Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter

Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world casestudy. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much larger number of conditioning piezometric heads, multiple point geostatistics and ERT could improve aquifer characterization. This shows that state of the art stochastic methods need to be supported by abundant and high-quality subsurface data

Assimilation of Cosmogenic Neutron Counts for Improved Soil Moisture Prediction in a Distributed Land Surface Model

Cosmic-Ray Neutron Sensing (CRNS) offers a non-invasive method for estimating soil moisture at the field scale, in our case a few tens of hectares. The current study uses the Ensemble Adjustment Kalman Filter (EAKF) to assimilate neutron counts observed at four locations within a 655 km$^{2}$ pre-alpine river catchment into the Noah-MP land surface model (LSM) to improve soil moisture simulations and to optimize model parameters. The model runs with 100 m spatial resolution and uses the EU-SoilHydroGrids soil map along with the Mualem–van Genuchten soil water retention functions. Using the state estimation (ST) and joint state–parameter estimation (STP) technique, soil moisture states and model parameters controlling infiltration and evaporation rates were optimized, respectively. The added value of assimilation was evaluated for local and regional impacts using independent root zone soil moisture observations. The results show that during the assimilation period both ST and STP significantly improved the simulated soil moisture around the neutron sensors locations with improvements of the root mean square errors between 60 and 62% for ST and 55–66% for STP. STP could further enhance the model performance for the validation period at assimilation locations, mainly by reducing the Bias. Nevertheless, due to a lack of convergence of calculated parameters and a shorter evaluation period, performance during the validation phase degraded at a site further away from the assimilation locations. The comparison of modeled soil moisture with field-scale spatial patterns of a dense network of CRNS observations showed that STP helped to improve the average wetness conditions (reduction of spatial Bias from –0.038 cm$^{3}$ cm$^{-3}$ to –0.012 cm$^{3}$ cm$^{-3}$) for the validation period. However, the assimilation of neutron counts from only four stations showed limited success in enhancing the field-scale soil moisture patterns

An empirical vegetation correction for soil water content quantification using cosmic ray probes

Cosmic ray probes are an emerging technology to continuously monitor soil water content at a scale significant to land surface processes. However, the application of this method is hampered by its susceptibility to the presence of aboveground biomass. Here we present a simple empirical framework to account for moderation of fast neutrons by aboveground biomass in the calibration. The method extends the N0-calibration function and was developed using an extensive data set from a network of 10 cosmic ray probes located in the Rur catchment, Germany. The results suggest a 0.9% reduction in fast neutron intensity per 1 kg of dry aboveground biomass per m2 or per 2 kg of biomass water equivalent per m2. We successfully tested the novel vegetation correction using temporary cosmic ray probe measurements along a strong gradient in biomass due to deforestation, and using the COSMIC, and the hmf method as independent soil water content retrieval algorithms. The extended N0-calibration function was able to explain 95% of the overall variability in fast neutron intensity

Seasonal soil moisture and crop yield prediction with fifth-generation seasonal forecasting system (SEAS5) long-range meteorological forecasts in a land surface modelling approach

