In this contribution, I will – with examples from hydrology - make the case for information theory as a general language and framework for i) characterizing systems, ii) quantifying the information content in data, iii) evaluating how well models can learn from data, and iv) measuring how well models do in prediction. In particular, I will discuss how information measures can be used to characterize systems by the state space volume they occupy, their dynamical complexity, and their distance from equilibrium. Likewise, I will discuss how we can measure the information content of data through systematic perturbations, and how much information a model absorbs (or ignores) from data during learning. This can help building hybrid models that optimally combine information in data and general knowledge from physical and other laws, which is currently among the key challenges in machine learning applied to earth science problems.

While I will try my best to convince everybody of taking an information perspective henceforth, I will also name the related challenges: Data demands, binning choices, estimation of probability distributions from limited data, and issues with excessive data dimensionality.

How to cite: Ehret, U.: Information Theory: A Swiss Army Knife for system characterization, learning and prediction, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3034, https://doi.org/10.5194/egusphere-egu21-3034, 2021.

  While it is tempting in experimental practice to seek as high a  data rate as possible, oversampling can become an issue if one takes measurements too densely.  These effects can take many  forms, some of which are easy to detect: e.g., when the data sequence contains multiple copies of the same measured value.  In other situations, as when there is mixing—in the measurement apparatus and/or the system itself—oversampling effects can be harder to detect.  We propose a novel, model-free technique to detect local mixing in time series using an information-theoretic technique called permutation entropy.  By varying the temporal resolution of the calculation and analyzing the patterns in the results, we can determine whether the data are mixed locally, and on what scale.  This can be used by practitioners to choose appropriate lower bounds on scales at which to measure or report data.  After validating this technique on several synthetic examples, we demonstrate its effectiveness on data from a chemistry experiment, methane records from Mauna Loa, and an Antarctic ice core.

How to cite: Bradley, E., Neuder, M., Garland, J., White, J., and Dlugokencky, E.: Detection of Local Mixing in Time-Series Data Using Permutation Entropy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-95, https://doi.org/10.5194/egusphere-egu21-95, 2020.

Accurate hydrologic modelling is critical to effective water resource management. As catchment attributes strongly influence the hydrologic behaviors in an area, they can be used to inform hydrologic models to better predict the discharge in a basin. Some basins may be more difficult to accurately predict than others. The difficulty in predicting discharge may also be related to the complexity of the discharge signal. The study establishes the relationship between a catchment’s static attributes and hydrologic model performance in those catchments, and also investigates the link to complexity, which we quantify with measures of compressibility based in information theory. 

The project analyzes a large national dataset, comprised of catchment attributes for basins across the United States, paired with established performance metrics for corresponding hydrologic models. Principal Component Analysis (PCA) was completed on the catchment attributes data to determine the strongest modes in the input. The basins were clustered according to their catchment attributes and the performance within the clusters was compared. 

Significant differences in model performance emerged between the clusters of basins. For the complexity analysis, details of the implementation and technical challenges will be discussed, as well as preliminary results.

How to cite: Eugeni, S., Vaags, E., and Weijs, S. V.: Predictably Predictable -  The Role of Catchment Characteristics and Complexity., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14146, https://doi.org/10.5194/egusphere-egu21-14146, 2021.

Long-standing questions in multivariate statistics, information theory and machine learning reduce to estimating multivariate densities. However, this is still an unresolved problem and one of the biggest challenge in general, and for Earth system data analysis in particular, due to the high dimensionality (spatial, temporal and/or spectral) of the data streams. Gaussianization is a class of generative models (normalizing flows) that is effective in computing density estimates by using  a sequence of composite invertible transformations which transform data from its original domain to a multivariate Gaussian distribution. The methodology in turn allows us to estimate information theory measures (ITMs), which are relevant for the analysis and characterization of Earth system data superseding the mean, variance and correlation, as higher order measures, thereby capturing more complexity and providing more insight into various problems. We show that our Rotation-Based Iterative Gaussianization (RBIG) method allows us to compute ITMs from multivariate (spatio-spectral-temporal) Earth data efficiently in both computation and memory terms, directly from the Gaussianizing transformation, while being robust to data dimensionality . We demonstrate how Gaussianization is useful in various Earth observation data analysis problems, from hyperspectral image analysis to drought detection in data cubes.

