HS3.3

Societies seek to ensure sustainable development in the face of climate change, population increase, and increased demands for natural resources. Understanding, modeling, and forecasting the spatiotemporal patterns of precipitation are central to this effort [1-3]. Spatiotemporal models of precipitation with global validity are not available. This is due to the non-Gaussian distribution of precipitation as well as its intermittent nature and strong dependence on the geographic location and the space-time scales analyzed.  Herein we investigate the spatiotemporal patterns of precipitation on a Mediterranean island using geostatistical methods. 

We use ERA5 reanalysis precipitation products from the Copernicus Climate Change Service [4].  The dataset includes 31980 values of monthly precipitation height (mm) for a period of 492 consecutive months (January 1979 to December 2019) at the nodes of a 5 × 13 spatial grid that covers the island of Crete (Greece). This results in an average spatial resolution of approximately 0.28 degrees (corresponding to an approximate grid cell size of 31 km).  

We construct a spatial model of monthly precipitation using Gaussian anamorphosis (GA). GA employs nonlinear transformations to normalize the probability distribution of the data. It is extensively used in various environmental applications [5-6].  The methodology that we follow involves (i) normalizing the precipitation data per month using GA with Hermite polynomials, (ii) estimating spatial correlations and fitting them to the Spartan variogram family [6], (iii) ordinary kriging (OK) of the normalized data in order to generate precipitation estimates on a denser map grid, and (iv) application of the inverse GA transform to generate monthly precipitation maps. We also use cross-validation analysis to determine the kriging interpolation performance, first using the untransformed precipitation data and then the Hermite-polynomial GA approach outlined above. We find that Hermite-polynomial GA significantly improves the cross-validation measures.

Keywords: Gaussian anamorphosis, Hermite polynomials, Mediterranean island, non-Gaussian, ordinary kriging, Spartan variogram

References

1. D. Allard, and M. Bourotte, 2015. Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Stochastic Environ. Res. Risk Assess, 29(2), pp. 453– 462. https://doi.org/10.1007/s00477-014-0913-4.

2. A. Baxevani, and J. Lennartsson, 2015. A spatiotemporal precipitation generator based on a censored latent Gaussian field, Water Resources Research, 51(6), 4338–4358. https://doi.org/10.1002/2014WR016455.

3. C. Lussana, T. N. Nipen, I. A. Seierstad, and C. A. Elo, 2020. Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation. Nonlinear Processes in Geophysics, 1–43. https://doi.org/10.5194/npg-2020-20.

4. C3S, C. C. C. S., 2018. ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate. Data retrieved from: https://cds.climate.copernicus.eu/cdsapp#!/home.

5. N. Cressie, 1993. Spatial Statistics. John Wiley and Sons, New York.

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

How to cite: Agou, V. D., Pavlides, A., and Hristopulos, D. T.: Space-Time Analysis of Precipitation Reanalysis Data for the Island of Crete using Gaussian Anamorphosis with Hermite Polynomials, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3088, https://doi.org/10.5194/egusphere-egu21-3088, 2021.

Abstract

Most of the time series in nature are nonlinear and nonstationary affected by climate change particularly. It is inevitable that Taiwan has also experienced frequent drought events in recent years. However, drought events are natural disasters with no clear warnings and their influences are cumulative. The difficulty of detecting and analyzing the drought phenomenon remains. To deal with the above-mentioned problem, Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD) is introduced to analyze the temperature and rainfall data from 1975~2018 in this study, which is a powerful method developed for the time-frequency analysis of nonlinear, nonstationary time series. This method can not only analyze the spatial locality and temporal locality of signals but also decompose the multiple-dimensional time series into several Intrinsic Mode Functions (IMFs). By the set of IMFs, the meaningful instantaneous frequency and the trend of the signals can be observed. Considering stochastic and deterministic influences, to enhance the accuracy this study also reconstruct IMFs into two components, stochastic and deterministic, by the coefficient of auto-correlation.

In this study, the influences of temperature and precipitation on the drought events will be discussed. Furthermore, to decrease the significant impact of drought events, this study also attempts to forecast the occurrences of drought events in the short-term via the Artificial Neural Network technique. And, based on the CMIP5 model, this study also investigates the trend and variability of drought events and warming in different climatic scenarios.

