Sparse Point Measurements Research Articles

Spatiotemporal wind field prediction based on physics-informed deep learning and LIDAR measurements

Spatiotemporal wind field information is of great interest in wind industry e.g. for wind resource assessment and wind turbine/farm monitoring & control. However, its measurement is not feasible because only sparse point measurements are available with the current sensor technology such as LIDAR. This work fills the gap by developing a method that can achieve spatiotemporal wind field predictions by combining LIDAR measurements and flow physics. Specifically, a deep neural network is constructed and the Navier–Stokes equations, which provide a good description of atmospheric flows, are incorporated in the deep neural network by employing the physics-informed deep learning technique. The training of this physics-incorporated deep learning model only requires the sparse LIDAR measurement data while the spatiotemporal wind field in the whole domain (which cannot be measured) can be predicted after training. This study, which can discover complex wind patterns that do not present in the training dataset, is totally distinct from previous machine learning based wind prediction studies which treat machine learning models as “black-box” and require the corresponding input and target values to learn complex relations. The numerical results on the prediction of the wind field in front of a wind turbine show that the proposed method predicts the spatiotemporal flow velocity (including both downwind and crosswind components) in the whole domain very well for a wide range of scenarios (including various measurement noises, resolutions, LIDAR look directions, and turbulence levels), which is promising given that only line-of-sight wind speed measurements at sparse locations are used.

Parameter Optimization of Reduced Fluid Model via Sparse Point Measurements

Model order reduction is a modeling method that can facilitate the analysis and the control synthesis of distributed parameter systems, which are governed by partial differential equations. Many techniques have been proposed to further improve the property of the reduced order model based on full state information, which is usually not available in practical applications. In this paper, a reduced-order modeling method based on sparse point measurements is proposed for the benchmark system of flow past a cylinder. This method involves solving the dynamic optimization problems online, whose objective functions measure the differences between the predicted and observed variables on each time horizon. In this method, the sensor placement is also discussed, and we determine the sensor locations depending on a model-free optimization technique. Several numerical examples of different scenarios are simulated not only to illustrate the effectiveness of the proposed method but also to verify the discussion on the sensor placement strategy.

Anomalously high geothermal flux near the South Pole

Melting at the base of the Antarctic Ice Sheet influences ice dynamics and our ability to recover ancient climatic records from deep ice cores. Basal melt rates are affected by geothermal flux, one of the least constrained properties of the Antarctic continent. Estimates of Antarctic geothermal flux are typically regional in nature, derived from geological, magnetic or seismic data, or from sparse point measurements at ice core sites. We analyse ice-penetrating radar data upstream of South Pole revealing a ~100 km long and 50 km wide area where internal ice sheet layers converge with the bed. Ice sheet modelling shows that this englacial layer configuration requires basal melting of up to 6 ± 1 mm a−1 and a geothermal flux of 120 ± 20 mW m−2, more than double the values expected for this cratonic sector of East Antarctica. We suggest high heat producing Precambrian basement rocks and hydrothermal circulation along a major fault system cause this anomaly. We conclude that local geothermal flux anomalies could be more widespread in East Antarctica. Assessing their influence on subglacial hydrology and ice sheet dynamics requires new detailed geophysical observations, especially in candidate areas for deep ice core drilling and at the onset of major ice streams.

Hydraulic heterogeneity and its impact on kinematic porosity in Swedish coastal terrains

Hydrogeology in crystalline rock aquifers is often problematic due to the heterogeneity and anisotropy in the fracture network. Kinematic porosity of the host rock is exceedingly important for municipal decision makers in assessing sustainably extractable water supply volumes and assessing contaminant transport behavior within the matrix. This study explores heteroscedasticity in the hydrogeological characteristics of the fracture network and estimation of kinematic porosity from superficial fracture measurements. Estimates were based on the geometrical properties of the fractures including: fracture frequency, aperture and orientation. The estimates were adjusted for aperture changes with depth, connectivity of the fracture network, fracture continuity and measurement orientation bias. The results were compared with well archive data and correlations were found to be significant with more than 95% confidence. Erratic behaviour of well data relative to fracture measurements indicates that well orientation with respect to the fracture network gives incomplete hydrogeological data. Spatial heterogeneity of the bedrock was examined using spatial statistics and geographic information systems. The results from the spatial statistical analyses of well data showed that the heterogeneity within the bedrock is sufficiently high that spatial correlations cease to exist in nearly all investigated rock types at distances greater than 500 m, and in some rocks, particularly sedimentary gneisses, no spatial correlations were observed. Arbitrarily grouped samples with similar geology and topography showed evidence of non-stationary variance. Results indicate that regional generalizations based on sparse point measurements are highly error prone and potential exists in complementary field-based estimates.

