HS3.3

Long-range dependence (LRD) estimators are traditionally applied in the lag domain (e.g., through the autocovariance or variogram) or in the frequency domain (e.g., through the power-spectrum), but not as often in the scale domain (e.g., through variance vs. scale). It has been contended that the latter case introduces large estimation bias and thus, corresponds to "bad estimators" of the LRD. However, this reflects a misrepresentation or misuse of the concept of variance vs. scale. Specifically, it is shown that if the LRD estimator of variance vs. scale is properly defined and assessed (see literature studies for the so-called climacogram estimator), then the stochastic analysis of variance in the scale domain can be proven to be a robust means to identify and model any LRD process ranging from small scales (fractal behavior) to large scales (LRD, else known as the Hurst-Kolmogorov dynamics) for any marginal distribution. Here, we show how the above definitions can be applied both in spatial and temporal scales, with various applications in geophysical processes, key hydrological-cycle processes, and related natural hazards.

How to cite: Dimitriadis, P., Iliopoulou, T., Sargentis, G.-F., and Koutsoyiannis, D.: Spatial and temporal long-range dependence in the scale domain, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13051, https://doi.org/10.5194/egusphere-egu22-13051, 2022.

A common problem in geochemical exploration projects is the limited number of collected samples due to budgetary, time, and other constraints. Therefore, to study spatial mineralisation patterns using available samples in both sampled and unsampled areas, the interpolation of the available data is essential to assign estimates to unsampled areas. Because interpolation estimates are based on the data available only within the search window, in continuous field geochemical modelling such interpolations using any single method are often the main source of uncertainty. Error propagation analysis needs to be considered to evaluate interpolation errors’ effects in geochemical anomaly detection. One method for analysing the propagation of errors in models and evaluating their stability is Monte Carlo Simulation (MCSIM). In this method, the P50 (median) value (called ‘return’) and the uncertainty value (called ‘risk’) are calculated. Here the uncertainty is calculated as 1/(P90-P10) for which P10 (lower decile) and P90 (upper decile) are the average 10th and 90th percentiles of the multiple simulated values, correspond to each element. We have applied this method to Swedish till data, collected throughout the country by the Geological Survey of Sweden. The main concern is whether to evaluate if the samples are sufficient and representative of the target elements concentrations for geochemical studies. To address this concern, the sampling uncertainty in a statistical sense (not geochemical) per element was studied using the return-risk matrix. This matrix was applied to volcanogenic massive sulfide (VMS) target elements, then subsequently to the samples per bedrock. Therefore, a large number of simulated values (e.g., 5,000, which is higher than the number of the samples, i.e., 2,578) was generated using MCSIM. Where the quantified return is low or negative, and the quantified uncertainty is high, particularly higher than its relevant return, additional sampling is required to achieve the minimum required spatial continuity in the data or the stability of the later applied classification models. This affects the certainty of the models generated in the study area. In the Sweden data, all the elements assessed have relatively high returns and low uncertainty, demonstrating the stability of the parameters. The process was subsequently applied to samples separated into the main lithological categories or geological domains to determine if the stability in the patterns is affected by rock type (and associate natural variability in the background). In Swedish till samples, the statistical sampling quality is acceptable in the bedrocks of Exotic Terranes, Archean, Baltoscandian, and Idefjorden. However, it is not acceptable in the Palaeoproterozoic units and the Eastern Segment, due to the risks being higher than the returns, which may increase the error propagation effect on the interpolated map and efficiency of the classes obtained by different classification models.

How to cite: Sadeghi, B., Cohen, D., and Müller, D.: Improved decision-making in geochemical sampling based on both frequency and Bayesian frameworks, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-14, https://doi.org/10.5194/egusphere-egu22-14, 2022.