Keywords: Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD), Intrinsic Mode Function(IMF), Drought

How to cite: Tang, C.-H. and Tsai, C. W.: Spatiotemporal Trend and Variability of Precipitation in Taiwan Based on Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD), EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10609, https://doi.org/10.5194/egusphere-egu21-10609, 2021.

This study aims to propose the use of spatio-temporal Remote Sensing information and Machine learning techniques (ML) for Active Moving Area Identification and Forecast. Mass Movements are frequent in Central American countries, mainly due to the combined extreme hydro-meteorological events with the seismic activity and the characteristics of the geological formations in the region. Ometepe Island is located in Lake Cocibolca, Nicaragua; it has two volcanoes (one active) and Mass Movements happen quite often in the area, where many of them represent a big risk for the population. The triggering factors for these Mass Movements are mainly volcanic activity in conjunction with high and quick precipitations. The process of identification of a Mass Movement from Remote Sensing images is used first as a way to characterise the data, and then a lagged time step was used to evaluate the forecasting capabilities in a time window of precipitation forecast. For this, Remote Sensing was used to create the Active Moving Area Inventory, using InSAR technique with Sentinel-1 SAR images. SNAP software was used to locate occurrences of displacements in the island. This inventory was used to develop ML models that had Rainfall and Soil Moisture as dynamic variables; and DEM, Land Use, Geomorphology, and others as static variables. These were trained and evaluated using Logistic Regression (LR), Random Forest (RF) and Long Short-Term Memory (LSTM) to detect occurrence of Displacement in a particular area of the island. The results were analysed performance-wise and compared to each other. The results of this methodology are a first step into a larger framework of spatiotemporal analysis for forecasting using Machine Learning.

How to cite: Arcia, V., Corzo, G., and Calderón, H.: Active Moving Area Identification using Machine Learning. Case study: Ometepe Island, Nicaragua, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8462, https://doi.org/10.5194/egusphere-egu21-8462, 2021.

The North Atlantic Oscillation (NAO) is often cited as the primary atmospheric-oceanic circulation or teleconnection influencing regional climate in Great Britain. As our ability to predict the NAO several months in advance improves, it is important that we also continue to develop our spatial and temporal understanding of the rainfall signatures which the circulation produces.

We present a novel application of spatial statistics to explore variability in monthly NAO rainfall signatures using a 5km gridded monthly Standardised Precipitation Index (SPI) dataset. We first use the Getis-Ord Gi* statistic to map spatially significant hot and cold spots (clusters of high/wet and low/dry SPI values) in average monthly rainfall signatures under NAO Positive and Negative conditions over the period 1900-2015. We then look across the record and explore the temporal variability in these signatures, in other words how often a location is in a significant spatial hot/cold spot (high/low SPI) at a monthly scale under NAO Positive/Negative conditions.

The two phases of the NAO are typically more distinctive in the winter months, with stronger and more variable NAO Index values. The average monthly SPI analysis reveals a north-west/south-east ‘spatial divide’ in rainfall response. NAO Positive phases result in a southerly North Atlantic Jet Stream bringing warm and wet conditions from the tropics, increasing rainfall particularly in the north-western regions. However, under NAO Negative phases which result in a northerly Jet Stream, much drier conditions in the north-west prevail. Meanwhile in the south-eastern regions under both NAO phases a weaker and opposite wet/dry signal is observed. This north-west/south-east ‘spatial divide’ is marked by the location of spatially extensive hot/cold spots. The Getis-Ord Gi* result identifies that the spatial pattern we detect in average winter rainfall is statistically significant. Looking across the record, this NW/SE opposing response appears to have a relatively high degree of spatio-temporal consistency. This suggests that there is a high probability that NAO Positive and Negative phases will result in this NW/SE statistically significant spatial pattern.

Even though the phases of the NAO in the summer months are less distinctive they still produce rainfall responses which are evident in the monthly average SPI. However, the spatiality in wet/dry conditions is more homogenous across the country. In other words the ‘spatial divide’ observed in winter is diluted in summer. As a result, the occurrence of significant hot/cold spots is more variable in space and time.

Our analysis demonstrates a novel application of the Getis-Ord Gi* statistic which allows for spatially significant patterns in the monthly SPI data to be mapped for each NAO phase. In winter months particularly, this analysis reveals statistically significant opposing rainfall responses, which appear to have long-term spatio-temporal consistency. This is important because as winter NAO forecasting skill improves, the findings of our research enable a more spatially reliable estimate of the likely impacts of NAO-influenced rainfall distribution.

