External Drift Research Articles

A Texas-specific VS30 map incorporating geology and VS30 observations

A Texas-specific [Formula: see text] map that uses geostatistical kriging integrated with a region-specific geologic proxy, field measurements of [Formula: see text], and P-wave seismogram estimates of [Formula: see text] is developed. The region-specific geologic proxy is used first to predict [Formula: see text] from the surface geologic conditions across the state, and then geostatistical kriging with an external drift is used to incorporate the local [Formula: see text] measurements/estimates into the map. Compared with the [Formula: see text] map of Texas developed from a topographic slope proxy, the Texas-specific [Formula: see text] map predicts larger [Formula: see text] values across much of Texas, except for the Gulf Coast region where the values are similar. The utilization of kriging brings the Texas-specific [Formula: see text] map into better agreement with the in situ measurements and estimates of [Formula: see text]. The sensitivity of predicted ground motions by ShakeMap to changes in [Formula: see text] values is evaluated with a scenario earthquake in the Dallas–Fort Worth area. The results suggest smaller predicted ground motions due to the generally larger values of [Formula: see text] in the Texas-specific [Formula: see text] map as compared to the [Formula: see text] from the topographic proxy.

Utilization of Weather Radar Data for the Flash Flood Indicator Application in the Czech Republic

In the past few years, demands on flash flood forecasting have grown. The Flash Flood Indicator (FFI) is a system used at the Czech Hydrometeorological Institute for the evaluation of the risk of possible occurrence of flash floods over the whole Czech Republic. The FFI calculation is based on the current soil saturation, the physical-geographical characteristics of every considered area, and radar-based quantitative precipitation estimates (QPEs) and forecasts (QPFs). For higher reliability of the flash flood risk assessment, calculations of QPEs and QPFs are crucial, particularly when very high intensities of rainfall are reached or expected. QPEs and QPFs entering the FFI computations are the products of the Czech Weather Radar Network. The QPF is based on the COTREC extrapolation method. The radar-rain gauge-combining method MERGE2 is used to improve radar-only QPEs and QPFs. It generates a combined radar-rain gauge QPE based on the kriging with an external drift algorithm, and, also, an adjustment coefficient applicable to radar-only QPEs and QPFs. The adjustment coefficient is applied in situations when corresponding rain gauge measurements are not yet available. A new adjustment coefficient scheme was developed and tested to improve the performance of adjusted radar QPEs and QPFs in the FFI.

Identifying meaningful covariates that can improve the interpolation of monsoon rainfall in a low‐lying tropical region

AbstractThe assessment of spatio‐temporal distribution of rainfall over the entire monsoon season is critical for the water resources management in a tropical low‐lying region like Bangladesh. The primary objective is to find suitable interpolation methods for each monsoon month as well as the accumulated rainfall for the entire season in Bangladesh. As the unique position of Bangladesh and monsoon system both contribute the variation in rainfall, the identification of associated suitable covariates can offer reliable estimates when applied with the appropriate interpolation model. Several potential covariates are identified diligently including the remotely sensed annul average monsoon rainfall (RAAMR), distance to Bay‐of‐Bengal and distance to Hindu‐Kush Himalayan Region, among others. This study mainly considers the multivariate approach: kriging with external drift (KED) which is able to take external information to positive impact. The method is then compared with the more traditional univariate, ordinary kriging (OK) and the inverse distance weighting (IDW) method using the cross‐validation technique. Daily rainfall data from 1970 to 2016 at 34 stations were used for the assessment. Result shows that the KED model is identified suitable for the considered variants of June, August, September and annual average monsoon rainfall whereas the OK is appropriate for July. Overall, the KED is found superior model with the incorporation of RAAMR data. The successful inclusion of remotely sensed data in the kriging system paves a new dimension in the climatological research for countries where climate‐measuring resources are limited.

Mapping Urban Air Quality from Mobile Sensors Using Spatio-Temporal Geostatistics.