How to cite: Johnson, J. E., Piles, M., Laparra, V., and Camps-Valls, G.: Gaussianization for Multivariate, High-dimensional Earth Observation data Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14519, https://doi.org/10.5194/egusphere-egu21-14519, 2021.

The present study aims at investigating uncertainty of external factors, namely the solar/geomagnetic forcing on the terrestrial variables as the Danube discharge and the atmospheric indices at the large scale. Our analysis was performed separately for each season, for two time periods, 1901-2000 and 1948-2000.

The relationship between terrestrial variables and external factors was achieved by applying the information theory elements as synergy, redundancy, total correlation and transfer entropy. 

The results differ depending on the time of year and the analysed variables.

From this analysis resulted that the two external forcings can be considered together as predictors for certain cases, while for others they are very redundant, therefore the one that produces the lowest uncertainty connection was selected.

How to cite: Mares, I., Mares, C., Dobrica, V., and Demetrescu, C.: Uncertainty analysis of solar/geomagnetic activity impact on terrestrial variables, based on the information theory , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4603, https://doi.org/10.5194/egusphere-egu21-4603, 2021.

Since Horton’s famous reinterpretation of Playfair’s law hydrologists have marvelled over the organization of drainage networks in catchments and on hillslopes. We start at the cross junction of hillslope hydraulics and geomorphology, trying to interpret the formation of hydraulic networks and erosion alike and wondering why movement of fluid creates structure at all.

In its most basic form structure and form has been explained as the result of optimization, either of certain types of energy such as free energy or its thermodynamic counterpart entropy. Research has shown that river networks and river junctions tend to minimize dissipation of kinetic energy and it has been suggested that simultaneously other forms of free energy, such as sediment transport tend to increase along the flow path. Studies have focused on hydraulic networks on the hillslope scale as well as on the catchment scale. Surprisingly little attention has been given to the question why these networks exists in the first place and why discharge confluences towards the catchment outlet.

In the first part of our study we put Hortonian surface runoff into a thermodynamic framework and derive the energy balance for steady state runoff. We derive the equations on the hillslope scale, where we observe the transition from evenly distributed potential energy (the rainfall) to spatially organized discharge in micro rills to larger rills and gullies. In hydraulic terms we distinguish between sheet- and rill flow. We then apply Manning-Strickler’s equation to estimate the distribution of hydraulic variables and compare energy conversion rates on typical 1D hillslope profiles for sheet- and rill flow. Interestingly, we find that only certain hillslope forms lead to spatial maxima of stream power.

In the second part of the study we extend the energy balance to transient flow and analyse power maxima during typical rainfall-runoff events. Finally, we relate our findings to observable, measurable hydraulic structures such as rill systems and estimate past work on sediments. We believe that current energy dynamics of surface runoff reflects past optimization and therefore holds potential for the understanding of landscape evolution and surface runoff contributions alike.

How to cite: Schroers, S. and Zehe, E.: Hortonian Surface Runoff, Hillslope Form and Energy Dynamics, can we read the fingerprints?, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14440, https://doi.org/10.5194/egusphere-egu21-14440, 2021.

The Simulation Environment for Geomorphology, Hydrodynamics and Ecohydrology in Integrated form (SERGHEI) model framework is a multi-dimensional, multi-domain and multi-physics model framework. It is designed to provide a modelling environment for hydrodynamics, ecohydrology, morphodynamics, and, importantly, interactions and feedbacks among such processes, at different levels of complexity and across spatiotemporal scales. SERGHEI is in essence, a terrestrial landscape simulator based on a hydrodynamics core, designed with an outlook towards Earth System Modelling applications. Consequently, efficient mathematical and numerical formulations, as well as HPC implementations are at its core. SERGHEI intends to enable large scale and high resolution problems, which will allow to acknowledge and simulate emergent behaviours rising from the small-scale interactions and feedbacks between different environmental processes, that often manifest at larger spatiotemporal scales.