Long-range weather forecasts provide predictions of atmospheric, ocean and land surface conditions that can potentially be used in land surface and hydrological models to predict the water and energy status of the land surface or in crop growth models to predict yield for water resources or agricultural planning. However, the coarse spatial and temporal resolutions of available forecast products have hindered their widespread use in such modelling applications, which usually require high-resolution input data. In this study, we applied sub-seasonal (up to 4 months) and seasonal (7 months) weather forecasts from the latest European Centre for Medium-Range Weather Forecasts (ECMWF) seasonal forecasting system (SEAS5) in a land surface modelling approach using the Community Land Model version 5.0 (CLM5). Simulations were conducted for 2017–2020 forced with sub-seasonal and seasonal weather forecasts over two different domains with contrasting climate and cropping conditions: the German state of North Rhine-Westphalia (DE-NRW) and the Australian state of Victoria (AUS-VIC). We found that, after pre-processing of the forecast products (i.e. temporal downscaling of precipitation and incoming short-wave radiation), the simulations forced with seasonal and sub-seasonal forecasts were able to provide a model output that was very close to the reference simulation results forced by reanalysis data (the mean annual crop yield showed maximum differences of 0.28 and 0.36 t ha−1 for AUS-VIC and DE-NRW respectively). Differences between seasonal and sub-seasonal experiments were insignificant. The forecast experiments were able to satisfactorily capture recorded inter-annual variations of crop yield. In addition, they also reproduced the generally higher inter-annual differences in crop yield across the AUS-VIC domain (approximately 50 % inter-annual differences in recorded yields and up to 17 % inter-annual differences in simulated yields) compared to the DE-NRW domain (approximately 15 % inter-annual differences in recorded yields and up to 5 % in simulated yields). The high- and low-yield seasons (2020 and 2018) among the 4 simulated years were clearly reproduced in the forecast simulation results. Furthermore, sub-seasonal and seasonal simulations reflected the early harvest in the drought year of 2018 in the DE-NRW domain. However, simulated inter-annual yield variability was lower in all simulations compared to the official statistics. While general soil moisture trends, such as the European drought in 2018, were captured by the seasonal experiments, we found systematic overestimations and underestimations in both the forecast and reference simulations compared to the Soil Moisture Active Passive Level-3 soil moisture product (SMAP L3) and the Soil Moisture Climate Change Initiative Combined dataset from the European Space Agency (ESA CCI). These observed biases of soil moisture and the low inter-annual differences in simulated crop yield indicate the need to improve the representation of these variables in CLM5 to increase the model sensitivity to drought stress and other crop stressors.</p

Estimating Groundwater Recharge in Fully Integrated pde-Based Hydrological Models

Groundwater recharge is the main forcing of regional groundwater flow. In traditional partial-differential-equation (pde)-based models that treat aquifers as separate compartments, groundwater recharge needs to be defined as a boundary condition or it is a coupling condition to other compartments. Integrated models that treat the vadose and phreatic zones as a continuum allow for a more sophisticated calculation of subsurface fluxes, as feedbacks between both zones are captured. However, they do not contain an explicit groundwater-recharge term so it needs to be estimated by post-processing. Groundwater recharge consists of changes in groundwater storage and of the flux crossing the water table, which can be calculated based on hydraulic gradients. We introduce a method to evaluate the change of groundwater storage by a time-cumulative water balance over the depth section of water table fluctuations, avoiding the use of a specific yield. We demonstrate the approach first by a simple 1-D vertical model that does not allow for lateral outflow and illustrates the ambiguity of computing groundwater recharge by different methods. We then apply the approach to a 3-D model with a complex topography and subsurface structure. The latter example shows that groundwater recharge is highly variable in space and time with notable differences between regional and local estimates. Local heterogeneity of topography or subsurface properties results in complex redistribution patterns of groundwater. In fully integrated models, river-groundwater exchange flow may severely bias the estimate of groundwater recharge. We, therefore, advise masking out groundwater recharge at river locations

Evaluating the value of a network of cosmic-ray probes for improving land surface modelling

Land surface models can model matter and energy fluxes between the land surface and atmosphere, and provide a lower boundary condition to atmospheric circulation models. For these applications, accurate soil moisture quantification is highly desirable but not always possible given limited observations and limited subsurface data accuracy. Cosmic-ray probes (CRPs) offer an interesting alternative to indirectly measure soil moisture and provide an observation that can be assimilated into land surface models for improved soil moisture prediction. Synthetic studies have shown the potential to estimate subsurface parameters of land surface models with the assimilation of CRP observations. In this study, the potential of a network of CRPs for estimating subsurface parameters and improved soil moisture states is tested in a real-world case scenario using the local ensemble transform Kalman filter with the Community Land Model. The potential of the CRP network was tested by assimilating CRP-data for the years 2011 and 2012 (with or without soil hydraulic parameter estimation), followed by the verification year 2013. This was done using (i) the regional soil map as input information for the simulations, and (ii) an erroneous, biased soil map. For the regional soil map, soil moisture characterization was only improved in the assimilation period but not in the verification period. For the biased soil map, soil moisture characterization improved in both periods strongly from a ERMS of 0.11 cm3/cm3 to 0.03 cm3/cm3 (assimilation period) and from 0.12 cm3/cm3 to 0.05 cm3/cm3 (verification period) and the estimated soil hydraulic parameters were after assimilation closer to the ones of the regional soil map. Finally, the value of the CRP network was also evaluated with jackknifing data assimilation experiments. It was found that the CRP network is able to improve soil moisture estimates at locations between the assimilation sites from a ERMS of 0.12 cm3/cm3 to 0.06 cm3/cm3 (verification period), but again only if the initial soil map was biased