With the advancement of technology and the arrival of miniaturized environmental sensors that offer greater performance, the idea of building mobile network sensing for air quality has quickly emerged to increase our knowledge of air pollution in urban environments. However, with these new techniques, the difficulty of building mathematical models capable of aggregating all these data sources in order to provide precise mapping of air quality arises. In this context, we explore the spatio-temporal geostatistics methods as a solution for such a problem and evaluate three different methods: Simple Kriging (SK) in residuals, Ordinary Kriging (OK), and Kriging with External Drift (KED). On average, geostatistical models showed 26.57% improvement in the Root Mean Squared Error (RMSE) compared to the standard Inverse Distance Weighting (IDW) technique in interpolating scenarios (27.94% for KED, 26.05% for OK, and 25.71% for SK). The results showed less significant scores in extrapolating scenarios (a 12.22% decrease in the RMSE for geostatisical models compared to IDW). We conclude that univariable geostatistics is suitable for interpolating this type of data but is less appropriate for an extrapolation of non-sampled places since it does not create any information.

Conditional simulation of spatial rainfall fields using random mixing: a study that implements full control over the stochastic process

Abstract. The accuracy of spatial precipitation estimates with relatively high spatiotemporal resolution is of vital importance in various fields of research and practice. Yet the intricate variability and intermittent nature of precipitation make it very difficult to obtain accurate spatial precipitation estimates. Radars and rain gauges are two complementary sources of precipitation information: the former are inaccurate in general but are valid indicators of the spatial pattern of the rainfall field; the latter are relatively accurate but lack spatial coverage. Several radar–gauge merging techniques that can provide spatial precipitation estimates have been proposed in the scientific literature. Conditional simulation has great potential to be used in spatial precipitation estimation. Unlike commonly used interpolation methods, conditional simulation yields a range of possible estimates due to its Monte Carlo framework. However, one obstacle that hampers the application of conditional simulation in spatial precipitation estimation is the need to obtain the marginal distribution function of the rainfall field with sufficient accuracy. In this work, we propose a method to obtain the marginal distribution function from radar and rain gauge data. A conditional simulation method, random mixing (RM), is used to simulate rainfall fields. The radar and rain gauge data used in the application of the proposed method are derived from a stack of synthetic rainfall fields. Due to the full control over the stochastic process, the accuracy of the estimates is verified comprehensively. The results from the proposed approach are compared with those from three well-known radar–gauge merging techniques: ordinary Kriging, Kriging with external drift, and conditional merging, and the sensitivity of the approach to two factors – the number of rain gauges and the random error in the radar estimates – is analysed in the same experimental context.

Extreme rainfall estimation at ungauged locations: Information that needs to be included in low-lying monsoon climate regions like Bangladesh

Bangladesh, a tropical low-lying region, is stranded between the Bay of Bengal in the south and the Himalayas in the north. The unique characteristics allow receiving huge rainfall, in particular, in the monsoon season. The physical phenomena such as the Bay of Bengal, the Himalayas and the monsoon season dominate the extreme rainfall pattern in Bangladesh. However, how to include that information to good effect in the estimation of extreme rainfall at ungauged locations is yet to be investigated. The objective of this work is to examine the information that needs to be included in the estimation of extreme rainfall in such regions. The approach that permits parameters of an extreme value distribution to vary spatially is used to determine the probability model. The methodology, subsequently, authorizes the frequency analysis to be performed at ungauged conditions. The geostatistical technique in the form of kriging with external drift (KED) which has the ability to take secondary information is used to produce spatial maps of the parameters. This study primarily assessed KED interpolation scheme and its ability to accurately predict the model parameters. The scheme was compared against the more widely used ordinary kriging (OK) model. The cross- validation was used to find the robust scheme for each parameter. Annual maximum daily rainfall data from 34 measuring stations were used for the assessment. The KED with the covariate annual mean monsoon rainfall (AMMR) appears to be the best model for location parameter. However, for the scale and shape parameter the KED models were unable to score past the OK model. The availability of parameter maps allows the estimation of extreme rainfall at locations where rainfall records were absent and offers a much better elucidation than the traditional at-site quantile based interpolation. Overall, the inclusion of monsoon rainfall and spatial information are deemed necessary for the estimation of extreme rainfall at ungauged locations in a low-lying monsoon region.