At the core of the technical innovation in SERGHEI is its HPC implementation, built from scratch on the Kokkos programming model and C++ library. This approach facilitates portability from personal computers to Tier-0 HPC systems, including GPU-based and heterogeneous systems. This is achieved by relying on Kokkos handling memory models, thread management and computational policies for the required backend programming models. In particular, using Kokkos, SERGHEI can be compiled for multiple CPUs and GPUs using a combination of OpenMP, MPI, and CUDA.

In this contribution, we introduce the SERGHEI model framework, and specially its first operational module for solving shallow water equations (SERGHEI-SWE). This module is designed to be applicable to hydrological, environmental and consequently Earth System Modelling problems, but also to classical engineering problems such as fluvial or urban flood modelling. We also provide a first showcase of the applicability of the SERGHEI-SWE solver to several well-known benchmarks, and the performance of the solver on large-scale hydrological simulation and flooding problems. We also show and discuss the scaling properties of the solver (on several Tier-0 systems)  and sketch out its current and future development.

How to cite: Morales-Hernández, M., Özgen-Xian, I., and Caviedes-Voullième, D.: The SERGHEI model and its core shallow water solver, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9568, https://doi.org/10.5194/egusphere-egu21-9568, 2021.

A cyclone passed over Western Crete in October 17, 2006 and caused a heavy precipitation event producing a flash flood in a small agricultural basin. The only rain gauge in the studied basin recorded daily rainfall of 196.2 mm with a time-step of 15 minutes while 117 mm was recorded in 4 hours. Simulation of the flow hydrograph was performed with the semi-distributed hydrological model HBV-light and the calibration with the post-flood field data from witnesses that indicated the time to peak flow and the maximum water depth of the passing flood wave. The warming-up period of the model was sixteen days and the previous observed rainfall was 21 mm which was recorded on October 12^th. Potential evaporation was estimated through the Blaney-Criddle method. The basin was divided into various elevation zones representing three vegetation classes. The parameters regarding the soil moisture routine were applied per vegetation class. Sensitivity analysis, performed by changing one parameter at a time shows that the parameters concerning the response and routing routine affected mostly the peak hydrograph. Initial results for the peak hydrograph were compared with the one validated with HEC-HMS model and produced a very good Nash-Sutcliffe coefficient. There is on-going research of the effect of HBV-light parameters and further results will appear on the poster.

How to cite: Sarchani, S. and Tsanis, I.: Analysis of a short-duration severe precipitation event in a small ungauged basin through a semi-distributed hydrological model, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15324, https://doi.org/10.5194/egusphere-egu21-15324, 2021.

Over the past 20 years, the climate on the East European plain tends to be significantly warmer and drier. Winters became shorter and spring freshet’s conditions have been changed significantly. Maximum snow depth was the most important factor of spring freshet formation 30 years ago, but nowadays it has no significance at all and main factor today is melt water losses on infiltration and evaporation.

We registered a decrease in the period of stable snow accumulation (on average by 20% in the southern and southwestern parts of the East European Plain) because of the increase in winter temperatures. More often during first part of winter snow cover disappeared totally. The number of thaws and their duration at the end of the winter also increase and this leads to earlier and more prolonged melting of the snow pack. In these conditions, an extremely low spring freshet is formed. Our studies show that with the condition of an equal maximum snow depth the slow snowmelt forms the spring freshet up to 4 times less in volume than the fast melting.

Soil moisture also plays an important role in the melt water losses. The most part of the East European Plain is characterized by a decrease in soil moisture in late autumn, which indicates increased losses during snow melting period.

Still, the most significant changes in the structure of the factors of spring freshet formation are common to the southern and southwestern parts of the East European Plain. In the northern part, conservative factors still dominate, although this area is characterized by the significant increase in winter temperatures.

