SIMULATION OF THE HEAT TRANSPORT PROBLEMS WITH RADIATION IN PLATE

In the literature [1 -5 ] simple and effective algorithms for mathematical modelling processes of distribution of heat in multilayered spaces are created. In the given work the way of improvement o f accuracy of algorithms is considered at approximation of integrals derivatives more the supreme orders are used

SIMPLE METHODS OF ENGINEERING CALCULATION FOR SOLVING STATIONARY 2 –D HEAT TRANSFER PROBLEMS IN MULTILAYER MEDIA

There are well-known different numerical methods for solving the boundary value problems for partial differential equations. Some of them are: finite difference method (FDM), finite element method (FEM), boundary element methods (BEM), and others. In the given work two methods FDM and BEM for the mathematical model of stationary distribution of heat in the multilayer media are considered. These methods were used for the reduction of the two-dimensional heat transfer problem described by a partial differential equation to a boundary – value problem for a system of ordinary differential equations. (ODEs). Such a procedure allows obtaining simple engineering algorithms for solving heat transfer equation in mulyilayer domain. In the case of three layers the system of ODEs is possible for solving analytically

FIZIKĀLU PROCESU SKAITLISKĀ MODELĒŠANA PLĀNOS SLĀŅOS

Apakšzemes slāņainās sistēmās fizikālie parametri vertikālā virzienā ir konstanti lielumi, kuru vērtības mainās plānos slāņos ar lēcieniem. Ņemot vērā sistēmas kārtaino struktūru, aprēķinot fizikālos lielumus (temperatūru, koncentrāciju slāņos), lieto dažāda tipa viduvēšanas [3] vai režģa metodes, izvēloties katrā slānī vismaz vienu režģa līniju [1,2]. Līdz ar to iespējams samazināt risināmās problēmas dimensitāti: paraboliskā vai eliptiskā tipa parciālā diferenciālvienādojuma vietā var risināt 1. un 2. kārtas parasto diferencālvienādojumu sistēmu. Šīs metodes ir taišņu metodes pamatā. Svarīgi ir pēc iespējas samazināt parasto diferenciālvienādojumu skaitu nepieciešamās precizitātes sasniegšanai.Viduvēšanas rezultātā katrā slānī rodas viens diferenciālvienādojums, bet režģa metodē, lietojot integrēšanu un interpolāciju vai galīgo tilpumu elementus, vismaz viens diferenciālvienādojums (1.veida robežnosacījumu gadījumā) vai 3 vienādojumi (3.veida robežnosacījumu gadījumā). Izrādās, ka ar režģa metodi var iegūt 2 diferenciālvienādojumu sistēmu, kuri jāintegrē pa dažādu vidu saskares līnijām, pie tam precizitāte ir augstāka nekā vienkāršai viduvēšanas metodei. Konstantu koeficientu gadījumā ir iespējams iegūt analītiskos atrisinājumus formulu veidā

Increasing of accuracy for engineering calculation of heat transfer problems in two layer media

In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differential equations is taken. Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equations in two layered domain of Cartesian, cylindrical (with axial symmetry) and spherical coordinates (with radial symmetry). In a stationary case the exact finite difference scheme is obtained. Šiame straipsnyje yra nagrinejami paprasti dvisluoksnes srities šilumos laidumo problemos modeliavimo algoritmai, keičiant diferencialines lygtis dalinemis išvestinemis i paprastas diferencialines lygtis. Parodoma, kad didesnio tikslumo pasiekimui, vietoje pirmos eiles paprastu diferencialiniu lygčiu pradinio uždavinio nagrinejamos antros eiles diferencialines lygtys. Ši proced ura leidžia gauti paprasta inžinerini dvisluoksies srities šilumos laidumo lygties sprendini stačiakampeje, cilindrineje (su ašiu simetrija) ir sferineje (su spinduline simetrija) koordinačiu sistemoje. Tiksli baigtiniu skirtumu schema buvo sudaryta stacionariam atvejui. First Published Online: 14 Oct 201

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Field Intercomparison of Radiometers Used for Satellite Validation in the 400–900 nm Range

An intercomparison of radiance and irradiance ocean color radiometers (the second laboratory comparison exercise—LCE-2) was organized within the frame of the European Space Agency funded project Fiducial Reference Measurements for Satellite Ocean Color (FRM4SOC) May 8–13, 2017 at Tartu Observatory, Estonia. LCE-2 consisted of three sub-tasks: (1) SI-traceable radiometric calibration of all the participating radiance and irradiance radiometers at the Tartu Observatory just before the comparisons; (2) indoor, laboratory intercomparison using stable radiance and irradiance sources in a controlled environment; (3) outdoor, field intercomparison of natural radiation sources over a natural water surface. The aim of the experiment was to provide a link in the chain of traceability from field measurements of water reflectance to the uniform SI-traceable calibration, and after calibration to verify whether different instruments measuring the same object provide results consistent within the expected uncertainty limits. This paper describes the third phase of LCE-2: The results of the field experiment. The calibration of radiometers and laboratory comparison experiment are presented in a related paper of the same journal issue. Compared to the laboratory comparison, the field intercomparison has demonstrated substantially larger variability between freshly calibrated sensors, because the targets and environmental conditions during radiometric calibration were different, both spectrally and spatially. Major differences were found for radiance sensors measuring a sunlit water target at viewing zenith angle of 139° because of the different fields of view. Major differences were found for irradiance sensors because of imperfect cosine response of diffusers. Variability between individual radiometers did depend significantly also on the type of the sensor and on the specific measurement target. Uniform SI traceable radiometric calibration ensuring fairly good consistency for indoor, laboratory measurements is insufficient for outdoor, field measurements, mainly due to the different angular variability of illumination. More stringent specifications and individual testing of radiometers for all relevant systematic effects (temperature, nonlinearity, spectral stray light, etc.) are needed to reduce biases between instruments and better quantify measurement uncertainties