Groundwater level assessment and prediction in the Nebraska Sand Hills using LIDAR-derived lake water level

The spatial variability of groundwater levels is often inferred from sparsely located hydraulic head observations in wells. The spatial correlation structure derived from sparse observations is associated with uncertainties that spread to estimates at unsampled locations. In areas where surface water represents the nearby groundwater level, remote sensing techniques can estimate and increase the number of hydraulic head measurements. This research uses light detection and ranging (LIDAR) to estimate lake surface water level to characterize the groundwater level in the Nebraska Sand Hills (NSH), an area with few observation wells. The LIDAR derived lake groundwater level accuracy was within 40 cm mean square error (MSE) of the nearest observation wells. The lake groundwater level estimates were used to predict the groundwater level at unsampled locations using universal kriging (UK) and kriging with an external drift (KED). The results indicate unbiased estimates of groundwater level in the NSH. UK showed the influence of regional trends in groundwater level while KED revealed the local variation present in the groundwater level. A 10-fold cross-validation demonstrated KED with better mean squared error (ME) [−0.003, 0.007], root mean square error (RMSE) [2.39, 4.46], residual prediction deviation (RPD) [1.32, 0.71] and mean squared deviation ratio (MSDR) [1.01, 1.49] than UK. The research highlights that the lake groundwater level provides an accurate and cost-effective approach to measure and monitor the subtle changes in groundwater level in the NSH. This methodology can be applied to other locations where surface water bodies represent the water level of the unconfined aquifer and the results can aid in groundwater management and modeling.

GPM Annual and Daily Precipitation Data for Real-Time Short-Term Nowcasting: A Pilot Study for a Way Forward in Data Assimilation

This study explores the quality of data produced by Global Precipitation Measurement (GPM) and the potential of GPM for real-time short-term nowcasting using MATLAB and the Short-Term Ensemble Prediction System (STEPS). Precipitation data obtained by rain gauges during the period 2015 to 2017 were used in this comparative analysis. The results show that the quality of GPM precipitation has different degrees efficacies at the national scale, which were revealed at the performance analysis stage of the study. After data quality checking, five representative precipitation events were selected for nowcasting evaluation. The GPM estimated precipitation compared to a 30 min forecast using STEPS precipitation nowcast results, showing that the GPM precipitation data performed well in nowcasting between 0 to 120 min. However, the accuracy and quality of nowcasting precipitation significantly reduced with increased lead time. A major finding from the study is that the quality of precipitation data can be improved through blending processes such as kriging with external drift and the double-kernel smoothing method, which enhances the quality of nowcast over longer lead times.

Toward geostatistical unbiased predictions of flow duration curves at ungauged basins

Flow duration curves (FDCs) represent the percentage of time (or duration) during which a given streamflow is equaled or exceeded. Flow duration curves provide a rapid and direct response to the behavior of water resources in a basin. Thus, predicting FDCs is important in basins with little or no monitoring for both all-time and seasonal periods. The geostatistical approach for predicting FDCs at ungauged sites represents an advancement in this research topic. However, poor results have been observed, particularly overestimates (positive bias) for high durations, i.e., low flows. This study aims to predict FDCs in all-time and seasonal periods by using a geostatistical approach based on models, toward unbiased prediction. Streamflow data from 81 stream gauges made available by the Brazilian National Water Agency (ANA) have been used. These stations have a high spatial density and are well spread across the study area. To map the FDCs, and consequently, all their quantiles, the scale and shape parameters of the FDCs were modeled geostatistically. First, some basic assumptions for the FDC parameters such as data normality and spatial stationarity were verified. After an inference by the maximum likelihood method was performed to fit the geostatistical models and estimate the best model forms, we compared them with the benchmark models (i.e. regression models). Finally, the spatial interpolation was performed and the performance was assessed by a leave-one-out cross-validation. The geostatistical models yielded better fits and performance for mapping the FDCs than the regression models. Both the median of relative residuals for all-time and seasonal periods were unbiased for the entire duration. We suggest that the fixed effect modeling of the geostatistical models, associated with external drifts, led to this better and unbiased performance.