The study was supported by Russian Science Foundation Proj. №19-77-10032

How to cite: Kharlamov, M., Kireeva, M., and Varentsova, N.: Spring freshet on East European plain: changes in drivers and conditions during last three decades, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13477, https://doi.org/10.5194/egusphere-egu21-13477, 2021.

Climate warming cause the transformation of hydrological cycle in cold regions of the Northern Hemisphere. The aim of this research is to study the climate change impact on water exchange processes in the cryolithozone of the North-East of Russia.

The study presents the results of the analysis of changes in the characteristics of the climate (air temperature, precipitation), water discharge, soil temperature at the 80 cm depth and river-ice cover for a period of 50 years (1966-2018) and historical and modern data of aufeis area.

Climate. The annual air temperature in the region increased by 2.3 °C on average. The analysis of annual precipitation showed multidirectional changes. However, most of the stations are characterized by a significant negative trend of precipitation in the winter and a positive annual trend of mixed and liquid precipitation with an increase in their share in the autumn months.

Permafrost. The average annual soil temperature at the 80 cm depth increased by 1.7˚С at 7 of the 11 stations in the studied area. The maximum change reached 4.8˚С in June at the Verkhoyansk station.

Streamflow. Significant increase of streamflow in the autumn-winter period (from August to December) at most of the rivers have been established. Even though permafrost warming is leading to deepening of active layer, we hypothesized that the main reason of base flow increase is the transition of precipitation from solid to liquid and corresponding increase of streamflow in September, continuing in the following months. There is a significant shift in the dates of spring freshet floods in May. But it does not lead to a decrease of runoff in June. This may indicate an increase of contribution to streamflow of such sources as thawing permafrost, glaciers and aufeis.

The river-ice cover. There are significant changes in the characteristics of the river ice cover and the time of the river ice formation. On average, at 19 analyzed river gauges the decrease of river ice cover maximum depth was 41 cm (28%) and the period of formation of river ice with a thickness of 60 cm (necessary for using winter roads for passenger cars) has shifted to later period by 7-40 days.

The aufeis. Aufeis is an important part of groundwater and surface flow interaction in the studied area. The analysis of the historical data and its comparison to modern distribution of aufeis in the region have shown significant changes. The total number (area) of aufeis was 4642 (7181 km²), according to the historical data (Cadastre of aufeis, 1958), and 6217 (3579 km²), according to Landsat data (2013-2019), which is 1.3 times higher by number, but 2 times less by total area.

The study indicates that considerable transformations are going on in all parts of hydrological cycle. The analysis results are used as the base for planning new multidisciplinary research to assess and project the changes in the natural conditions and water cycle in the cryolithozone of the North-East of Russia.

The study was carried out with the support of RFBR (projects 19-35-90090, 19-55-80028).

How to cite: Nesterova, N., Makarieva, O., Zemlyanskova, A., and Ostashov, A.: Climate change impact on water exchange processes in the cryolithozone of the North-East of Russia, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-204, https://doi.org/10.5194/egusphere-egu21-204, 2020.

