982 resultados para Ground-based observations


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Atmospheric downwelling longwave radiation is an important component of the terrestrial energy budget; since it is strongly related with the greenhouse effect, it remarkably affects the climate. In this study, I evaluate the estimation of the downwelling longwave irradiance at the terrestrial surface for cloudless and overcast conditions using a one-dimensional radiative transfer model (RTM), specifically the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). The calculations performed by using this model were compared with pyrgeometer measurements at three different European places: Girona (NE of the Iberian Peninsula), Payerne (in the East of Switzerland), and Heselbach (in the Black Forest, Germany). Several studies of sensitivity based on the radiative transfer model have shown that special attention on the input of temperature and water content profiles must be held for cloudless sky conditions; for overcast conditions, similar sensitivity studies have shown that, besides the atmospheric profiles, the cloud base height is very relevant, at least for optically thick clouds. Also, the estimation of DLR in places where radiosoundings are not available is explored, either by using the atmospheric profiles spatially interpolated from the gridded analysis data provided by European Centre of Medium-Range Weather Forecast (ECMWF), or by applying a real radiosounding of a nearby site. Calculations have been compared with measurements at all sites. During cloudless sky conditions, when radiosoundings were available, calculations show differences with measurements of -2.7 ± 3.4 Wm-2 (Payerne). While no in situ radiosoundings are available, differences between modeling and measurements were about 0.3 ± 9.4 Wm-2 (Girona). During overcast sky conditions, when in situ radiosoundings and cloud properties (derived from an algorithm that uses spectral infrared and microwave ground based measurements) were available (Black Forest), calculations show differences with measurements of -0.28 ± 2.52 Wm2. When using atmospheric profiles from the ECMWF and fixed values of liquid water path and droplet effective radius (Girona) calculations show differences with measurements of 4.0 ± 2.5 Wm2. For all analyzed sky conditions, it has been confirmed that estimations from radiative transfer modeling are remarkably better than those obtained by simple parameterizations of atmospheric emissivity.