Spatial interpolation of the extreme hourly precipitation at different return levels in the Haihe River basin

The return level is an important measure for the extreme precipitation, and maps of the return level are used to derive information for the design of hydrological and hydraulic engineering projects. The interpolation of hourly extreme precipitation is challenging due to low station density and high inhomogeneity. Hourly precipitation observations at 232 weather stations in the Haihe River basin from 1961 to 2012 were used to evaluate six interpolation methods including Inverse Distance Weighted (IDW), Ordinary Kriging (OK), Kriging with External Drift (KED) assisted by different covariables and Empirical Bayesian Kriging (EBK) for generating 2-, 5-, 10-, 20-, 50-, and 100-year return level maps for the basin. Leave-one-out cross-validation showed that although there was a high correlation coefficient between hourly extreme precipitation and the elevation (DEM), KED incorporating DEM as the covariable (KED_DEM) did not improve the interpolation efficiency compared with OK. KED with the annual average precipitation as the covariable (KED_AP), which had the largest Nash-Sutcliffe efficiency coefficient (NSE, 0.89–0.45) and the smallest root mean square error (RMSE, 2.23–15.05 mm) for the six return levels, outperformed the other five methods compared. The return levels varied from 13 to 46, 20–66, 24–78, 26–89, 29–110 and 30–134 mm, with mean values of 30, 40, 48, 57, 67 and 75 mm for the 2-, 5-, 10-, 20-, 50- and 100-year return levels, respectively, in the Haihe River basin. The return level maps of extreme hourly precipitation in the Haihe River basin were generated based on the KED_AP method and showed a spatial distribution of decreasing trend from the southeastern part to the northwestern part of the basin. The high-value centre moved from the eastern coastal area for smaller return level maps to the southern area for the 50- and 100-year return level maps. This study may provide some insights into the spatial interpolation of extreme precipitation on an hourly scale.

Mapping long-period soil resonances in the Kathmandu basin using microtremors

This study reports the geostatistical analysis of a set of 40 single-station horizontal-to-vertical spectral ratio (HVSR) passive seismic survey data collected in the Kathmandu basin (Nepal). The Kathmandu basin is characterized by a heterogeneous sedimentary cover and by a complex geo-structural setting, inducing a high spatial variability of the bedrock depth. Due to the complex geological setting, the interpretation and analysis of soil resonance periods derived from the HVSR surveys is challenging, both from the perspective of bedrock depth estimation as well as of seismic-site effects characterization. To exploit the available information, the HVSR data are analyzed by means of a geostatistical approach. First, the spatial continuity structure of HVSR data is investigated and interpreted taking into consideration the geological setting and available stratigraphic and seismic information. Then, the exploitation of potential auxiliary variables, based on surface morphology and distance from outcropping bedrock, is evaluated. Finally, the mapping of HVSR resonance periods, together with the evaluation of interpolation uncertainty, is obtained by means of kriging with external drift interpolation. This work contributes to the characterization of local seismic response of the Kathmandu basin. The resulting map of soil resonance periods is compatible with the results of preceding studies and it is characterized by a high spatial variability, even in areas with a deep bedrock and long resonance periods.