Lakes play a valuable role in the surface water resources of Mongolia. Understanding surface water dynamics and climate change over various spatiotemporal scales from local to regional are essential in Mongolia today. This study presents how lakes in the Mongolian Altai, Khuvsgul, and Khentii Mountain Ranges at high latitudes in northern Mongolia responded to the climate change during the past 50 years. The temporal trend shows that the lakes had extended in the area during the first three decades but reduced during the last two decades. However, Lakes Khoton and Khurgan in the Mongolian Altai and Lake Khangal in the Khentii increased in the area during 1970–2000 and since 2010, but decreased from 2000 to 2010. Lake Tolbo in the Mongolian Altai dropped in the area during 1970–2000, and continuously increased since 2000. Whereas Lakes Erkhel and Khargal in the Khuvsgul and Lake Gurem in the Khentii extended in 1970–2000 but reduced during 2000–2020. The spatial trend in lake area changes shows similar patterns for glacial lakes at an elevation above 2000 m a.s.l. in the Mongolian Altai and for tectonic and fluvial lakes at an elevation below 1500 m a.s.l. in the Khuvsgul and Khentii. Anomalies of seasonal variations in air temperature and precipitation in the lake basins show that the Lake Khangal basin in the Khentii is warmer and wetter than other lake basins. Moreover, the Lake Khargal basin in the Khuvsgul is cooler in winter and autumn but warmer in spring and summer compared to the basins. Whereas Lakes Tolbo, Khoton, and Khurgan basins in the Mongolian Altai are drier than others. The correlation analysis shows that hydrological dynamics of Lake Khargal in the Khuvsgul are strongly dependent on summer precipitation (r = 0.71), and autumn (r = 0.67) and summer (r = 0.47) air temperatures. However, the linear regression shows that the lake area is moderately related to the summer precipitation (R² = 0.5318) and the autumn air temperature (R² = 0.4555). Overall, the lakes in northern Mongolia show the distinct responses of hydrological dynamics to the changing climate depending on their physiographic conditions.

How to cite: Orkhonselenge, A., Gerelsaikhan, D., and Davaagatan, T.: Spatial and Temporal Responses of Lakes in Northern Mongolia to Climate Change, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9344, https://doi.org/10.5194/egusphere-egu21-9344, 2021.

The presented research examines what minimum combination of input variables are required to obtain state-of-the-art fractional snow cover (FSC) estimates for heterogeneous alpine-forested terrains. Currently, one of the most accurate FSC estimators for alpine regions is based on training an Artificial Neural Network (ANN) that can deconvolve the relationships among numerous compounded and possibly non-linear bio-geophysical relations encountered in alpine terrain. Under the assumption that the ANN optimally extracts available information from its input data, we can exploit the ANN as a tool to assess the contributions toward FSC estimation of each of the data sources, and combinations thereof. By assessing the quality of the modeled FSC estimates versus ground equivalent data, suitable combinations of input variables can be identified. High spatial resolution IKONOS images are used to estimate snow cover for ANN training and validation, and also for error assessment of the ANN FSC results. Input variables are initially chosen representing information already incorporated into leading snow cover estimators (ex. two multispectral bands for NDSI, etc.). Additional variables such as topographic slope, aspect, and shadow distribution are evaluated to observe the ANN as it accounts for illumination incidence and directional reflectance of surfaces affecting the viewed radiance in complex terrain. Snow usually covers vegetation and underlying geology partially, therefore the ANN also has to resolve spectral mixtures of unobscured surfaces surrounded by snow. Multispectral imagery if therefore acquired in the fall prior to the first snow of the season and are included in the ANN analyses for assessing the baseline reflectance values of the environment that later become modified by the snow. In this study, nine representative scenarios of input data are selected to analyze the FSC performance. Numerous selections of input data combinations produced good results attesting to the powerful ability of ANNs to extract information and utilize redundancy. The best ANN FSC model performance was achieved when all 15 pre-selected inputs were used. The need for non-linear modeling to estimate FSC was verified by forcing the ANN to behave linearly. The linear ANN model exhibited profoundly decreased FSC performance, indicating that non-linear processing more optimally estimates FSC in alpine-forested environments.

How to cite: Wisniewski, E. and Wisniewski, W.: Assessment of nominal data requirements for robust estimation of fractional snow cover in alpine-forested terrain, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14212, https://doi.org/10.5194/egusphere-egu21-14212, 2021.

Typical applications of process- or physically-based models aim to gain a better process understanding of certain natural phenomena or to estimate the impact of changes in the examined system caused by anthropogenic influences, such as land-use or climate change. To adequately represent the physical system, it is necessary to include all (essential) processes in the applied model and to observe relevant inputs in the field. However, model errors, i.e. deviations between observed and simulated values, can still occur. Other than large systematic observation errors, simplified, misrepresented or missing processes are potential sources of errors. This study presents a set of methods and a proposed workflow for analyzing errors of process-based models as a basis for relating them to process representations.