Simultaneous retrieval of selected optical water quality indicators from Landsat-8, Sentinel-2, and Sentinel-3

Constructing multi-source satellite-derived water quality (WQ) products in inland and nearshore coastal waters from the past, present, and future missions is a long-standing challenge. Despite inherent differences in sensors’ spectral capability, spatial sampling, and radiometric performance, research efforts focused on formulating, implementing, and validating universal WQ algorithms continue to evolve. This research extends a recently developed machine-learning (ML) model, i.e., Mixture Density Networks (MDNs) (Pahlevan et al., 2020; Smith et al., 2021), to the inverse problem of simultaneously retrieving WQ indicators, including chlorophyll-a (Chla), Total Suspended Solids (TSS), and the absorption by Colored Dissolved Organic Matter at 440 nm (acdom(440)), across a wide array of aquatic ecosystems. We use a database of in situ measurements to train and optimize MDN models developed for the relevant spectral measurements (400–800 nm) of the Operational Land Imager (OLI), MultiSpectral Instrument (MSI), and Ocean and Land Color Instrument (OLCI) aboard the Landsat-8, Sentinel-2, and Sentinel-3 missions, respectively. Our two performance assessment approaches, namely hold-out and leave-one-out, suggest significant, albeit varying degrees of improvements with respect to second-best algorithms, depending on the sensor and WQ indicator (e.g., 68%, 75%, 117% improvements based on the hold-out method for Chla, TSS, and acdom(440), respectively from MSI-like spectra). Using these two assessment methods, we provide theoretical upper and lower bounds on model performance when evaluating similar and/or out-of-sample datasets. To evaluate multi-mission product consistency across broad spatial scales, map products are demonstrated for three near-concurrent OLI, MSI, and OLCI acquisitions. Overall, estimated TSS and acdom(440) from these three missions are consistent within the uncertainty of the model, but Chla maps from MSI and OLCI achieve greater accuracy than those from OLI. By applying two different atmospheric correction processors to OLI and MSI images, we also conduct matchup analyses to quantify the sensitivity of the MDN model and best-practice algorithms to uncertainties in reflectance products. Our model is less or equally sensitive to these uncertainties compared to other algorithms. Recognizing their uncertainties, MDN models can be applied as a global algorithm to enable harmonized retrievals of Chla, TSS, and acdom(440) in various aquatic ecosystems from multi-source satellite imagery. Local and/or regional ML models tuned with an apt data distribution (e.g., a subset of our dataset) should nevertheless be expected to outperform our global model

Laboratory Intercomparison of Radiometers Used for Satellite Validation in the 400–900 nm Range

An intercomparison of radiance and irradiance ocean color radiometers (The Second Laboratory Comparison Exercise—LCE-2) was organized within the frame of the European Space Agency funded project Fiducial Reference Measurements for Satellite Ocean Color (FRM4SOC) May 8–13, 2017 at Tartu Observatory, Estonia. LCE-2 consisted of three sub-tasks: 1) SI-traceable radiometric calibration of all the participating radiance and irradiance radiometers at the Tartu Observatory just before the comparisons; 2) Indoor intercomparison using stable radiance and irradiance sources in controlled environment; and 3) Outdoor intercomparison of natural radiation sources over terrestrial water surface. The aim of the experiment was to provide one link in the chain of traceability from field measurements of water reflectance to the uniform SI-traceable calibration, and after calibration to verify whether different instruments measuring the same object provide results consistent within the expected uncertainty limits. This paper describes the activities and results of the first two phases of LCE-2: the SI-traceable radiometric calibration and indoor intercomparison, the results of outdoor experiment are presented in a related paper of the same journal issue. The indoor experiment of the LCE-2 has proven that uniform calibration just before the use of radiometers is highly effective. Distinct radiometers from different manufacturers operated by different scientists can yield quite close radiance and irradiance results (standard deviation s < 1%) under defined conditions. This holds when measuring stable lamp-based targets under stationary laboratory conditions with all the radiometers uniformly calibrated against the same standards just prior to the experiment. In addition, some unification of measurement and data processing must be settled. Uncertainty of radiance and irradiance measurement under these conditions largely consists of the sensor’s calibration uncertainty and of the spread of results obtained by individual sensors measuring the same object

Data Descriptor : A European Multi Lake Survey dataset of environmental variables, phytoplankton pigments and cyanotoxins

Under ongoing climate change and increasing anthropogenic activity, which continuously challenge ecosystem resilience, an in-depth understanding of ecological processes is urgently needed. Lakes, as providers of numerous ecosystem services, face multiple stressors that threaten their functioning. Harmful cyanobacterial blooms are a persistent problem resulting from nutrient pollution and climate-change induced stressors, like poor transparency, increased water temperature and enhanced stratification. Consistency in data collection and analysis methods is necessary to achieve fully comparable datasets and for statistical validity, avoiding issues linked to disparate data sources. The European Multi Lake Survey (EMLS) in summer 2015 was an initiative among scientists from 27 countries to collect and analyse lake physical, chemical and biological variables in a fully standardized manner. This database includes in-situ lake variables along with nutrient, pigment and cyanotoxin data of 369 lakes in Europe, which were centrally analysed in dedicated laboratories. Publishing the EMLS methods and dataset might inspire similar initiatives to study across large geographic areas that will contribute to better understanding lake responses in a changing environment.Peer reviewe