Floods are a major threat to the security of populations worldwide. Their impact is dependent on the flood extension and water levels,  topographic factors, and many other variables. Meteorological factors such as precipitation, snow melt and base flow also influence the magnitude of flood events. Factors like river morphology, slopes, presence of flood plains, vegetation and soil types determine the response of the river or lake to meteorological conditions and hydrological events. Meteorological factors tend to be cyclical while topography is generally considered to remain constant over extended periods of time. However, river bathymetry is subject to changes over time due to sediment transport. For example, sediment re-positioning and accumulation can modify the bathymetry of water bodies.  Furthermore, lakes or reservoirs receive and accumulate sediments transported from upstream which could influence flood levels. In this study we use a two-dimensional hydraulic model (Telemac2D) to simulate different flood scenarios coupled with several different bathymetries of Trois-Lacs Lake in the province of Quebec, Canada. Four bathymetries were obtained between November 2020 and August 2021 and 3 historical bathymetries were also provided (yrs, 1974, 2004, and 2019).  To compare the bathymetries, total ‘available water volume’ is calculated, taking a common and constant reference water surface elevation. Streamflows entering the lake system were estimated using Hydrotel, a physics-based semi distributed hydrological model. These streamflows are used to calibrate the two-dimensional hydraulic model with measured water levels.  The project may help to establish a direct relation between sediment shifting and deposition and water distribution for extreme flood events, while also allowing the local community to improve measures for civil security and land-use planning at a regional scale.

How to cite: Redondo, S., Boucher, M.-A., Lacey, J., and Parent, J.: Quantifying the impact of bathymetry changes on flood  events for the Trois-Lacs Basin, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5381, https://doi.org/10.5194/egusphere-egu22-5381, 2022.

The element phosphorus total (Pt) is considered a basic element for life on earth. It controls key processes of CO2 absorption from tropical forests to food production. For the Amazon region, estimates of Pt in the soil are scarce. In this study, we developed models through equations of pedotransfer function (PTF's) using data collected in the field (RAINFOR data). Were generated 16 regression models based on the Akaike information criteria (AIC) with R² above 65% was validated with independent RAINFOR data. The results Pt distribution were spatialized using interpolations by geostatistical method of inverse distance weights (IDW) and shown through maps.

How to cite: Maia, M. R. D. S. A., Anderson, L. O., and Quesada, C. A. N.: Estimates of total phosphorus for Amazonia based on an expanded harmonized soil database, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11000, https://doi.org/10.5194/egusphere-egu22-11000, 2022.

Drought events are more common nowadays than it used to be in the past in different areas around the world. Some of its consequences are the reduction of cropping areas, lower rates of percolation for recharge of aquifers and scarcity of drinkable water. To analyse and identify droughts location, dates of occurrence and severity, it is necessary to collect meteorological data. However, based on the location of the study region, some places do not have measurement stations, hence, spatiotemporal databases are the best alternative. Present paper shows the analysis of the past and future scenarios of hydrological droughts due to climate change in the Jiet river basin in Romania. Spatiotemporal data from remote sensing with different resolutions is analysed and processed. Data from year.1990. to year 2020. At a resolution of 0.1̊ is compared to projection scenario RCp 8.5 during 2030 to 2060.

An assessment of hydrological droughts for past scenarios is made by defining a statistical threshold (85 percentile) from historical data. Further, an analysis of characteristics of hydrological drought events is performed for present and future scenarios. Drought is measured through soil moisture analysis, using results from HEC – HMS v4.9 BETA, hydrological modelling tool. This study presents the results of the first stage of the process were a spatiotemporal analysis of the calibration performance of the of the hydrological model and the droughts found are characterized. 

How to cite: Beltran Mora, C., Popescu, I., Jonoski, A., Corzo, G., de Ruijter, M., and Dudau, D.: Climate change analysis of hydrological droughts in Jiet catchment, Romania., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12878, https://doi.org/10.5194/egusphere-egu22-12878, 2022.

Many regions in the world are threaten by Climate change, and there is a large global concern on the dependency of water contributions from neighbouring countries. In order to understand more how the water contributions from other region affect a river basin, global spatiotemporal information could be used to obtain budgets balance. This study proposes a methodology to analyse the atmospheric moisture balance around hydrological units (watersheds) using ERA 5 reanalysis data sets, allowing the evaluation of the role of spatiotemporal patterns associated with the transport of regional moisture fluxes and understanding how these components modulate regional water heterogeneity, sources and sinks. This study consists of 3 phases: 1) collection and validation of the required hydrometeorological sets and variables and two-dimensional discretization of the hydrographic domain or unit establishing the boundaries for computational analysis; then, estimation and evaluation of the contribution patterns of transported moisture fluxes based on the Eulerian model developed by Brubaker,1993. Finally, for each region, we proceed to estimate the spatiotemporal variations of the atmospheric water balance by establishing the calculation of the precipitation recycling rate as well as the fractions of horizontal moisture flux contributions from each direction or boundary, as well as their seasonality and interannual variability, magnitudes and concentration rates associated with flux divergence. As a case study, the Pamplonita river basin in Colombia was selected. Here we present these results, that have provided valuable information related to the identification of biases in the estimation of atmospheric water supplies, monitoring strategies and hydrological balance.