The evaluated approach consists of three steps: (1) prediction of model errors with a machine learning (ML) model using data that might be associated with model errors (e.g., model input data), (2) derivation of variable importance (i.e. contribution of each input variable to prediction) for each predicted model error using SHapley Additive exPlanations (SHAP), (3) clustering of SHAP values of all predicted errors to derive groups with similar error generation characteristics. By analyzing these groups of different error/variable association, hypotheses on error generation and corresponding processes can be formulated. This analysis framework can ultimately lead to improving hydrologic understanding and prediction.

The framework is applied to the physically-based stream water temperature model HFLUX in a case study for modelling an alpine stream in the Canadian Rocky Mountains. Initial statistical tests show a significant association of model errors with available meteorological and hydrological variables. By using these variables as input features, the applied ML model is able to predict model residuals. Clustering of SHAP values results in four distinct error groups that can be related to tree shading, sensible and latent heat flux and longwave radiation emitted by trees.

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.

How to cite: Roesky, B., Feigl, M., Herrnegger, M., Schulz, K., and Hayashi, M.: Learning from mistakes - Assessing the performance and uncertainty in process-based models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6312, https://doi.org/10.5194/egusphere-egu21-6312, 2021.

Strategic narratives (persuasive use of story systems) in science communication have been gathering
increasing support, especially in the face of misunderstandings about high-impact climatic change and hydrometeorologic extremes.
The use of these narratives reveals, in line with linguistic research, that traditional scientific discourse
conception has become outdated. Should scientific discourse be centered on the description of discoveries?
Should the role of political discourse be to convince someone to act? Before answering these, it is necessary to
understand the crucial function that uncertainty plays in communication, along with its consequences in the
concepts of objectivity and truth. More importantly, understanding its role in scientific society and sustainability.
Unable to eliminate uncertainty altogether, science becomes an essential escort to recognize, manage
and communicate its pertinency. However, the most popular strategic narratives sideline uncertainty as a threat.
Denialists follow a similar approach, though they communicate uncertainty to discredit evidence. Comparatively,
in their latest Assessment Report, the IPCC characterized uncertainty whilst stating: “uncertainty about impacts
does not prevent immediate action”.
Scientific discourse outputs and social reality constructions influence each other. The moralization of
science communication reveals how XVII century revolutionary skepticism can now be perceived as a threat, and
facts expected from science can be deemed dogmatic truths and perceived as decrees through rationalism and as
an extension of Judeo-Christian philosophical influence. Equally important, uncertainty reinforces individual
freedom, while society grasps and recognizes certainty as security and demands it from institutions, accepting
degrees of authoritarianism to maintain a tolerable living condition.
From “Climate Emergency” to “Thousand-Year Flood”, public interest in climatic change and extremes
increases following high-impact events, yet trust in science plunges into a deep polarized divide among absolute
acceptance and outright rejection relative to the bold headlines conveyed not only in the media but also in some
scientific literature.
Political, religious and activist leaders strike one as prophets acting in the name of science. From
rationalism to rationality, scientific culture is pivotal to the analysis of complexity, objectivity, and uncertainty in
the definition of truth (absent from epistemological discussions for centuries). Humor/sarcasm, literature or
dialectic are examples of how to communicate entropy of scientific models, while reflecting about the role,
uncertainty, and mistake, retain in life.
“People want certainty, not knowledge”, said Bertrand Russel. However, neither science nor democracy
work like that, rather taking reality as having shades of grey instead of a reduced black-or-white dichotomy.
Science is not about giving just one single number to problems clearly not reducible to such, as that gives a false
sense of certainty and security in an entropic world where we cannot control everything.
In order to objectively analyze discourses in light of their uncertainty features, detecting whether they
contain polarized, absolutistic narrative patterns, we introduce a new process-consistent Artificial Intelligence
framework, building from Perdigão (2020, https://doi.org/10.46337/200930). The complementarity of our
approach relative to both social and information technologies is brought out, along with ways forward to reinforce
the fundamental role of uncertainty in scientific communication, and to strengthen public confidence in the
scientific endeavor.

