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Water losses from water distribution means have a high environmental impact in terms of natural resource depletion (water, energy, ecosystems). This work aims to develop an optical airborne surveillance service for the detection of water leaks (WADI—Water-tightness Airborne Detection Implementation) to provide water utilities with adequate and timely information on leaks in water transportation mains outside urban areas. Firstly, a series of measurement campaigns were performed with two hyperspectral cameras and a thermal infrared camera in order to select the most appropriate wavelengths and combinations thereof for best revealing high moisture areas, which are taken as a proxy for water leakage. The Temperature-Vegetation-Index method (T-VI, also known as Triangle/Trapezoid method) was found to provide the highest contrast-to-noise ratio. This preliminary work helped select the most appropriate onboard instrumentation for two types of aerial platforms, manned (MAV) and unmanned (UAV). Afterwards, a series of measurement campaigns were performed from 2017 to 2019 in an operational environment over two water distribution networks in France and Portugal. Artificial leaks were introduced and both remote sensing platforms successfully detected them when excluding the unfavorable situations of a recent rain event or high vegetation presence. With the most recent equipment configuration, known and unknown real leaks in the overflown part of a water transportation network in Portugal have been detected. A significant number of false alarms were also observed which were due either to natural water flows (groundwater exfiltration, irrigation runoff and ponds) or to vegetation-cover variability nearby water-distribution nodes. Close interaction with the water utilities, and ancillary information like topographic factors (e.g., slope orientation), are expected to reduce the false alarm rates and improve WADI’s methodology performance.

Surface soil moisture (SM) plays a fundamental role in energy and water partitioning in the soil–plant–atmosphere continuum. A reliable and operational algorithm is much needed to retrieve regional surface SM at high spatial and temporal resolutions. Here, we provide an operational framework of estimating surface SM at fine spatial resolutions (using visible/thermal infrared images and concurrent meteorological data) based on a trapezoidal space defined by remotely sensed vegetation cover (Fc) and land surface temperature (LST). Theoretical solutions of the wet and dry edges were derived to achieve a more accurate and effective determination of the Fc/LST space. Subjectivity and uncertainty arising from visual examination of extreme boundaries can consequently be largely reduced. In addition, theoretical derivation of the extreme boundaries allows a per-pixel determination of the VI/LST space such that the assumption of uniform atmospheric forcing over the entire domain is no longer required. The developed approach was tested at the Tibetan Plateau Soil Moisture/Temperature Monitoring Network (SMTMN) site in central Tibet, China, from August 2010 to August 2011 using Moderate Resolution Imaging Spectroradiometer (MODIS) Terra images. Results indicate that the developed trapezoid model reproduced the spatial and temporal patterns of observed surface SM reasonably well, with showing a root-mean-square error of 0.06 m3·m−3 at the site level and 0.03 m3·m−3 at the regional scale. In addition, a case study on 2 September 2010 highlighted the importance of the theoretically calculated wet and dry edges, as they can effectively obviate subjectivity and uncertainties in determining the Fc/LST space arising from visual interpretation of satellite images. Compared with Land Surface Models (LSMs) in Global Land Data Assimilation System-1, the remote sensing-based trapezoid approach gave generally better surface SM estimates, whereas the LSMs showed systematic underestimation. Sensitivity analyses suggested that the trapezoid method is most sensitive to field capacity and temperature but less sensitive to other meteorological observations and parameters.

Evapotranspiration (ET) is a critical component of the earth's water budget, a critical modulator of land–atmosphere interactions, and also plays a crucial role in managing the earth's energy balance. In this study, the feasibility of generating spatially continuous daily evaporative fraction (EF) and ET from minimal remotely sensed and meteorological inputs in a trapezoidal framework is demonstrated. A total of four variables, normalized difference vegetation index, land surface temperature (T_s ), gridded daily average temperature (T_a ), and elevation (z) are required to estimate EF. Then, ET can be estimated with the available soil heat flux (G) and net radiation (Rn) data. First, the crucial model variable T_s - T_a is examined how well it characterizes the variation in EF using in-situ data recorded at two eddy correlation flux towers in Southern Great Plains, USA in 2011. Next, the accuracy of satellite-based T_s\ is compared to ground-based T_s. Finally, EF and ET estimates are validated. The results reveal that the model performed satisfactorily in modeling EF and ET variation at winter wheat and deciduous forest during the high evaporative months. Even though the model works best with the observed Moderate Resolution Imaging Spectroradiometer-T_s as opposed to temporally interpolated T_s, results obtained from interpolated T_s are able to close the gaps with reasonable accuracy. Due to the fact that T_s - T_a is not a good indicator of EF outside the growing season when deciduous forest is dormant, potential improvements to the model are proposed to improve accuracy in EF and ET estimates at the expense of adding more variables. [ABSTRACT FROM PUBLISHER]

Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one-dimensional implicitly defined discrete dynamical systems. The backward Euler method and the trapezoid method for numeric solutions of ordinary differential equations fall in the category of implicit dynamical systems. Examples of bifurcations are given for some implicit dynamical systems including bifurcations for the backward Euler method when the step size is changed. [ABSTRACT FROM AUTHOR]