How to cite: West, H., Quinn, N., and Horswell, M.: Mapping Spatio-Temporal Variability in NAO Rainfall Signatures, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10982, https://doi.org/10.5194/egusphere-egu21-10982, 2021.

Arachthos River is the largest river in Epirus and the 8^th largest in Greece; it is 110 km long and its drainage area is 2209 km2. After emanating from Pindus mountains (near Metsovo), it enters into the Pournari Reservoir in Arta, passes through Arta and discharges into the Ambracian Gulf near Kommeno. Arachthos River prevents flooding of the city of Arta and supplies water to most of Epirus.

The design of flood protection works in Arachthos River is currently in progress; it is performed by a consortium of Greek Consulting Firms for the Ministry of Infrastructure and Transportation. In the present work, we examine the effect of Flood Retention Ponds on the inundation area and the subsequent flood risk for the city of Arta. The Flood Retention Ponds are constructed immediately downstream of the Pournari Reservoir and 5600 m upstream of the historic Bridge of Arta; their exact locations were identified after a preliminary study and field surveys. Firstly, we performed the design of the Flood Retention Ponds, based on international standards and specifications found in the international literature; then, we performed hydrodynamic calculations using the Hydrologic Engineering Center's-River Analysis System (HEC-RAS) 1D/2D with and without the Flood Retention Ponds. Thirdly, we compared the calculations and the corresponding inundation areas and derive conclusions on the effect of Flood Retention Ponds.

How to cite: Rontiris, G., Mitsopoulos, G., Panagiotatou, E., and Stamou, A. I.: Modelling the effect of Flood Retention Ponds in Arachthos River (Arta, Greece) , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15381, https://doi.org/10.5194/egusphere-egu21-15381, 2021.

Floods are one of the worst natural hazards around the globe and around 40% of all losses worldwide due to natural hazard have been caused by floods since 1980s. In India, more than 40 million hectares of area are affected by floods annually which makes it one of the worst affected country in the world. In particular, the Ganga river basin in northern India which hosts nearly half a billion people, is one of the worst floods affected regions in the country. The Ghaghra river is one of the highest discharge-carrying tributaries of the Ganga river, which originates from High Himalaya. Despite severally affected by floods each year, flood frequencies of the Ghaghra river are poorly understood, making it one of the least studied river basins in the Ganga basin. It is important to note that, like several other rivers in India, the Ghaghra also has several hydrological stations where only stage data is available, and therefore traditional flood frequency analysis using discharge data becomes difficult. In this work, we have performed flood frequency analysis using both stage and discharge dataset at three different gauge stations in the Ghaghra river basin to compare the results using statistical methods. The L-moment analysis is applied to assess the probability distribution for the flood frequency analysis. Further, we have used the TanDEM-x 90m digital elevation model (DEM) to map the flood inundation regions. Our results suggest the Weibull is statistically significant distribution for the discharge dataset. However, stage above danger level (SADL) follows General Pareto (GP3) and Generalized Extreme Value (GEV) distributions. The quantile-quantile plot analysis suggests that the SADL probability distributions (GP3 and GEV) are closely following the theoretical probability distributions. However, the discharge distribution (Weibull) is showing a relatively weak corelation with the theoretical probability distribution. We further used the probability distribution to assess the SADL frequencies at 5-, 10-, 20-, 50- and 100-year return periods. The magnitudes of SADL at different return periods were then used to map the water inundation areas around different gauging stations. These inundation maps were cross-validated with the globally available flooding extent maps provided by Dartmouth flood observatory. Overall, this work exhibits a simple and novel technique to generate inundation maps around the gauging locations without using any sophisticated hydraulics models.

How to cite: Singh, S., Swarnkar, S., and Sinha, R.: Exploring stage-based flood frequency analysis for flood inundation mapping, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1924, https://doi.org/10.5194/egusphere-egu21-1924, 2021.

Abstract

The flash flood in Mandra on the 15^th of November 2017 was the third most disastrous “November” flood in Attica; it was characterized by heavy sediment and debris transport that can be easily observed in Figure 1.

We applied the Hydrologic Engineering Center's-River Analysis System (HEC-RAS) to model sediment transport using the Ackers-White sediment transport equation that is engraved in HEC-RAS to analyze sediment transport characteristics. The required input data were based on a limited number of available studies, which mainly include a survey performed by the Hellenic Centre for Marine Research in the coastal area of the Elefsis Bay where sediments were deposited after the catastrophic event. We compared the results of the model with calculations performed within a previous Thesis in 2018 using TELEMAC-2D and SISYPHE.