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En les últimes dècades, l'increment dels nivells de radiació solar ultraviolada (UVR) que arriba a la Terra (principalment degut a la disminució d'ozó estratosfèric) juntament amb l'augment detectat en malalties relacionades amb l'exposició a la UVR, ha portat a un gran volum d'investigacions sobre la radiació solar en aquesta banda i els seus efectes en els humans. L'índex ultraviolat (UVI), que ha estat adoptat internacionalment, va ser definit amb el propòsit d'informar al públic general sobre els riscos d'exposar el cos nu a la UVR i per tal d'enviar missatges preventius. L'UVI es va definir inicialment com el valor màxim diari. No obstant, el seu ús actual s'ha ampliat i té sentit referir-se a un valor instantani o a una evolució diària del valor d'UVI mesurat, modelitzat o predit. El valor concret d'UVI està afectat per la geometria Sol-Terra, els núvols, l'ozó, els aerosols, l'altitud i l'albedo superficial. Les mesures d'UVI d'alta qualitat són essencials com a referència i per estudiar tendències a llarg termini; es necessiten també tècniques acurades de modelització per tal d'entendre els factors que afecten la UVR, per predir l'UVI i com a control de qualitat de les mesures. És d'esperar que les mesures més acurades d'UVI s'obtinguin amb espectroradiòmetres. No obstant, com que els costs d'aquests dispositius són elevats, és més habitual trobar dades d'UVI de radiòmetres eritemàtics (de fet, la majoria de les xarxes d'UVI estan equipades amb aquest tipus de sensors). Els millors resultats en modelització s'obtenen amb models de transferència radiativa de dispersió múltiple quan es coneix bé la informació d'entrada. No obstant, habitualment no es coneix informació d'entrada, com per exemple les propietats òptiques dels aerosols, la qual cosa pot portar a importants incerteses en la modelització. Sovint, s'utilitzen models més simples per aplicacions com ara la predicció d'UVI o l'elaboració de mapes d'UVI, ja que aquests són més ràpids i requereixen menys paràmetres d'entrada. Tenint en compte aquest marc de treball, l'objectiu general d'aquest estudi és analitzar l'acord al qual es pot arribar entre la mesura i la modelització d'UVI per condicions de cel sense núvols. D'aquesta manera, en aquest estudi es presenten comparacions model-mesura per diferents tècniques de modelització, diferents opcions d'entrada i per mesures d'UVI tant de radiòmetres eritemàtics com d'espectroradiòmeters. Com a conclusió general, es pot afirmar que la comparació model-mesura és molt útil per detectar limitacions i estimar incerteses tant en les modelitzacions com en les mesures. Pel que fa a la modelització, les principals limitacions que s'han trobat és la falta de coneixement de la informació d'aerosols considerada com a entrada dels models. També, s'han trobat importants diferències entre l'ozó mesurat des de satèl·lit i des de la superfície terrestre, la qual cosa pot portar a diferències importants en l'UVI modelitzat. PTUV, una nova i simple parametrització pel càlcul ràpid d'UVI per condicions de cel serens, ha estat desenvolupada en base a càlculs de transferència radiativa. La parametrització mostra una bona execució tant respecte el model base com en comparació amb diverses mesures d'UVI. PTUV ha demostrat la seva utilitat per aplicacions particulars com ara l'estudi de l'evolució anual de l'UVI per un cert lloc (Girona) i la composició de mapes d'alta resolució de valors d'UVI típics per un territori concret (Catalunya). En relació a les mesures, es constata que és molt important saber la resposta espectral dels radiòmetres eritemàtics per tal d'evitar grans incerteses a la mesura d'UVI. Aquest instruments, si estan ben caracteritzats, mostren una bona comparació amb els espectroradiòmetres d'alta qualitat en la mesura d'UVI. Les qüestions més importants respecte les mesures són la calibració i estabilitat a llarg termini. També, s'ha observat un efecte de temperatura en el PTFE, un material utilitzat en els difusors en alguns instruments, cosa que potencialment podria tenir implicacions importants en el camp experimental. Finalment, i pel que fa a les comparacions model-mesura, el millor acord s'ha trobat quan es consideren mesures d'UVI d'espectroradiòmetres d'alta qualitat i s'usen models de transferència radiativa que consideren les millors dades disponibles pel que fa als paràmetres òptics d'ozó i aerosols i els seus canvis en el temps. D'aquesta manera, l'acord pot ser tan alt dins un 0.1º% en UVI, i típicament entre menys d'un 3%. Aquest acord es veu altament deteriorat si s'ignora la informació d'aerosols i depèn de manera important del valor d'albedo de dispersió simple dels aerosols. Altres dades d'entrada del model, com ara l'albedo superficial i els perfils d'ozó i temperatura introdueixen una incertesa menor en els resultats de modelització.

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The Marbled Murrelet (Brachyramphus marmoratus) is a threatened alcid that nests almost exclusively in old-growth forests along the Pacific coast of North America. Nesting habitat has significant economic importance. Murrelet nests are extremely difficult and costly to find, which adds uncertainty to management and conservation planning. Models based on air photo interpretation of forest cover maps or assessments by low-level helicopter flights are currently used to rank presumed Marbled Murrelet nesting habitat quality in British Columbia. These rankings are assumed to correlate with nest usage and murrelet breeding productivity. Our goal was to find the models that best predict Marbled Murrelet nesting habitat in the ground-accessible portion of the two regions studied. We generated Resource Selection Functions (RSF) using logistic regression models of ground-based forest stand variables gathered at plots around 64 nests, located using radio-telemetry, versus 82 random habitat plots. The RSF scores are proportional to the probability of nests occurring in a forest patch. The best models differed somewhat between the two regions, but include both ground variables at the patch scale (0.2-2.0 ha), such as platform tree density, height and trunk diameter of canopy trees and canopy complexity, and landscape scale variables such as elevation, aspect, and slope. Collecting ground-based habitat selection data would not be cost-effective for widespread use in forestry management; air photo interpretation and low-level aerial surveys are much more efficient methods for ranking habitat suitability on a landscape scale. This study provides one method for ground-truthing the remote methods, an essential step made possible using the numerical RSF scores generated herein.