Improving Mean Annual Precipitation Prediction Incorporating Elevation and Taking into Account Support Size

Accounting for secondary exhaustive variables (such as elevation) in modelling the spatial distribution of precipitation can improve their estimate accuracy. However, elevation and precipitation data are associated with different support sizes and it is necessary to define methods to combine such different spatial data. The paper was aimed to compare block ordinary cokriging and block kriging with an external drift in estimating the annual precipitation using elevation as covariate. Block ordinary kriging was used as reference of a univariate geostatistical approach. In addition, the different support sizes associated with precipitation and elevation data were also taken into account. The study area was the Calabria region (southern Italy), which has a spatially variable Mediterranean climate because of its high orographic variability. Block kriging with elevation as external drift, compared to block ordinary kriging and block ordinary cokriging, was the most accurate approach for modelling the spatial distribution of annual mean precipitation. The three measures of accuracy (MAE, mean absolute error; RMSEP, root-mean-squared error of prediction; MRE, mean relative error) have the lowest values (MAE = 112.80 mm; RMSEP = 144.89 mm, and MRE = 0.11), whereas the goodness of prediction (G) has the highest value (75.67). The results clearly indicated that the use of an exhaustive secondary variable always improves the precipitation estimate, but in the case of areas with elevations below 120 m, block cokriging makes better use of secondary information in precipitation estimation than block kriging with external drift. At higher elevations, the opposite is always true: block kriging with external drift performs better than block cokriging. This approach takes into account the support size associated with precipitation and elevation data. Accounting for elevation allowed to obtain more detailed maps than using block ordinary kriging. However, block kriging with external drift produced a map with more local details than that of block ordinary cokriging because of the local re-evaluation of the linear regression of precipitation on block estimates.

Assessment of High Resolution Air Temperature Fields at Rocky Mountain National Park by Combining Scarce Point Measurements with Elevation and Remote Sensing Data

There is necessity of considering air temperature to simulate the hydrology and management within water resources systems. In many cases, a big issue is considering the scarcity of data due to poor accessibility and limited funds. This paper proposes a methodology to obtain high resolution air temperature fields by combining scarce point measurements with elevation data and land surface temperature (LST) data from remote sensing. The available station data (SNOTEL stations) are sparse at Rocky Mountain National Park, necessitating the inclusion of correlated and well-sampled variables to assess the spatial variability of air temperature. Different geostatistical approaches and weighted solutions thereof were employed to obtain air temperature fields. These estimates were compared with two relatively direct solutions, the LST (MODIS) and a lapse rate-based interpolation technique. The methodology was evaluated using data from different seasons. The performance of the techniques was assessed through a cross validation experiment. In both cases, the weighted kriging with external drift solution (considering LST and elevation) showed the best results, with a mean squared error of 3.7 and 3.6 °C2 for the application and validation, respectively.

Relevance of merging radar and rainfall gauge data for rainfall nowcasting in urban hydrology

Accurate Quantitative Precipitation Forecasts (QPF) at high spatial and temporal resolution are a perquisite for urban flood prediction. Commonly Lagrangian extrapolation of the rainfall patterns recognized by radar data, forms the basis of such forecasts for the near future (up to 2 h lead time) – referred here as nowcasting. Nevertheless, due to the intermittent nature of the rainfall at such fine scales, the predictability of storms is limited to about 20 min. The predictability loss is caused mainly by the inability of the radar to capture the true rainfall field and because the Lagrangian Persistence is unable to model the temporal evolution of the rainfall field. In this study we focus on the first problem, on how to extend the predictability limit of rainfall at such scales by improving the rainfall field fed into the nowcast model. To overcome the errors associated with the radar intensities, merging techniques between radar and gauge measurements are advised. Among different employed techniques (mean field bias, kriging with external drift and quantile mapping based correction) the conditional merging between the radar and rainfall-gauge measurements seems to capture at best the spatial and temporal patterns of the rainfall at the desired fine scales (1 km2 and 5 min). Moreover, when fed to two nowcast models, the conditional merging doesn’t only increase the predictability of storms from 20 min to longer than 1 h, but as well it improves the agreement of radar based QPF with the gauge measurements. The results are drawn from 110 events observed in the period 2000–2018 by the Hannover Radar (Germany) in an area with a radius of 115 km, where 100 recording gauges were available. As the urban hydrological models are commonly validated on gauge measurements, nowcasting with conditionally merged data, provides a useful tool for urban flood prediction for lead times up to 1 h.