The present paper is based on the Diploma Thesis of the first author; it was performed within the project “National Network on Climate Change and its Impacts (CLIMPACT)” of the General Secretariat of Research and Technology.

Figure 1. The greater area of Mandra (a) before and (b) after the flood event

How to cite: Sant, V., Mitsopoulos, G., Bloutsos, A., and Stamou, A.: Modelling Sediment Transport in the disastrous Flash Flood of November 2017 in Mandra (Attica, Greece) , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10561, https://doi.org/10.5194/egusphere-egu21-10561, 2021.

The region of Attica is characterized by a relatively large number of floods over a long period of time. The flash flood in Mandra on the 15^th of November 2017 was the third most disastrous “November” flood in Attica; most of the population was affected by the flood (23 deaths and 24 people injured), while basements and ground floors of buildings in the town were seriously impacted.

The two main streams that pass through the town of Mandra are Soures and Agia Aikaterini, whose catchment area is equal to 23.0 and 22.0 km², respectively. These streams are characterized by significant morphological changes due to the intensive construction activities in the greater area that resulted in a dramatic decrease of their available cross-sectional areas and the occurrence of floods even at low flow rates.

We applied the HEC-RAS 1D/2D to model the flash flood using a high resolution Digital Surface Model (DSM) and topographic survey data, to obtain the most accurate representation of the area of Mandra. Moreover, we imported to the model all technical works, such as culverts and bridges that affect the flow. For the model calibration, we employed (a) videos, photographs, information from the local population and satellite images to determine the inundation area and (b) in situ measurements of the flood water depth, in various locations within the town of Mandra. The results of the model were compared with calculations performed within a previous Thesis in 2018 using TELEMAC-2D.

The present paper is based on the Master Thesis of the first author; it was performed within the project “National Network on Climate Change and its Impacts (CLIMPACT)” of the General Secretariat of Research and Technology.

How to cite: Tsokanis, K., Mitsopoulos, G., Bloutsos, A., and Stamou, A. I.: Modelling the disastrous Flash Flood of November 2017 in Mandra (Attica, Greece) , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15041, https://doi.org/10.5194/egusphere-egu21-15041, 2021.

Drought is often conceptualised as an extreme weather event generated by anomalies in water resources availabilities. Understanding the behaviour and spatiotemporal distribution of drought events has become very important due to the possible teleconnections of drought propagation patterns. This understanding and if is possible representation of teleconnections between patterns could lead to better prediction and management of extreme events.
This study develops a methodology to monitor spatiotemporal drought events in the dry corridor of Central America using the drought index SPI and SPEI for the period 1981 to 2020.
This methodology consists of five stages. 1) collection and quality validation of the data sets used. 2) ERA5 and Observation datasets allow calibrating the precipitation and temperature values from historical gauge measurements. 3) Then, by the estimation and trend analysis of the drought index in different time scales (3, 6, 12 months) an initial baseline is defined. 4) Spatiotemporal association algorithms (based on computer vision) are used to characterise and monitoring the most extensive drought events. For this, the extreme and severe events (DI values below -1) threshold is estimated. 5)  Synchronic Integration between temporal patterns and spatial propagation is carried out to evaluate possible interactions or connections of drought events along the dry corridor of Central America. These results provide valuable information to evaluate the impacts on different sectors threatened by drought throughout the territory. This work presents preliminary results of an extended project looking at the dry corridor in Central America. 

How to cite: Sanchez Hernandez, K. A., Corzo Perez, G. A., and Santos Granados, G. R.: Spatiotemporal and Synchronous Monitoring of Drought in the Dry Corridor of Central America, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13870, https://doi.org/10.5194/egusphere-egu21-13870, 2021.