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Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

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The s–x model of microwave emission from soil and vegetation layers is widely used to estimate soil moisture content from passive microwave observations. Its application to prospective satellite-based observations aggregating several thousand square kilometres requires understanding of the effects of scene heterogeneity. The effects of heterogeneity in soil surface roughness, soil moisture, water area and vegetation density on the retrieval of soil moisture from simulated single- and multi-angle observing systems were tested. Uncertainty in water area proved the most serious problem for both systems, causing errors of a few percent in soil moisture retrieval. Single-angle retrieval was largely unaffected by the other factors studied here. Multiple-angle retrievals errors around one percent arose from heterogeneity in either soil roughness or soil moisture. Errors of a few percent were caused by vegetation heterogeneity. A simple extension of the model vegetation representation was shown to reduce this error substantially for scenes containing a range of vegetation types.

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Remote sensing can potentially provide information useful in improving pollution transport modelling in agricultural catchments. Realisation of this potential will depend on the availability of the raw data, development of information extraction techniques, and the impact of the assimilation of the derived information into models. High spatial resolution hyperspectral imagery of a farm near Hereford, UK is analysed. A technique is described to automatically identify the soil and vegetation endmembers within a field, enabling vegetation fractional cover estimation. The aerially-acquired laser altimetry is used to produce digital elevation models of the site. At the subfield scale the hypothesis that higher resolution topography will make a substantial difference to contaminant transport is tested using the AGricultural Non-Point Source (AGNPS) model. Slope aspect and direction information are extracted from the topography at different resolutions to study the effects on soil erosion, deposition, runoff and nutrient losses. Field-scale models are often used to model drainage water, nitrate and runoff/sediment loss, but the demanding input data requirements make scaling up to catchment level difficult. By determining the input range of spatial variables gathered from EO data, and comparing the response of models to the range of variation measured, the critical model inputs can be identified. Response surfaces to variation in these inputs constrain uncertainty in model predictions and are presented. Although optical earth observation analysis can provide fractional vegetation cover, cloud cover and semi-random weather patterns can hinder data acquisition in Northern Europe. A Spring and Autumn cloud cover analysis is carried out over seven UK sites close to agricultural districts, using historic satellite image metadata, climate modelling and historic ground weather observations. Results are assessed in terms of probability of acquisition probability and implications for future earth observation missions. (C) 2003 Elsevier Ltd. All rights reserved.

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1. Jerdon's courser Rhinoptilus bitorquatus is a nocturnally active cursorial bird that is only known to occur in a small area of scrub jungle in Andhra Pradesh, India, and is listed as critically endangered by the IUCN. Information on its habitat requirements is needed urgently to underpin conservation measures. We quantified the habitat features that correlated with the use of different areas of scrub jungle by Jerdon's coursers, and developed a model to map potentially suitable habitat over large areas from satellite imagery and facilitate the design of surveys of Jerdon's courser distribution. 2. We used 11 arrays of 5-m long tracking strips consisting of smoothed fine soil to detect the footprints of Jerdon's coursers, and measured tracking rates (tracking events per strip night). We counted the number of bushes and trees, and described other attributes of vegetation and substrate in a 10-m square plot centred on each strip. We obtained reflectance data from Landsat 7 satellite imagery for the pixel within which each strip lay. 3. We used logistic regression models to describe the relationship between tracking rate by Jerdon's coursers and characteristics of the habitat around the strips, using ground-based survey data and satellite imagery. 4. Jerdon's coursers were most likely to occur where the density of large (>2 m tall) bushes was in the range 300-700 ha(-1) and where the density of smaller bushes was less than 1000 ha(-1). This habitat was detectable using satellite imagery. 5. Synthesis and applications. The occurrence of Jerdon's courser is strongly correlated with the density of bushes and trees, and is in turn affected by grazing with domestic livestock, woodcutting and mechanical clearance of bushes to create pasture, orchards and farmland. It is likely that there is an optimal level of grazing and woodcutting that would maintain or create suitable conditions for the species. Knowledge of the species' distribution is incomplete and there is considerable pressure from human use of apparently suitable habitats. Hence, distribution mapping is a high conservation priority. A two-step procedure is proposed, involving the use of ground surveys of bush density to calibrate satellite image-based mapping of potential habitat. These maps could then be used to select priority areas for Jerdon's courser surveys. The use of tracking strips to study habitat selection and distribution has potential in studies of other scarce and secretive species.