Optimization of proton imaging system including fringe field of magnetic lens

The proton imaging system is composed of four quadrupole magnetic lenses and a collimator. The quadrupole magnetic lenses can realize point-to-point imaging, and the collimator can improve image quality by controlling proton flux and realize material diagnosis. The magnetic field gradient of an ideal quadrupole lens becomes zero at the edge. Inside the lens, the magnetic field gradient is constant along the axis, while the magnetic field boundary of the actual lens extends outward. In the proton imaging system, the fringing field will affect the proton transport state and the performance of the imaging system as well. In this paper, a method to optimize the system is presented when the fringe field is considered. A proton imaging system of 1.6 GeV is established with the Geant 4 program, in which the magnetic field gradient distribution of the actual lens is approximated by the Bell function. In an ideal imaging system, the external drift length is 1.2 m, the internal drift length is 0.5 m, the length of the magnet is 0.8 m, and the magnetic field gradient is 8.09 T/m. The parameters of the practical imaging system can be obtained by using the optimization method: when the integral difference in magnetic field gradient distribution between the actual lens and the ideal lens is equal to zero, the outer drift length of the imaging system is 1.203 m and the inner drift length is 0.506 m; when the integral difference in the magnetic field gradient distribution between the actual lens and the ideal lens is equal to 1%, the outer drift length is 1.208 m and the inner drift length is 0.516 m. In the numerical simulation, a 1mm-thick copper plate and a concentric ball are chosen as the objects, and the influence of the fringing field on the collimator aperture and that on the proton flux error are studied. The results show that the optimized imaging system can reduce the flux error of protons passing through the object, and the difference in the aperture of collimator is on the order of 10<sup>–2</sup> when the integral difference is on the order of 10<sup>–2</sup> in magnitude.

A Machine Learning Approach for Rainfall Estimation Integrating Heterogeneous Data Sources

Providing an accurate rainfall estimate at individual points is a challenging problem in order to mitigate risks derived from severe rainfall events, such as floods and landslides. Dense networks of sensors, named rain gauges (RGs), are typically used to obtain direct measurements of precipitation intensity in these points. These measurements are usually interpolated by using spatial interpolation methods for estimating the precipitation field over the entire area of interest. However, these methods are computationally expensive, and to improve the estimation of the variable of interest in unknown points, it is necessary to integrate further information. To overcome these issues, this work proposes a machine learning-based methodology that exploits a classifier based on ensemble methods for rainfall estimation and is able to integrate information from different remote sensing measurements. The proposed approach supplies an accurate estimate of the rainfall where RGs are not available, permits the integration of heterogeneous data sources exploiting both the high quantitative precision of RGs and the spatial pattern recognition ensured by radars and satellites, and is computationally less expensive than the interpolation methods. Experimental results, conducted on real data concerning an Italian region, Calabria, show a significant improvement in comparison with Kriging with external drift (KED), a well-recognized method in the field of rainfall estimation, both in terms of the probability of detection (0.58 versus 0.48) and mean-square error (0.11 versus 0.15).

Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. In this work, the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles, free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis. The momentum space distribution is determined by a random walk argument, and the position space distribution is determined by employing the equiprobability and ergodicity principles. The expressions for energy, entropy, free energy, and pressures are then deduced, and the relation among external force, drift velocity, and temperature is also established. Moreover, the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.