Abstract

Human activity is directly responsible for land use and land cover changes, affecting different ecosystem services. Thus, from the perspective of land use management is critical to project potential future land-use changes. This study aimed: (i) to detect possible changes in land-use structure in response to different four scenarios, namely: business as usual, urbanization, afforestation and land abandonment, and agricultural intensification scenario; and (ii) to measure the landscape habitat quality (an ecosystem services proxy) according to those projected futures. We selected as case study Lithuania due to the potential future increased human pressures on the landscape, and due to the high landscape value of this territory. The projected year was 2050, and we used the Cellular Automata method (applying the Dinamica EGO software) to project future land-use changes, and the InVEST model to assess the habitat quality. The land-use scenarios outcomes were validated using a fuzzy comparison function, and 80% of accuracy was achieved (comparing a simulated land use map of 2018, and the observed map for the same year). The results showed that the agricultural intensification scenario represents the greatest predicted landscape deterioration (from 0.71 in 2018 to 0.64). In the urbanization scenario, the highest landscape degradation prediction is identified around the most important cities (Vilnius, Kaunas, and Klaipėda). In the opposite direction, the afforestation and land abandonment scenario show the highest improvement on the habitat quality, from 0.71 in 2018 to 0.74. 

Acknowledgements

“Lithuanian National Ecosystem Services Assessment and Mapping (LINESAM)” No. 09.3.3-LMT-K-712-01-0104 is funded by the European Social Fund according to the activity “Improvement of researchers’ qualification by implementing world-class R&D projects” of Measure No. 09.3.3-LMT-K-712.

How to cite: Pereira, P., Gomes, E., Inacio, M., Bogdzevič, K., Karnauskaite, D., and Kalinauskas, M.: Mapping and assessment of future land use change impacts on habitat quality in Lithuania, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3267, https://doi.org/10.5194/egusphere-egu21-3267, 2021.

The multi-resolution approximation approach (MRA) [1] provides an efficient representation of Gaussian processes that scales beyond millions of observations. MRA leaves flexibility in the selection of covariance functions and allows to trade off computation time against prediction performance, depending on the selection of parameters. Recent work [2] has shown how MRA can be used for global spatiotemporal processes by integrating nonstationary covariance functions, where parameters vary over space and/or time following a kernel convolution approach. As such, MRA turns out to be a promising approach for geostatistical modelling of global spatiotemporal datasets, such as those coming from Earth observation satellites.

In this work, we show how MRA can be used for spatiotemporal analysis from a practical perspective. In the first part, we will discuss the influence of parameters (spatiotemporal shape of partitioning regions, the number of basis functions, and the number of partitioning levels) by analyzing a real world dataset. In the second part, we will present and discuss our implementation as an R package stmra[3]. We will demonstrate how traditional models as from the gstat package can be implemented efficiently with MRA, and how non-stationary models can be defined by users in a relatively simple way. 

[1] Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. Journal of the American Statistical Association, 112(517), 201-214

[2] Appel, M., & Pebesma, E. (2020). Spatiotemporal multi-resolution approximations for analyzing global environmental data. Spatial Statistics, 38, 100465.

[3] https://github.com/appelmar/stmra

How to cite: Appel, M. and Pebesma, E.: Implementation of geostatistical models for large spatiotemporal datasets using multi-resolution approximations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6585, https://doi.org/10.5194/egusphere-egu21-6585, 2021.

The gridded interpolated daily precipitation data has a vast application in hydrometeorology. The fine resolution gridded precipitation gained terrestrial measurements is a tool to evaluate satellite, reanalysis, and radar-based gridded products. In this study, the daily time series of 1561 rain gauges over Iran for the period of 2003-20010 is used to compute 1 km * 1 km interpolated maps. The nearest neighborhood, Inverse Distance Weighting (IDW), Ordinary Kriging (OK), External Drift Kriging (EDK), and Quantile Kriging (QK) interpolation methods are applied to compare their performance. Due to the large size of the interpolated region and different climates, six clusters for estimating the variogram function are determined. The distinct interpolation methods lead to different daily precipitation estimates, however in the same spatial resolution, OK is showed slightly better results with the mean RMSE and correlation equal to 2.355 and 0.766, respectively. Also, the spatially aggregated gridded maps illustrated that the interpolation methods only play a significant role in the fine resolutions than the coarser ones.

How to cite: Modiri, E. and Bárdossy, A.: A new insight to daily precipitation estimation using different interpolation methods, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15958, https://doi.org/10.5194/egusphere-egu21-15958, 2021.