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A ground-based millimetre wave radar, AVTIS (All-weather Volcano Topography Imaging Sensor), has been developed for topographic monitoring. The instrument is portable and capable of measurements over ranges up to similar to 7 km through cloud and at night. In April and May 2005, AVTIS was deployed at Arenal Volcano, Costa Rica, in order to determine topographic changes associated with the advance of a lava flow. This is the first reported application of mm-wave radar technology to the measurement of lava flux rates. Three topographic data sets of the flow were acquired from observation distances of similar to 3 km over an eight day period, during which the flow front was detected to have advanced similar to 200 m. Topographic differences between the data sets indicated a flow thickness of similar to 10 m, and a dense rock equivalent lava flux of similar to 0.20 +/- 0.08 m(3) s(-1).

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In April–July 2008, intensive measurements were made of atmospheric composition and chemistry in Sabah, Malaysia, as part of the "Oxidant and particle photochemical processes above a South-East Asian tropical rainforest" (OP3) project. Fluxes and concentrations of trace gases and particles were made from and above the rainforest canopy at the Bukit Atur Global Atmosphere Watch station and at the nearby Sabahmas oil palm plantation, using both ground-based and airborne measurements. Here, the measurement and modelling strategies used, the characteristics of the sites and an overview of data obtained are described. Composition measurements show that the rainforest site was not significantly impacted by anthropogenic pollution, and this is confirmed by satellite retrievals of NO2 and HCHO. The dominant modulators of atmospheric chemistry at the rainforest site were therefore emissions of BVOCs and soil emissions of reactive nitrogen oxides. At the observed BVOC:NOx volume mixing ratio (~100 pptv/pptv), current chemical models suggest that daytime maximum OH concentrations should be ca. 105 radicals cm−3, but observed OH concentrations were an order of magnitude greater than this. We confirm, therefore, previous measurements that suggest that an unexplained source of OH must exist above tropical rainforest and we continue to interrogate the data to find explanations for this.

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1. Jerdon's courser Rhinoptilus bitorquatus is a nocturnally active cursorial bird that is only known to occur in a small area of scrub jungle in Andhra Pradesh, India, and is listed as critically endangered by the IUCN. Information on its habitat requirements is needed urgently to underpin conservation measures. We quantified the habitat features that correlated with the use of different areas of scrub jungle by Jerdon's coursers, and developed a model to map potentially suitable habitat over large areas from satellite imagery and facilitate the design of surveys of Jerdon's courser distribution. 2. We used 11 arrays of 5-m long tracking strips consisting of smoothed fine soil to detect the footprints of Jerdon's coursers, and measured tracking rates (tracking events per strip night). We counted the number of bushes and trees, and described other attributes of vegetation and substrate in a 10-m square plot centred on each strip. We obtained reflectance data from Landsat 7 satellite imagery for the pixel within which each strip lay. 3. We used logistic regression models to describe the relationship between tracking rate by Jerdon's coursers and characteristics of the habitat around the strips, using ground-based survey data and satellite imagery. 4. Jerdon's coursers were most likely to occur where the density of large (>2 m tall) bushes was in the range 300-700 ha(-1) and where the density of smaller bushes was less than 1000 ha(-1). This habitat was detectable using satellite imagery. 5. Synthesis and applications. The occurrence of Jerdon's courser is strongly correlated with the density of bushes and trees, and is in turn affected by grazing with domestic livestock, woodcutting and mechanical clearance of bushes to create pasture, orchards and farmland. It is likely that there is an optimal level of grazing and woodcutting that would maintain or create suitable conditions for the species. Knowledge of the species' distribution is incomplete and there is considerable pressure from human use of apparently suitable habitats. Hence, distribution mapping is a high conservation priority. A two-step procedure is proposed, involving the use of ground surveys of bush density to calibrate satellite image-based mapping of potential habitat. These maps could then be used to select priority areas for Jerdon's courser surveys. The use of tracking strips to study habitat selection and distribution has potential in studies of other scarce and secretive species.

