It is installed on the edge of roofs, in drains and gutters, in places where snow and ice can accumulate. During operation of the heating cable, melt water passes freely through all elements of the drainage system to the ground. Freezing and destruction of the elements of the roof, the facade of the building and the drainage system itself does not occur in this case.

For correct operation systems need:

• Determine the most problematic areas on the roof and in the drainage system;
• Make a correct calculation of the power of the heating system;
• Use a special heating cable of the required power and length (for outdoor installation, resistant to ultraviolet radiation);
• Select fasteners depending on the material and construction of the roof and gutter system;
• Select the necessary heating control equipment.

Installation of anti-icing system on roofs.

When calculating the required capacity of a snow and ice melting system for a roof, it is important to consider the type, construction of the roof, and local weather conditions.

Conventionally, roofs can be divided into three types:

1. "Cold roof". A roof with good insulation and low heat loss through its surface. On such a roof, ice usually forms only when the snow melts in the sun, while the minimum melting temperature is not lower than -5 ° C. When calculating the required power of the anti-icing system for such roofs, the minimum power of the heating cable will be sufficient (250-350 W/m² for roofs and 30-40 W/m for gutters).

2. "Warm roof". Roof with poor insulation. On such roofs, snow melts when enough low temperatures air, then the water flows down to the cold edge and to the drains, where it freezes. The minimum melting temperature is not lower than -10 °C. Most of the roofs of administrative buildings with an attic belong to this type. When calculating the anti-icing system for "warm roofs", the power of the heating cable at the edge of the roof and in the gutters should be increased. This will ensure the efficiency of the system even at low temperatures. (Fig. 1).

3. "Hot roof". A roof with poor thermal insulation, in which the attic is often used for technical purposes or as living space. On such roofs, snow melts even at low air temperatures (below -10 °C). For "hot roofs", in addition to using a heating cable with high power, it is desirable to use a weather station or thermostat to reduce energy costs.

If the cable is laid on a roof with a soft covering (eg roofing felt), the maximum output of the heating cable must not exceed 20 W/m.

Installation area	"Cold Roof"	"Warm Roof"	"Hot Roof"	Cable power
Roof surface, valley	250 – 350 W/m²	300 – 400 W/m²		15 – 40 W/m
Gutters, plastic gutters
Gutters, metal gutters, diameter 20 cm or more	30 – 40 W/m	50 – 70 W/m
Gutters, wooden gutters	30 – 40 W/m

Installation of an anti-icing system in gutters and gutters.

When calculating the anti-icing system, it is necessary to take into account:

1. Drainpipe and gutter diameter. When the diameter of the vertical downpipe is less than 10 cm, it is recommended to install one line of heating cable.
2. The material from which the drain is made. (See table).

In most cases, the heating cable is laid in two lines: in the gutters with the help of special plates, in the gutters with the help of a pigtail (a cable with special fasteners that fix the cable). Fastenings provide reliable fixation and do not allow heating cable lines to cross.

If there is a possibility of clogging the gutters or drains with foliage, needles, etc. It is recommended to use a self-regulating heating cable. Since a conventional resistive heating cable can overheat in places of clogging and fail over time.

Vertical downpipes are most susceptible to freezing during the winter. In long pipes (15 m or more), due to air convection, hypothermia of the lower part of the pipe is possible. To avoid freezing, additional heating cable lines are installed (power increases) in the lower part of the pipe at a length of 0.5 - 1 m (Fig. 2).

It is necessary to eliminate the formation of icicles and frost on the edge of the roof and prevent the drainage system from freezing. The length of the roof edge is 10 m, thermal insulation does not completely eliminate heat loss (warm roof). The length of the gutter is 10 m, two drains are 6 m long. The gutter and drain are made of plastic, the diameter of the drains is 10 cm, the width of the gutter is 20 cm.

Solution:

In this case, the option with separate heating of the roof edge (Fig. 3) and the gutter system is optimal.

Fig.3

Calculation of the heating system for the roof:

1. According to the table, we determine the power required to heat the edge of the "warm roof" per 1 square meter – 300 - 400 W.
2. Determine the total heating area ( S): (heating must be carried out along the entire length of the roof (10 m), depending on the slope of the roof, we determine the width of the heating area, in our case - 50 cm). S = 10m × 0.5m = 5 m²
3. We select a heating cable, the power and length of which will meet the requirements specified above. The minimum cable power will be:

5 m² × 300 W = 1500 W

Option 1. Heating cable Nexans TXLP/1, 28W/m, 1800W, 64.2m.

In this case, the power (W) per 1 m² will be:

where Wtot. - full power of the heating cable, S - number of heated square meters.