The bathymetry of the riverbed is essential in flood risk assessment at large rivers, and yet its acquisition is a slow process and endowed with a high budget economic. Moreover, recent research works have shown the importance of improving the geometrical characterization inside the riverbed, which is an issue due to the inability of light to penetrate water bodies. So, most of LiDAR techniques allow us for high resolution surface topography data but not for water occupied river channels. This, apart from making these jobs more difficult, sometimes generates the renouncement of it, using the topography of the water sheet as a riverbed, or the simplification of river channel configuration (trapezoidal transversal sections) which frequently generate an overestimation of flood zones. To overcome these deficiencies, a novel methodological approach has been developed to simulate this bathymetry using simplified models. The proposed approach is based upon the calibration of the flow roughness parameters (Manning´s n value) inside the riverbed. The use of abnormally low Manning´s n values has made it possible to reproduce both the extent of the flooded area and the water depth value within it in an acceptable manner: first results from hydrodynamic modelling of 500-year return period peak flow show the reduction of the water depth average error from 50-75 cm to only about 10 cm; and a direct economic flood damage differences reduction from 25-30% to values of about 5%.

The present work proposes to go further with these investigations and perform a robust geostatistical analysis of hydrodynamic modelling outputs obtained with modified Manning’s n values. The methodology scheme is to characterize the spatial distribution of the results and its spatial correlation with other variables, as the distance to the riverbank or flow rates (for different return periods), through variogram models. This quantitative statistical description of the floodable areas, depending on the Manning’s n value model used and the return period considered, could be used to perform geostatistical simulations that allow to quantify the spatial uncertainties associated to the studied models; as well as to calibrate the optimal spatial distribution of modified Manning’s n values inside the riverbed. These findings will be analysed as guidelines to construct more robust and reliable flood risk estimations; and can be applied to many other study cases around the world, saving analysis time and execution costs, but without losing its scientific rigour.

How to cite: Guardiola-Albert, C., Garrote-Revilla, J., González-Jiménez, M., and Díez-Herrero, A.: A new methodological proposal for improving flood risk mapping using geostatistical techniques in Central-Western Spain, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6269, https://doi.org/10.5194/egusphere-egu21-6269, 2021.

This paper aims to develop a spatiotemporal model to estimate monthly low flow quantiles Q95 [P(Q<Q95=0.05)] standardized by catchment area in Austria. Our dataset consists of 325 gauging stations that where consistently monitored between 1976 to 2015, and it covers about 60% of the national territory of Austria.

In a first step we are adapting a spatiotemporal model initially designed for modeling air pollution data. This approach is based on empirical orthogonal functions (EOF), that should capture the temporal structure of the spatiotemporal model. The EOFs are weighted by regression coefficients estimated by universal kriging. We extend the model by using GLM-boosting, LASSO, Principal Component Regression (PCR) and Random Forest (RF) for selecting the regression coefficients of the EOFs. Furthermore, we do not limit the kriging structure of the residual field to geographical coordinates but use a broader approach of physiographic kriging. In a second step we implement separate models for the mean parts of the model and the residual parts of the model. The mean field is defined by statistical learning methods as RF, GAM-boosting, LASSO and Support Vector Machines (SVM). For the residual field we define two different approaches, either the method developed in the first step or spatiotemporal kriging.

Model performance is evaluated by cross validation and the best model is selected by the mean squared error (MSE).

How to cite: Laimighofer, J., Melcher, M., Parajka, J., and Laaha, G.: Combining statistical learning and geostatistical approaches in a spatiotemporal framework for low flow estimation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7501, https://doi.org/10.5194/egusphere-egu21-7501, 2021.

A significant issue in all geochemical anomaly classification methods is uncertainty in the identification of different populations and allocation of samples to those populations, including the critical category of geochemical anomalies or patterns that are associated with the effects of mineralisation. This is a major challenge where the effects of mineralisation are subtle. There are various possible sources of such uncertainty, such as (i) gaps in coverage of geochemical sampling within a study area; (ii) errors in geochemical data analysis, spatial measurement, interpolation; (iii) misunderstanding of geological and geochemical processes; (iv) fuzziness or vagueness of the threshold between geochemical background and geochemical anomalies. In this research, the well-established concentration-area (C-A) and the newly established concentration-concentration (C-C) fractal models were applied to centered-logratio (clr) transformed data, and highly correlated elements of Cu-Te, respectively. Such models were applied to the available till samples (2578 samples) collected by the Geological Survey of Sweden (SGU) from 75% of the country area, to generate the Cu volcanic massive sulfide (VMS) geochemical anomaly classified map and define the highly promising areas for further exploration. However, to be confident more about the robustness of each class recognised by the thresholds obtained from the C-A and C-C log-log plots, Monte Carlo simulation (MCSIM) was applied to each class to simulate a higher number of values per class and consider the relevant error propagation. Under the MCSIM approach, the P50 value (the average 50^th percentile of the multiple simulated distributions represents a neutral probability in decision-making) is defined as the expected ‘return’. The uncertainty is calculated, in this approach, as 1/(P90-P10) for which P10 (lower decile) and P90 (upper decile) are the average 10^th and 90^th percentiles of the multiple simulated values, associated with each class. The most reliable classes are those with high returns and low risks. Based on the results obtained, C-A could not provide robust enough results since in the defined classes, the risk was almost equal or even higher than the return, however, the C-C model provided high returns and very low uncertainties, demonstrating the robustness of C-C compared to C-A. This approach can improve the quality of the decision-making in choosing the most robust classification models, and consequently getting more reliable results.