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Cloud radar and lidar can be used to evaluate the skill of numerical weather prediction models in forecasting the timing and placement of clouds, but care must be taken in choosing the appropriate metric of skill to use due to the non- Gaussian nature of cloud-fraction distributions. We compare the properties of a number of different verification measures and conclude that of existing measures the Log of Odds Ratio is the most suitable for cloud fraction. We also propose a new measure, the Symmetric Extreme Dependency Score, which has very attractive properties, being equitable (for large samples), difficult to hedge and independent of the frequency of occurrence of the quantity being verified. We then use data from five European ground-based sites and seven forecast models, processed using the ‘Cloudnet’ analysis system, to investigate the dependence of forecast skill on cloud fraction threshold (for binary skill scores), height, horizontal scale and (for the Met Office and German Weather Service models) forecast lead time. The models are found to be least skillful at predicting the timing and placement of boundary-layer clouds and most skilful at predicting mid-level clouds, although in the latter case they tend to underestimate mean cloud fraction when cloud is present. It is found that skill decreases approximately inverse-exponentially with forecast lead time, enabling a forecast ‘half-life’ to be estimated. When considering the skill of instantaneous model snapshots, we find typical values ranging between 2.5 and 4.5 days. Copyright c 2009 Royal Meteorological Society

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A first step in interpreting the wide variation in trace gas concentrations measured over time at a given site is to classify the data according to the prevailing weather conditions. In order to classify measurements made during two intensive field campaigns at Mace Head, on the west coast of Ireland, an objective method of assigning data to different weather types has been developed. Air-mass back trajectories calculated using winds from ECMWF analyses, arriving at the site in 1995–1997, were allocated to clusters based on a statistical analysis of the latitude, longitude and pressure of the trajectory at 12 h intervals over 5 days. The robustness of the analysis was assessed by using an ensemble of back trajectories calculated for four points around Mace Head. Separate analyses were made for each of the 3 years, and for four 3-month periods. The use of these clusters in classifying ground-based ozone measurements at Mace Head is described, including the need to exclude data which have been influenced by local perturbations to the regional flow pattern, for example, by sea breezes. Even with a limited data set, based on 2 months of intensive field measurements in 1996 and 1997, there are statistically significant differences in ozone concentrations in air from the different clusters. The limitations of this type of analysis for classification and interpretation of ground-based chemistry measurements are discussed.

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This paper describes advances in ground-based thermodynamic profiling of the lower troposphere through sensor synergy. The well-documented integrated profiling technique (IPT), which uses a microwave profiler, a cloud radar, and a ceilometer to simultaneously retrieve vertical profiles of temperature, humidity, and liquid water content (LWC) of nonprecipitating clouds, is further developed toward an enhanced performance in the boundary layer and lower troposphere. For a more accurate temperature profile, this is accomplished by including an elevation scanning measurement modus of the microwave profiler. Height-dependent RMS accuracies of temperature (humidity) ranging from 0.3 to 0.9 K (0.5–0.8 g m−3) in the boundary layer are derived from retrieval simulations and confirmed experimentally with measurements at distinct heights taken during the 2005 International Lindenberg Campaign for Assessment of Humidity and Cloud Profiling Systems and its Impact on High-Resolution Modeling (LAUNCH) of the German Weather Service. Temperature inversions, especially of the lower boundary layer, are captured in a very satisfactory way by using the elevation scanning mode. To improve the quality of liquid water content measurements in clouds the authors incorporate a sophisticated target classification scheme developed within the European cloud observing network CloudNet. It allows the detailed discrimination between different types of backscatterers detected by cloud radar and ceilometer. Finally, to allow IPT application also to drizzling cases, an LWC profiling method is integrated. This technique classifies the detected hydrometeors into three different size classes using certain thresholds determined by radar reflectivity and/or ceilometer extinction profiles. By inclusion into IPT, the retrieved profiles are made consistent with the measurements of the microwave profiler and an LWC a priori profile. Results of IPT application to 13 days of the LAUNCH campaign are analyzed, and the importance of integrated profiling for model evaluation is underlined.