Assessing large-scale weekly cycles in meteorological variables

Several studies have claimed to have found significant weekly cycles of meteorological variables appearing over large domains, which can hardly be related to urban effects exclusively. Nevertheless, there is still an ongoing scientific debate whether these large-scale weekly cycles exist or not, and some other studies fail to reproduce them with statistical significance. In addition to the lack of the positive proof for the existence of these cycles, their possible physical explanations have been controversially discussed during the last years. In this work we review the main results about this topic published during the recent two decades, including a summary of the existence or non-existence of significant weekly weather cycles across different regions of the world, mainly over the US, Europe and Asia. In addition, some shortcomings of common statistical methods for analyzing weekly cycles are listed. Finally, a brief summary of supposed causes of the weekly cycles, focusing on the aerosol-cloud-radiation interactions and their impact on meteorological variables as a result of the weekly cycles of anthropogenic activities, and possible directions for future research, is presented

Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter

[EN] Real-time data from on-line sensors offer the possibility to update environmental simulation models in real-time. Information from on-line sensors concerning contaminant concentrations in groundwater allow for the real-time characterization and control of a contaminant plume. In this paper it is proposed to use the CPU-efficient Ensemble Kalman Filter (EnKF) method, a data assimilation algorithm, for jointly updating the flow and transport parameters (hydraulic conductivity and porosity) and state variables (piezometric head and concentration) of a groundwater flow and contaminant transport problem. A synthetic experiment is used to demonstrate the capability of the EnKF to estimate hydraulic conductivity and porosity by assimilating dynamic head and multiple concentration data in a transient flow and transport model. In this work the worth of hydraulic conductivity, porosity, piezometric head, and concentration data is analyzed in the context of aquifer characterization and prediction uncertainty reduction. The results indicate that the characterization of the hydraulic conductivity and porosity fields is continuously improved as more data are assimilated. Also, groundwater flow and mass transport predictions are improved as more and different types of data are assimilated. The beneficial impact of accounting for multiple concentration data is patent. © 2012 Elsevier B.V.The authors gratefully acknowledge the financial support by ENRESA (Project 0079000029) and the Spanish Ministry of Science and Innovation (Project CGL2011-23295). Extra travel Grants awarded to the first and second author by the Ministry of Education (Spain) are also acknowledged. Dr. Jichun Wu and an anonymous reviewer are grateful acknowledged for their comments which helped improving the final version of the manuscript.Li, L.; Zhou, H.; Gómez-Hernández, JJ.; Hendricks-Franssen, HJ. (2012). Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter. Journal of Hydrology. 428:152-169. https://doi.org/10.1016/j.jhydrol.2012.01.037S15216942

Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling

The ensemble Kalman filter (EnKF) is coupled with upscaling to build an aquifer model at a coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had been taken for the purpose of inverse modeling. Building an aquifer model at the support scale of observations is most often impractical since this would imply numerical models with many millions of cells. If, in addition, an uncertainty analysis is required involving some kind of Monte Carlo approach, the task becomes impossible. For this reason, a methodology has been developed that will use the conductivity data at the scale at which they were collected to build a model at a (much) coarser scale suitable for the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (1) Generate an ensemble of realizations of conductivities conditioned to the conductivity data at the same scale at which conductivities were collected. (2) Upscale each realization onto a coarse discretization; on these coarse realizations, conductivities will become tensorial in nature with arbitrary orientations of their principal components. (3) Apply the EnKF to the ensemble of coarse conductivity upscaled realizations in order to condition the realizations to the measured piezometric head data. The proposed approach addresses the problem of how to deal with tensorial parameters, at a coarse scale, in ensemble Kalman filtering while maintaining the conditioning to the fine-scale hydraulic conductivity measurements. We demonstrate our approach in the framework of a synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities, piezometric heads, or both is analyzed.The authors acknowledge Wolfgang Nowak and three anonymous reviewers for their comments on the previous versions of the manuscript, which helped substantially to improve it. 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