How to cite: Sadeghi, B.: Evaluation of geochemical anomaly classification models based on the relevant uncertainties and error propagation per class to select the most robust model(s) for the follow-up exploration, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1429, https://doi.org/10.5194/egusphere-egu21-1429, 2021.

Recently, there is a growing interest for the soil variable soil thickness in the soil science, geoscience and ecology communities. More and more scientists assume that soil thickness summarizes many different characteristics of the site that are important for plant growth, soil biodiversity and climate change. As such soil thickness can be an indicator of properties like water holding capacity, nutrient cycling, carbon storage, habitat for soil fauna and overall soil quality and productivity. At the same time, it takes a lot of effort to measure soil thickness, especially for larger and heterogeneous areas like mountain regions, which would require dense sampling. For these reasons, it is becoming increasingly important to spatially predict soil thickness as accurately as possible using models.
The typical difficulty in predicting variables in environmental sciences is the small number of samples in the field and resulting from this a small number of usable data points to train models in the spatial domain. One possibility to create valid models with sparse spatially distributed soil data is the combination of point measurements with domain knowledge. For soils and their properties such knowledge can be archived from related environmental data, for example, parent material and climate, and their spatial distribution neighboring the sample points. Frequently used machine learning methods for environmental modelling, especially in the geosciences, are the Gaussian Process Regression Models (GPRs), because a spatial correlation can already be implemented via the covariance kernel. One of the great advantages of using GPRs is the possibility to inform this algorithm directly with soil science knowledge. We can claim this knowledge in different ways.
In this paper we apply a new approach of implementing geographical knowledge into the Gaussian Processes by means of partial differential equations (PDEs), each describing a pedological process. These PDEs include information on how independent environmental variables influence the searched dependent variable. At first, we calculate for simple correlations between soil thickness and these variables, which we then convert into a PDE. As independent variables we initially use exclusively topographical variables derived from Digital Elevation Models (DEM) such as slope, different curvatures, aspect or the topographic wetness index. In this way, expert knowledge can adapt the GPR model in addition to the already existing assumption of spatial dependency given by prior covariance, where near things are more related than distant.
The algorithm will be applied to a data set from Andalusia, Spain, developed by Tobias Rentschler. Among land use information gained from remote sensing, it contains our target variable soil thickness.

How to cite: Rau, K., Gläßle, T., Rentschler, T., Hennig, P., and Scholten, T.: Spatial prediction of soil thickness with Gaussian Process Regression using pedological knowledge described by partial differential equations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3368, https://doi.org/10.5194/egusphere-egu21-3368, 2021.

Uncertainty analysis is a critical subject for many environmental studies. We have previously combined statistical learning and Information Theory in a geostatistical framework for overcoming parameterization with functions and uncertainty trade-offs present in many traditional interpolators (Thiesen et al. 2020). The so-called Histogram via entropy reduction (HER) relaxes normality assumptions, avoiding the risk of adding information not available in the data. The authors showed that, by construction, the method provides a proper framework for uncertainty estimation which accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. In this study, we explore HER method in the light of uncertainty analysis. In general, uncertainty at any particular unsampled location (local uncertainty) is frequently assessed by nonlinear interpolators such as indicator and multi-gaussian kriging. HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution without the need of modeling multiple indicator semivariograms, order-relation violations, interpolation/extrapolation of conditional cumulative distribution functions, or stronger hypotheses of data distribution. In this work, this nonparametric geostatistical framework is adapted to address local and spatial uncertainty in the context of risk mapping. We investigate HER for handling estimations of threshold-exceeding probabilities to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Finally, HER method is extended to assess spatial uncertainty (uncertainty when several locations are considered together) through sequential simulation. Its results are compared to indicator kriging and benchmark models available in the literature generated for this particular dataset.