Data fusion for air quality mapping using low-cost sensor observations: Feasibility and added-value

In Nantes, low-cost sensors were installed in the city center and deployed on driving school cars, ambulances and service vehicles to measure PM10 concentrations. This work aims to use the large amount of observations provided by the sensors for air quality mapping at the urban scale in order to show the potential added-value with respect to the dispersion model (ADMS-Urban) calculations. A preprocessing is applied to the raw sensor dataset to remove the unreliable observations based on an outlier detection technique and to compensate for the measurement drift by adjusting the estimated daily variation of the underlying background PM10 concentrations with the reference stations. Then, data fusion is performed by combining the preprocessed fixed and mobile low-cost sensor observations and the 2016 annual average of the ADMS-Urban outputs. The measurement uncertainty related to the low-cost sensors and the dispersion of the data are considered in data fusion as the Variance of Measurement Error (VME). The spatial interpolation is achieved at hourly resolution and results are presented for November 29th, 2018 from 7 am to 7 pm. Hourly fused maps show disparate responses to data fusion mainly depending on the variability of the sensor data and the correlation between the sensor observations and the drift. The data fusion performance has been investigated by comparing the daily average of the estimated concentrations, the reference observations and the hourly model outputs at each station of the Air Pays de la Loire network. Results show that considering the model alone implies 8% bias whereas including the LCS observations reduces the bias to 2.5%. However, the concentration distributions related to the data fusion are characterized by a lower dispersion than the reference observations and the model estimation. Thus, the fusion smooths the PM10 peaks. In addition, the effect of the measurement uncertainty has been investigated by doubling it or reducing it to the reference station measurement uncertainty. The sensitivity study demonstrates that the performance is increasing by reducing the uncertainty. This highlights the importance to estimate accurately the measurement uncertainty of the devices to ensure relevant air quality mapping. The method efficiency is also quite limited by the low correlation between the sensor observations and the model used as external drift in the kriging that may be explained by the remaining bias on LCS data. Efforts on this issue might increase the performance of the spatial interpolation.

Rotator drift: A sign of upper motor neuron leg weakness

ObjectiveThere are techniques for eliciting subtle arm weakness (pronator drift), but the accompanying abnormal reflex response (Hoffmann’s sign) is of limited value; conversely, in the leg there are no techniques for eliciting subtle weakness equivalent to pronator drift, but there is a robust abnormal reflex response (Babinski’s sign). Thus, there is a need to devise a simple and rapid technique for detecting leg weakness capable of being used in either cooperative or comatose patients. Patients and methodsUsing three patient groups (discovery set, training set, test set) a technique for detecting upper motor neuron (UMN) lesion leg weakness was devised. ResultsWith the patient supine, the examiner grasps both big toes, pointing them towards the ceiling with the long axis of the foot perpendicular to the bed; the patient is asked to maintain this position for 30 s. People with pyramidal tract weakness show external rotator drift on their weak side: on the normal side the foot is deviated 20−25⁰ from the perpendicular, on the paretic side the foot is deviated more than 30°. ConclusionThis rotator drift sign is a simple method for detecting subtle UMN leg weakness. When combined with the pronator drift sign, these two signs constitute “pyramidal drift” signs for the bedside detection of UMN hemiparetic weakness.

Spatiotemporal Precipitation Estimation from Rain Gauges and Meteorological Radar Using Geostatistics

Automatic interpolation of precipitation maps combining rain gauge and radar data has been done in the past but considering only the data collected at a given time interval. Since radar and rain gauge data are collected at short intervals, a natural extension of previous works is to account for temporal correlations and to include time into the interpolation process. In this work, rainfall is interpolated using data from the current time interval and the previous one. Interpolation is carried out using kriging with external drift, in which the radar rainfall estimate is the drift, and the mean precipitation is set to zero at the locations where the radar estimate is zero. The rainfall covariance is modeled as non-stationary in time, and the space system of reference moves with the storm. This movement serves to maximize the collocated correlation between consecutive time intervals. The proposed approach is analyzed for four episodes that took place in Catalonia (Spain). It is compared with three other approaches: (i) radar estimation, (ii) kriging with external drift using only the data from the same time interval, and (iii) kriging with external drift using data from two consecutive time intervals but not accounting for the displacement of the storm. The comparisons are performed using cross-validation. In all four episodes, the proposed approach outperforms the other three approaches. It is important to account for temporal correlation and use a Lagrangian system of coordinates that tracks the rainfall movement.