The Global Aerosol Synthesis and Science Project (GASSP): Measurements and Modeling to Reduce Uncertainty

Abstract The largest uncertainty in the historical radiative forcing of climate is caused by changes in aerosol particles due to anthropogenic activity. Sophisticated aerosol microphysics processes have been included in many climate models in an effort to reduce the uncertainty. However, the models are very challenging to evaluate and constrain because they require extensive in situ measurements of the particle size distribution, number concentration, and chemical composition that are not available from global satellite observations. The Global Aerosol Synthesis and Science Project (GASSP) aims to improve the robustness of global aerosol models by combining new methodologies for quantifying model uncertainty, to create an extensive global dataset of aerosol in situ microphysical and chemical measurements, and to develop new ways to assess the uncertainty associated with comparing sparse point measurements with low-resolution models. GASSP has assembled over 45,000 hours of measurements from ships and aircraft as well as data from over 350 ground stations. The measurements have been harmonized into a standardized format that is easily used by modelers and nonspecialist users. Available measurements are extensive, but they are biased to polluted regions of the Northern Hemisphere, leaving large pristine regions and many continental areas poorly sampled. The aerosol radiative forcing uncertainty can be reduced using a rigorous model–data synthesis approach. Nevertheless, our research highlights significant remaining challenges because of the difficulty of constraining many interwoven model uncertainties simultaneously. Although the physical realism of global aerosol models still needs to be improved, the uncertainty in aerosol radiative forcing will be reduced most effectively by systematically and rigorously constraining the models using extensive syntheses of measurements.

Interpolation of GPS and Geological Data Using InSAR Deformation Maps: Method and Application to Land Subsidence in the Alto Guadalentín Aquifer (SE Spain)

Land subsidence resulting from groundwater extractions is a global phenomenon adversely affecting many regions worldwide. Understanding the governing processes and mitigating associated hazards require knowing the spatial distribution of the implicated factors (piezometric levels, lithology, ground deformation), usually only known at discrete locations. Here, we propose a methodology based on the Kriging with External Drift (KED) approach to interpolate sparse point measurements of variables influencing land subsidence using high density InSAR measurements. In our study, located in the Alto Guadalentín basin, SE Spain, these variables are GPS vertical velocities and the thickness of compressible soils. First, we estimate InSAR and GPS rates of subsidence covering the periods 2003–2010 and 2004–2013, respectively. Then, we apply the KED method to the discrete variables. The resulting continuous GPS velocity map shows maximum subsidence rates of 13 cm/year in the center of the basin, in agreement with previous studies. The compressible deposits thickness map is significantly improved. We also test the coherence of Sentinel-1 data in the study region and evaluate the applicability of this methodology with the new satellite, which will improve the monitoring of aquifer-related subsidence and the mapping of variables governing this phenomenon.

Influence of persistent wind scour on the surface mass balance of Antarctica

Accurate quantification of surface snow accumulation over Antarctica is a key constraint for estimates of the Antarctic mass balance, as well as climatic interpretations of ice-core records. Over Antarctica, near-surface winds accelerate down relatively steep surface slopes, eroding and sublimating the snow. This wind scour results in numerous localized regions (< or = 200 sq km) with reduced surface accumulation. Estimates of Antarctic surface mass balance rely on sparse point measurements or coarse atmospheric models that do not capture these local processes, and overestimate the net mass input in wind-scour zones. Here we combine airborne radar observations of unconformable stratigraphic layers with lidar-derived surface roughness measurements to identify extensive wind-scour zones over Dome A, in the interior of East Antarctica. The scour zones are persistent because they are controlled by bedrock topography. On the basis of our Dome A observations, we develop an empirical model to predict wind-scour zones across the Antarctic continent and find that these zones are predominantly located in East Antarctica. We estimate that approx. 2.7-6.6% of the surface area of Antarctica has persistent negative net accumulation due to wind scour, which suggests that, across the continent, the snow mass input is overestimated by 11-36.5 Gt /yr in present surface-mass-balance calculations.