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The calibration of the CloudSat spaceborne cloud radar has been thoroughly assessed using very accurate internal link budgets before launch, comparisons with predicted ocean surface backscatter at 94 GHz, direct comparisons with airborne cloud radars, and statistical comparisons with ground-based cloud radars at different locations of the world. It is believed that the calibration of CloudSat is accurate to within 0.5–1 dB. In the present paper it is shown that an approach similar to that used for the statistical comparisons with ground-based radars can now be adopted the other way around to calibrate other ground-based or airborne radars against CloudSat and/or to detect anomalies in long time series of ground-based radar measurements, provided that the calibration of CloudSat is followed up closely (which is the case). The power of using CloudSat as a global radar calibrator is demonstrated using the Atmospheric Radiation Measurement cloud radar data taken at Barrow, Alaska, the cloud radar data from the Cabauw site, Netherlands, and airborne Doppler cloud radar measurements taken along the CloudSat track in the Arctic by the Radar System Airborne (RASTA) cloud radar installed in the French ATR-42 aircraft for the first time. It is found that the Barrow radar data in 2008 are calibrated too high by 9.8 dB, while the Cabauw radar data in 2008 are calibrated too low by 8.0 dB. The calibration of the RASTA airborne cloud radar using direct comparisons with CloudSat agrees well with the expected gains and losses resulting from the change in configuration that required verification of the RASTA calibration.

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The Along-Track Scanning Radiometers (ATSRs) provide a long time-series of measurements suitable for the retrieval of cloud properties. This work evaluates the freely-available Global Retrieval of ATSR Cloud Parameters and Evaluation (GRAPE) dataset (version 3) created from the ATSR-2 (1995�2003) and Advanced ATSR (AATSR; 2002 onwards) records. Users are recommended to consider only retrievals flagged as high-quality, where there is a good consistency between the measurements and the retrieved state (corresponding to about 60% of converged retrievals over sea, and more than 80% over land). Cloud properties are found to be generally free of any significant spurious trends relating to satellite zenith angle. Estimates of the random error on retrieved cloud properties are suggested to be generally appropriate for optically-thick clouds, and up to a factor of two too small for optically-thin cases. The correspondence between ATSR-2 and AATSR cloud properties is high, but a relative calibration difference between the sensors of order 5�10% at 660 nm and 870 nm limits the potential of the current version of the dataset for trend analysis. As ATSR-2 is thought to have the better absolute calibration, the discussion focusses on this portion of the record. Cloud-top heights from GRAPE compare well to ground-based data at four sites, particularly for shallow clouds. Clouds forming in boundary-layer inversions are typically around 1 km too high in GRAPE due to poorly-resolved inversions in the modelled temperature profiles used. Global cloud fields are compared to satellite products derived from the Moderate Resolution Imaging Spectroradiometer (MODIS), Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) measurements, and a climatology of liquid water content derived from satellite microwave radiometers. In all cases the main reasons for differences are linked to differing sensitivity to, and treatment of, multi-layer cloud systems. The correlation coefficient between GRAPE and the two MODIS products considered is generally high (greater than 0.7 for most cloud properties), except for liquid and ice cloud effective radius, which also show biases between the datasets. For liquid clouds, part of the difference is linked to choice of wavelengths used in the retrieval. Total cloud cover is slightly lower in GRAPE (0.64) than the CALIOP dataset (0.66). GRAPE underestimates liquid cloud water path relative to microwave radiometers by up to 100 g m�2 near the Equator and overestimates by around 50 g m�2 in the storm tracks. Finally, potential future improvements to the algorithm are outlined.