How to cite: Ribau, M., Perdigão, R., and Hall, J.: From rationalization to rationality: (In)sustainability of strategic narratives in  science communication, ranging from climatic change to hydro-meteorological extremes, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2360, https://doi.org/10.5194/egusphere-egu21-2360, 2021.

The Fokker-Planck equation (FPE) describes the time evolution of the distribution function of fluctuating macroscopic variables.  Although the FPE was originally derived for the Brownian motion, this framework can be applied to various physical processes.  In this presentation, applications in the snow accumulation and thaw process, which attributes to considerable spatial and temporal variations, are discussed. It is well known that snow process is a major source of heterogeneity in hydrological systems in high altitude or latitude regions; therefore, better treatment of the snow sub-grid variability is desirable. The main advantage of the FPE approach is that it can dynamically compute the probability density function (PDF) governed by an advection-diffusion type FPE without a prescribed PDF.

First, a bivariate FPE was derived from point scale process-based governing equations (Ohara et al., 2008). This FPE can express the evolution of the PDF of snow depth and temperature within a finite space, possibly a computational cell or small basin, whose shape is irrelevant. This conceptual model was proven to be effective through comparing to the corresponding Monte-Carlo simulation.  Then, the more realistic single variated FPE model for snow depth was implemented with the snow redistribution and snowmelt rate as the main sources of stochasticity. In this study, several realistic approximations were proposed to compute the time-space covariances describing effects induced by uneven snowmelt and snow redistribution.

Meanwhile, observed high-resolution snow depth data was analyzed using statistical methods to characterize the sub-grid variability of snow depth, which is essential to validate the FPE model for representing such sub-grid variability.  Airborne light detection and ranging (Lidar) provided the snow depth measurements at 0.5 m resolution over two mountainous areas in southwestern Wyoming, Snowy Range and Laramie Range (He et al., 2019). It was found that PDFs of snow depth tend to be Gaussian distributions in the forest areas. However, due to the no-snow areas effect, mainly caused by snow redistribution and uneven snowmelt, the PDFs are eventually skewed as non-Gaussian distribution.

The simulated results of the FPE model were validated using the measured time series of snow depth at one site and the spatial distributions of snow depth measured by ground penetrating radar (GPR) and airborne Lidar. The modeled and observed time series of the mean snow depth agreed very well while the simulated PDFs of snow depth within the study area were comparable to the observed PDFs of snow depth by GPR and Lidar (He and Ohara, 2019). Accordingly, the FPE model is capable to capture the main characteristics of the snow sub-grid variability in the nature.

References

Ohara, N., Kavvas, M. L., & Chen, Z. Q. (2008). Stochastic upscaling for snow accumulation and melt processes with PDF approach. Journal of Hydrologic Engineering, 13(12), 1103-1118.

He, S., Ohara, N., & Miller, S. N. (2019). Understanding subgrid variability of snow depth at 1‐km scale using Lidar measurements. Hydrological Processes, 33(11), 1525-1537.

He, S., & Ohara, N. (2019). Modeling subgrid variability of snow depth using the Fokker‐Planck equation approach. Water Resources Research, 55(4), 3137-3155.

How to cite: Ohara, N.: Dynamic Snow Distribution Modeling using the Fokker-Planck Equation Approach, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12532, https://doi.org/10.5194/egusphere-egu21-12532, 2021.

Complex System Dynamics, Causality and Predictability pose fundamental challenges even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known.

However, the edifice of complexity can be profoundly transformed by structural-functional coevolution and non-recurrent elusive mechanisms changing the very same invariants of motion that had been taken for granted. This leads to recurrence collapse and memory loss, precluding the ability of traditional stochastic-dynamic, information-theoretic and artificial intelligence approaches to provide reliable information about the non-recurrent emergence of fundamental new properties absent from the a priori kinematic geometric and statistical features.

Unveiling causal mechanisms and eliciting system dynamic predictability under such challenging conditions is not only a fundamental problem in mathematical and statistical physics, but also one of critical importance to dynamic modelling, risk assessment and decision support e.g. regarding non-recurrent critical transitions and extreme events.