In order to make the prediction of land surface heat fluxes more robust, two improvements were made to an operational two-layer model proposed previously by Zhang. These improvements are: 1) a surface energy balance method is used to determine the theoretical boundary lines (namely ‘true wet/cool edge’ and ‘true dry/warm edge’ in the trapezoid) in the scatter plot for the surface temperature versus the fractional vegetation cover in mixed pixels; 2) a new assumption that the slope of the Tm – f curves is mainly controlled by soil water content is introduced. The variables required by the improved method include near surface vapor pressure, air temperature, surface resistance, aerodynamic resistance, fractional vegetation cover, surface temperature and net radiation. The model predictions from the improved model were assessed in this study by in situ measurements, which show that the total latent heat flux from the soil and vegetation are in close agreement with the in situ measurement with an RMSE (Root Mean Square Error) ranging from 30 w/m2~50 w/m2,which is consistent with the site scale measurement of latent heat flux. Because soil evaporation and vegetation transpiration are not measured separately from the field site, in situ measured CO2 flux is used to examine the modeled λEveg. Similar trends of seasonal variations of vegetation were found for the canopy transpiration retrievals and in situ CO2 flux measurements. The above differences are mainly caused by 1) the scale disparity between the field measurement and the MODIS observation; 2) the non-closure problem of the surface energy balance from the surface fluxes observations themselves. The improved method was successfully used to predict the component surface heat fluxes from the soil and vegetation and it provides a promising approach to study the canopy transpiration and the soil evaporation quantitatively during the rapid growing season of winter wheat in northern China.

A simple technique for calculation of numerical integration errors for physically meaningful functions is presented. In this paper, first the function classes are introduced that relate a function studied directly to a particular physical problem. The matrix elements defining a particular class of functions are then directly incorporated into the error formula. The proposed technique relies on the extension of the concept of the Taylor series. Since the standard Taylor series can be used for calculating the errors for smooth functions, in this paper the behaviour of the error in the immediate vicinity of discontinuity is considered only. The extended Taylor series is obtained by performing the Taylor series expansion on both sides of the discontinuity, using a matrix to describe the behaviour of the function at the discontinuity position and finally summing up all terms proportional to the function value and of all its derivatives. For illustration, several basic classes of physically meaningful functions are introduced and the extended Taylor series is derived. The series is then used to calculate the local error of the numerical integration. The numerical results obtained confirm the accuracy of the derived formulae. [ABSTRACT FROM AUTHOR]

Water losses from water distribution means have a high environmental impact in terms of natural resource depletion (water, energy, ecosystems). This work aims to develop an optical airborne surveillance service for the detection of water leaks (WADI—Water-tightness Airborne Detection Implementation) to provide water utilities with adequate and timely information on leaks in water transportation mains outside urban areas. Firstly, a series of measurement campaigns were performed with two hyperspectral cameras and a thermal infrared camera in order to select the most appropriate wavelengths and combinations thereof for best revealing high moisture areas, which are taken as a proxy for water leakage. The Temperature-Vegetation-Index method (T-VI, also known as Triangle/Trapezoid method) was found to provide the highest contrast-to-noise ratio. This preliminary work helped select the most appropriate onboard instrumentation for two types of aerial platforms, manned (MAV) and unmanned (UAV). Afterwards, a series of measurement campaigns were performed from 2017 to 2019 in an operational environment over two water distribution networks in France and Portugal. Artificial leaks were introduced and both remote sensing platforms successfully detected them when excluding the unfavorable situations of a recent rain event or high vegetation presence. With the most recent equipment configuration, known and unknown real leaks in the overflown part of a water transportation network in Portugal have been detected. A significant number of false alarms were also observed which were due either to natural water flows (groundwater exfiltration, irrigation runoff and ponds) or to vegetation-cover variability nearby water-distribution nodes. Close interaction with the water utilities, and ancillary information like topographic factors (e.g., slope orientation), are expected to reduce the false alarm rates and improve WADI's methodology performance. [ABSTRACT FROM AUTHOR]

Power system analysis is the basis of operation and planning. Since power systems are very large and complex, however, long computation time is required for the analysis. Development of a fast calculation method for stability analysis is desirable. Recently, the method using multiple time-scale numerical integration algorithm was developed for analyzing long-term dynamics. This method has the problem of calculation time since the coefficient matrix is very large. It is expected that calculation time can be shortened using parallel processing. In order to increase the efficiency of parallel processing, the coefficient matrix must be divided since solution of a set of linear equations is the main part of stability analysis. In this paper, coefficient matrix is converted into BBDF matrix for effective calculation of parallel processing. Each subnetwork block can be divided again since it is sparse. The algorithm discussed in this paper was implemented on the nCUBE2S parallel processing computer system. The computing time is measured so that it can be compared to the computer time of a single-processor system. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 120(4): 14–22, 1997 [ABSTRACT FROM AUTHOR]