How to cite: Sanchez Hernandez, K. A. and Corzo Perez, G. A.: Bidimensional Spatiotemporal analysis of local atmospherically fluxes and regional moisture budgets in river basins, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12857, https://doi.org/10.5194/egusphere-egu22-12857, 2022.

The GeoStat Framework is a coherent ecosystem of Python packages for geostatistical applications and subsurface simulations. 
It provides an easily usable open source collection of software packages. They are well documented, including exhaustive hands-on guides and examples for helping non-programmers and non-domain-experts getting started. The main applications of the packages are:

• GSTools & PyKrige - spatial random field generation, kriging, data normalization & transformation, and geostatistical analyses based on variogram methods
• AnaFlow - (semi-)analytical solutions for specific groundwater-flow scenarios and the extended Generalized Radial Flow model
• welltestpy - store, manipulate, and analyze well-based field testing campaigns with a focus on estimating parameters of subsurface heterogeneity from pumping test data.
• ogs5py - pre-processing, operating, and post-processing of subsurface flow and transport simulations by providing a Python API for the FEM solver OpenGeoSys 5

With this collection of flexible toolboxes we aim to close the gap of missing software for real-world applications in the field of geostatistics. 
Especially GSTools is the first comprehensive Python-toolbox for covariance models, field generation, kriging, variogram estimation, data normalization and transformation. The formerly independed project PyKrige, developed by Benjamin Murphy, has been migrated to the GeoStat-Framework und we started to build a common Rust backend for the numerical heavy lifting called GSTools-Core.

We will show a set of complex workflow examples, like temperature trend analysis and pumping test ensemble simulations, and we will give an overview of the provided functionality and an outlook for the future. All workflows are made accessible as GeoStat-Examples repositories.

References

• GSTools: Müller, S., et. al. https://doi.org/10.5194/gmd-2021-301, 2021 (in review)
• AnaFlow: Müller, S., et. al. https://doi.org/10.1016/j.advwatres.2021.104027, 2021
• welltestpy: Müller, S., et. al. https://doi.org/10.1111/gwat.13121, 2021
• ogs5py: Müller, S., et. al. https://doi.org/10.1111/gwat.13017, 2020

Links

• Website: https://geostat-framework.org/
• GitHub: https://github.com/GeoStat-Framework
• GeoStat-Examples: https://github.com/GeoStat-Examples

How to cite: Müller, S., Schüler, L., Zech, A., and Heße, F.: The GeoStat-Framework: Create your geostatistical model in Python!, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8167, https://doi.org/10.5194/egusphere-egu22-8167, 2022.

Gaussian processes are a flexible machine learning framework that can be used for spatial interpolation and space-time prediction as well. Gaussian process regression (GPR) is quite similar to the geostatistical kriging method.  It encompasses various types of kriging (e.g., simple, ordinary, universal and regression kriging).  In addition, it is formulated in an inherently Bayesian framework which allows taking into account a priori beliefs regarding the distribution of the model’s hyper-parameters. Thus, it also incorporates Bayesian versions of kriging [1].  GPR is based on the assumption that the stochastic component of the observations follows a Gaussian distribution.  However, this is not the case for various environmental variables (e.g., amount of precipitation, hydraulic conductivity, wind speed), which follow skewed probability distributions.  The skewness is handled within the geostatistical framework using nonlinear transforms such that the marginal distribution of the data in the latent space becomes normal.  This procedure is known as Gaussian anamorphosis in geostatistics.  In the context of GPR, the term warped Gaussian process is used to denote the nonlinear transformation of the observations [2].   Gaussian anamorphosis (warping) is usually implemented using explicit, monotonically increasing nonlinear functions.  A different approach involves generating the warping function with the help of the empirically estimated cumulative probability distribution of the data.  This approach provides flexibility because the transformation is data-driven (non-parametric) and is thus not constrained by specific functional forms.  Furthermore, the cumulative distribution function of the data can be accurately estimated using smoothing kernels [3].  We investigate warped Gaussian process regression using synthetic datasets and precipitation reanalysis data from the Mediterranean island of Crete. Cross validation analysis is used to establish the advantages of non-parametric warping for the interpolation of incomplete data. We demonstrate that warped GPR equipped with data-driven warping provides enhanced flexibility compared to "bare" GPR and can lead to improved predictive accuracy for non-Gaussian data.  