Shallow Water Bathymetry from Multispectral Satellite Images: Extensions of Lyzenga's Method for Improving Accuracy

A high-resolution or complete bathymetric map of shallow water based on sparse point measurements (depth soundings) is often needed. One possible approach to such maps is passive remote sensing of water depth by using multispectral imagery in the popular method proposed by Lyzenga et al. [2006]; however, its application has been limited due to insufficient accuracy. To improve accuracy, we have developed 3 extensions of Lyzenga's method by addressing unrealistic optical and statistical assumptions in the method. The purpose of this paper is to compare the accuracy of Lyzenga's method, the 3 extensions, and the combination of the 3 extensions. The accuracy comparison test was performed for 2 coral reef sites by using cross validation.The results indicated that for both sites, the extended methods were more accurate than Lyzenga's method when sufficient training data were available. The most accurate extension was the one derived by modeling the spatial autocorrelation in the error term of the regression model used in Lyzenga's method. The combination of the 3 extensions was even more accurate than the extensions.The implementations of the extended methods are not difficult in terms of software availability and computational cost.

Statistical Combination of Spatial Interpolation and Multispectral Remote Sensing for Shallow Water Bathymetry

There is often a need for making a high-resolution or a complete bathymetric map based on sparse point measurements of water depth. Well-known feasible methods for this problem include spatial interpolation and passive remote sensing using readily available multispectral imagery, whose accuracies depend strongly on geometric and optical conditions, respectively. For a more accurate and robust water-depth mapping, in this letter, the two methods are combined into a new method in a statistically reasonable and beneficial manner. The new method is based on a semiparametric regression model that consists of a parametric imagery-based term and a nonparametric spatial interpolation term that complement one another. An accuracy comparison in a test site shows that the new method is more accurate than either of the existing methods when sufficient training data are available and far more accurate than the spatial interpolation method when the training data are scarce.

An Integrative Approach for Monitoring Water Movement in the Vadose Zone

Electrical resistivity tomography (ERT), during the past few years, has emerged as a potentially cost-effective, noninvasive tool for imaging changes of moisture content in the vadose zone. The accuracy of ERT surveys, however, has been the subject of debate because of its nonunique inverse solution and spatial variability in the constitutive relation between resistivity and moisture content. In this paper, an integrative inverse approach for ERT, based on a stochastic information fusion concept of Yeh and Simůnek, was developed to derive the best unbiased estimate of the moisture content distribution. Unlike classical ERT inversion approaches, this new approach assimilates prior information about the geological and moisture content structures in a given geological medium, as well as sparse point measurements of the moisture content, electrical resistivity, and electric potential. Using these types of data and considering the spatial variability of the resistivity–moisture content relation, the new approach directly estimates three-dimensional moisture content distributions instead of simply changes in moisture content in the vadose zone. Numerical experiments were conducted to investigate the effect of uncertainties in the prior information on the estimate. The effects of spatial variability in the constitutive relation were then examined on the interpretation of the change in moisture content, based on the change in electrical resistivity from the ERT survey. Finally, the ability of the integrative approach was tested by directly estimating moisture distributions in three-dimensional, heterogeneous vadose zones. Results show that the integrative approach can produce accurate estimates of the moisture content distributions and that incorporating some measurements of the moisture content is essential to improve the estimate.

An Integrative Approach for Monitoring Water Movement in the Vadose Zone

Electrical resistivity tomography (ERT), during the past few years, has emerged as a potentially cost‐effective, noninvasive tool for imaging changes of moisture content in the vadose zone. The accuracy of ERT surveys, however, has been the subject of debate because of its nonunique inverse solution and spatial variability in the constitutive relation between resistivity and moisture content. In this paper, an integrative inverse approach for ERT, based on a stochastic information fusion concept of Yeh and Šimůnek, was developed to derive the best unbiased estimate of the moisture content distribution. Unlike classical ERT inversion approaches, this new approach assimilates prior information about the geological and moisture content structures in a given geological medium, as well as sparse point measurements of the moisture content, electrical resistivity, and electric potential. Using these types of data and considering the spatial variability of the resistivity–moisture content relation, the new approach directly estimates three‐dimensional moisture content distributions instead of simply changes in moisture content in the vadose zone. Numerical experiments were conducted to investigate the effect of uncertainties in the prior information on the estimate. The effects of spatial variability in the constitutive relation were then examined on the interpretation of the change in moisture content, based on the change in electrical resistivity from the ERT survey. Finally, the ability of the integrative approach was tested by directly estimating moisture distributions in three‐dimensional, heterogeneous vadose zones. Results show that the integrative approach can produce accurate estimates of the moisture content distributions and that incorporating some measurements of the moisture content is essential to improve the estimate.