Thiesen S, Vieira DM, Mälicke M, Loritz R, Wellmann JF, Ehret U (2020) Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics. Hydrol Earth Syst Sci 24:4523–4540. https://doi.org/https://doi.org/10.5194/hess-24-4523-2020

How to cite: Thiesen, S. and Ehret, U.: Assessing local and spatial uncertainty with HER method, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-568, https://doi.org/10.5194/egusphere-egu21-568, 2021.

Oceanographic data belong to the wide class of vectorial data, for which the decomposition in modulus and direction is meaningful, and the vectorial components are characterized by homogeneous quantities, with the same unit of measurement. Another feature of oceanographic data is that they exhibit spatio-temporal dependence.
In Geostatistics, such data can be properly modelled by recalling the theory of complex-valued random fields. However, in the literature, only techniques for modeling and predicting the spatial evolution of these phenomena were proposed; while the temporal dependence was analyzed separately from the spatial one, or just time-varying complex covariance models were used. Thus, the novelty of this paper regards some advances of the complex formalism for analyzing complex data in space-time and new classes of spatio-temporal complex covariance models.
A case study on spatio-temporal complex estimating and modeling with oceanographic data is provided and a comparison between two classes of complex covariance models is also proposed.

How to cite: Maggio, S., Posa, D., De Iaco, S., and Cappello, C.: Estimating and modeling spatio-temporal complex-valued covariance functions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16382, https://doi.org/10.5194/egusphere-egu21-16382, 2021.

In environmental sciences, it is very common to observe spatio-temporal multiple data concerning several correlated variables which are measured in time over a monitored spatial domain. In multivariate Geostatistics, the analysis of these correlated variables requires the estimation and modelling of the spatio-temporal multivariate covariance structure.
In the literature, the linear coregionalization model (LCM) has been widely used, in order to describe the spatio-temporal dependence which characterizes two or more variables. In particular, the LCM model requires the identification of the basic independent components underlying the analyzed phenomenon, and this represents a tough task. In order to overcome the aforementioned problem, this contribution provides a complete procedure where all the necessary steps to be followed for properly detect the basic space-time components for the phenomenon under study, together with some computational advances which support the selection of an ST-LCM.
The implemented procedure and the related algorithms are applied on a space-time air quality dataset.
Note that the proposed procedure can help practitioners to reproduce all the modeling stages and to replicate the analysis for different multivariate spatio-temporal data.

How to cite: Cappello, C., De Iaco, S., Palma, M., and Maggio, S.: A step by step procedure for multivariate modeling, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16387, https://doi.org/10.5194/egusphere-egu21-16387, 2021.

Bedrock topography and sediment thickness can be modelled as stochastic functions in space. These two functions are important for water storage and runoff and they are therefore essential to understand hydrological response to drought and extreme rainfall events. Digital information from remote sensing, geological mapping, and public databases comprise information which make it possible to control the estimation uncertainty. Depending on the geological history, the bedrock topography might have a complex structure in space. We present results from a case study where bedrock outcrops were exposed small patchy areas and with some scattered point information from a public well database. We modelled the estimation uncertainty by standard geostatistical methods (kriging and co-kriging), and the results showed that by including information of the outcrop locations, we were able to reduce the estimation uncertainty (Kitterød, 2017). In addition to the kriging approach, we explored numerical solutions of the Poisson equation. By this method, we modelled the bedrock surface by fitting a parabolic function to sediment thickness. This was done by inverse modelling of a global load parameter in the Poisson equation. For future research, we suggest to substituting the constant load parameter by a stochastic function in space.

References:

Kitterød, N.-O. (2017): Estimating unconsolidated sediment cover thickness by using the horizontal distance to a bedrock outcrop as secondary information, Hydrol. Earth Syst. Sci., 21, 4195-4211, https://doi.org/10.5194/hess-21-4195-2017, doi:10.5194/hess-21-4195-2017.

How to cite: Kitterød, N.-O. and Leblois, É.: Modelling local trend of bedrock topography by inverse modelling of Poisson’s equation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16441, https://doi.org/10.5194/egusphere-egu21-16441, 2021.