Keywords: Gaussian processes, Mediterranean island, non-Gaussian, warping, precipitation

Funding: This research is co-financed by Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014-2020»in the context of the project “Gaussian Anamorphosis with Kernel Estimators for Spatially Distributed Data and Time Series and Applications in the Analysis of Precipitation” (MIS 5052133).

References

[1] T. Hristopulos, 2020. Random Fields for Spatial Data Modeling. Springer Netherlands, http://dx.doi.org/10.1007/978-94-024-1918-4.

[2] Snelson, E., Rasmussen, C.E. and Ghahramani, Z., 2004. Warped Gaussian processes. Advances in neural information processing systems, 16, pp.337-344.

[3] Pavlides, A., Agou, V., and Hristopulos, D. T., 2021. Non-parametric Kernel-Based Estimation of Probability Distributions for Precipitation Modeling. arXiv preprint arXiv:2109.09961.

How to cite: Hristopulos, D., Agou, V., and Pavlides, A.: Data-driven Warping of Gaussian Processes for Spatial Interpolation of Skewed Data, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6288, https://doi.org/10.5194/egusphere-egu22-6288, 2022.

Reducing the threat of severe spatiotemporal events like floods and droughts is raising concerns for water resource development and management. The severity of drought and floods increases more due to human interventions. Recent studies have focused on finding long-term solutions that mimic nature's process, while posing no environmental risks and targeting sustainability in traditional approaches. The terminology given in Europe for this natural solution is Nature-Based Solutions (NBS). Some examples of NBS are afforestation or reforestation, storage areas, vegetation buffers, and riparian forest. The main principle of NBS is that they slow down the rate of runoff by boosting interception, infiltration, or storage for flood water, hence mitigating the risk downstream. However, there is still not enough experimental nor theoretical experience on how they could be implemented to optimize their use. The way to represent NBS and the scale of implementation in models and real life is for now a process based on approximated propositions of the empirical knowledge of experts in the field. Although some experience have shown important contributions, this is not enough for an optimal implementation and a complete understanding of all possible outcomes. This is the problem expected to be addressed in this research. The main goal is to construct machine learning models to explore their use as an alternative (surrogate) that will aid in performing multiple scenario analyses of NBS, and quantifying their impacts. This approach will consider spatial and temporal data and create a link between several environmental variables and human actions without explicitly knowing the physical behavior of the system, yet clustering(grouping) behaviors or processes responses to structural properties of the hydrological model representation. The case study area for this research is the Bagmati River Basin of Nepal, covering a catchment area of 2822 sq. km, and the flow is dominated by spring and monsoon rainfall. Soil and Water Assessment Tool (SWAT) is used and the baseline scenario (without the implementation of NBS) is modeled. Different scenarios of afforestation, ponds, and conservation tillage will be intervened in the SWAT model and the changes made by those interventions will be replicated in Artificial Neural Network-Multi Layer Perceptron (ANN-MLP). Several unforeseen scenarios will also be tested in machine learning. Thus, the Spatio-temporal analysis will be done regarding the impact of NBS on the flows, and the machine learning model’s ability to replicate such complex systems will be evaluated.

The outcome presented here shows the construction of a SWAT model and the preliminary results of machine learning models capable of promptly predicting changes in flow induced by the adoption of various Nature-Based Solutions. It is anticipated to be a simple, effective, and time-saving way for studying the effectiveness of various Nature-Based Solutions for flood and drought mitigation. Thus, this study contributes to the experiences in interpreting and linking complex hydrological problems in machine learning systems.

Keywords: SWAT, Machine learning, Nature-Based Solutions, Hydrological extremes, Spatio-temporal analysis

How to cite: Gautam, K., Corzo, G., Maskey, S., and Solomatine, D.: Machine Learning Model to Reproduce Nature-Based Solutions for Flood and Drought Mitigation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11777, https://doi.org/10.5194/egusphere-egu22-11777, 2022.