In order to address these challenges, generalized metrics in non-ergodic information physics are hereby introduced for unveiling elusive dynamics, causality and predictability of complex dynamical systems undergoing far-from-equilibrium structural-functional coevolution, building from Perdigão (2017, 2018, 2020a, 2020b), Perdigão et al. (2020).

With these methodological developments at hand, hidden dynamic information is hereby brought out and explicitly quantified even beyond post-critical regime collapse, long after statistical information is lost. The added causal insights and operational predictive value are further highlighted by evaluating the new information metrics among statistically independent variables, where traditional techniques therefore find no information links. Notwithstanding the factorability of the distributions associated to the aforementioned independent variables, synergistic and redundant information are found to emerge from microphysical, event-scale codependencies in far-from-equilibrium nonlinear statistical mechanics.

The findings are illustrated to shed light onto fundamental causal mechanisms and unveil elusive dynamic predictability of non-recurrent critical transitions and extreme events across multiscale hydro-climatic problems.

References:

Perdigão R.A.P. (2017): Fluid Dynamical Systems: from Quantum Gravitation to Thermodynamic Cosmology. https://doi.org/10.46337/mdsc.5091.

Perdigão R.A.P. (2018): Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence. Entropy, 20(1), 26. https://doi.org/10.3390/e20010026.

Perdigão R.A.P. (2020a): Synergistic Dynamic Causation and Prediction in Coevolutionary Spacetimes. https://doi.org/10.46337/mdsc.5546.

Perdigão, R.A.P. (2020b): Information Physical Artificial Intelligence in Complex System Dynamics: Breaking Frontiers in Nonlinear Analytics, Model Design and Socio-Environmental Decision Support in a Coevolutionary World. https://doi.org/10.46337/200930.

Perdigão R.A.P., Ehret U., Knuth K.H. & Wang, J. (2020) Debates: Does information theory provide a new paradigm for Earth science? Emerging concepts and pathways of information physics. Water Resources Research, 56(2), 1-13. https://doi.org/10.1029/2019WR025270.

How to cite: Perdigão, R. A. P. and Hall, J.: Information Physical Complexity, Causality and Predictability across Coevolutionary Spacetimes: Theory and Hydro-Climatic Applications, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9678, https://doi.org/10.5194/egusphere-egu21-9678, 2021.

Describing the specific details and textures implicit in real-world hydro-climatic data sets is paramount for the proper description and simulation of variables such as precipitation, streamflow, and temperature time series. To this aim, a couple of decades ago, a deterministic geometric approach, the so-called fractal-multifractal (FM) method,^1,2 was introduced. Such is a holistic approach capable of faithfully encoding (describing)³, simulating⁴, and downscaling⁵ hydrologic records in time, as the outcome of a fractal function illuminated by a multifractal measure. This study employs the FM method to generate ensembles of daily precipitation and temperature sets obtained from global circulation models (GCMs). Specifically, this study uses data obtained via ten GCM models, two sets of daily records, as implied from the past, over a year, and three sets projected for the future, as downscaled via localized constructed analogs (LOCA) for a couple of sites in California. The study demonstrates that faithful representations of all sets may be achieved via the FM approach, using encodings relying on 10 and 8 geometric (FM) parameters for rainfall and temperature, respectively. They result in close approximations of the data's histogram, entropy, and autocorrelation functions. By presenting a sensitivity study of FM parameters' for historical and projected data, this work concludes that the FM representations are useful for tracking and foreseeing the records' complexity⁶ in the past and the future and other applications in hydrology such as bias correction.

References

How to cite: Maskey, M. L., Serrano Suarez, D. J., Viers, J. H., Medellin-Azuara, J., Sivakumar, B., and Diaz, L. E. G.: Fractal-multifractal ensembles of downscaled precipitation and temperature sets as implied by climate models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13741, https://doi.org/10.5194/egusphere-egu21-13741, 2021.