciplines related to spatially distributed earth system modelling.

We developed a combined drought index to better monitor agricultural drought events. To develop the index, different combinations of the temperature condition index, precipitation condition index, vegetation condition index, soil moisture condition index, gross primary productivity, and normalized difference water index were used to obtain a single drought severity index. To obtain more effective results, a mesoscale hydrologic model was used to obtain soil moisture values. The SHapley Additive exPlanations (SHAP) algorithm was used to calculate the weights for the combined index. To provide input to the SHAP model, crop yield was predicted using a machine learning model, with the training set yielding a correlation coefficient (R) of 0.8, while the test set values were calculated to be 0.68. The representativeness of the new index in drought situations was compared with established indices, including the Standardized Precipitation-Evapotranspiration Index (SPEI) and the Self-Calibrated Palmer Drought Severity Index (scPDSI). The index showed the highest correlation with an R-value of 0.82, followed by the SPEI with 0.7 and scPDSI with 0.48. This study contributes a different perspective for effective detection of agricultural drought events. The integration of an increased volume of data from remote sensing systems with technological advances could facilitate the development of significantly more efficient agricultural drought monitoring systems.