(this value satisfies the conditions of the table)

The laying step (N) of the cable will be:

WhereS- heating area,L- length of cable.

(For convenience during installation, it is possible to lay the heating cable in 8 cm increments, and mount a small cable residue on the free area of ​​the roof.)

Option 2: Hemstedt DAS 55 heating cable (1650 W, 55 m). According to the formulas indicated above, we determine the Required parameters.

(Power per 1 m² = 330 W, laying step = 9 cm)

Option 3: Heating cable Exxon Elite 2-23, 1630 W, 70 m

(Power per 1 m² = 326 W, laying step = 7 cm)

Note. In addition, it is possible to use self-regulating cables and cut-off resistive cables.

Calculation of the heating system for gutters:

1. According to the table, we determine the required power for the drain:

W= 40 – 50 W/m

1. We determine the required length of the heating cable based on the conditions indicated above.

Since the diameter of the drain is 10 cm, the heating cable must be installed in one core L V. = 6 + 6 = 12 m

For a gutter with a width of 20 cm, we select the cable with the calculation of laying in two cores.

L and. = 10 × 2 = 20 m.

Option 1: Self-regulating heating cable.

For each drain we use 6 meters of cable with a power of 40 W / m, and in the gutter 20 m of a cable with a power of 20 W / m, fastened every 40 cm with mounting plates.

Option 2: Heating cable Hemstedt Das 20 (for laying in a gutter in two cores) and 6 m each self-regulating cable 40 W/m (for laying in each drain.)

Task: It is necessary to prevent freezing of melt water in the drain.(The length of the drain is 15 m, the material is metal, the diameter is 20 cm, the water is drained from the “cold roof”)

In addition to heating the vertical pipe, it is necessary to provide heating of a horizontal drainage system(Fig. 4), into which melt and rain water flows from the drain and from the site with paving slabs in which it is located. The drain is 6.5 m long and 15 cm wide.

Solution:

1. Based on the parameters specified in the condition, according to the table, we determine the required power per 1 r.m. W = 30 - 40 W / m.
2. Determine the length of the heating cable. (For the diameter of the drain and drainage specified in the condition, it is necessary to lay the heating cable in 2 lines) L \u003d (15 + 6.5) × 2 \u003d 43 meters.
3. We select a heating cable of the appropriate length and power.

Option 1: Nexans TXLP/1 1280W, 45.7m. The cable is laid in two lines with a pigtail and connected in a convenient place (to the thermostat or to the weather station). The rest of the cable (2.7 meters) can be laid in the drain neck of the drain, or the heating section at the end of the drain can be extended.

Option 2 : Exxon-Elite 23, 995W, 43.6m.

Option 3: Nexans Defrost Snow TXLP/2R 1270W, 45.4m.

Option 4: Self-regulating or cut-off resistance heating cables.

In regions with difficult climatic conditions during the construction of engineering structures, it is necessary to take into account a number of criteria that are responsible for the reliability and safety of construction projects. These criteria, in particular, should take into account atmospheric and climatic factors that can adversely affect the state of structures and the process of operation of structures. One of these factors is atmospheric icing.

Icing is the process of formation, deposition and growth of ice on the surfaces of various objects. Icing can result from the freezing of supercooled droplets or wet snow, as well as from the direct crystallization of water vapor contained in the air. The danger of this phenomenon for construction objects lies in the fact that ice growths formed on its surfaces lead to a change in the design characteristics of structures (weight, aerodynamic characteristics, margin of safety, etc.), which affects the durability and safety of engineering structures.

Particular attention should be paid to the issue of icing in the design and construction of power lines (TL) and communication lines. Icing of the wires of power transmission lines disrupts their normal operation, and often leads to serious accidents and disasters (Fig. 1).

Fig.1. The consequences of icing power lines

It should be noted that the problems of icing of power lines have been known for a long time and there are various methods of dealing with ice growths. Such methods include coating with special anti-icing compounds, melting due to heating electric shock, mechanical removal of frost, sheathing, preventive heating of wires. But, not always and not all of these methods are effective, accompanied by high costs, energy losses.

To define and develop more effective ways struggle requires knowledge of the physics of the icing process. On early stages development of a new object, it is necessary to study and analyze the factors affecting the process, the nature and intensity of ice deposition, heat transfer of the icing surface, and identify potentially weak and most prone to icing places in the structure of the object. Therefore, the ability to model the icing process at various conditions and evaluate possible consequences of this phenomenon is an urgent task, both for Russia and for the world community.

The Role of Experimental Research and Numerical Simulation in Icing Problems

Modeling the icing of power transmission lines is a large-scale task, in solving which, in a complete formulation, it is necessary to take into account many global and local characteristics of the object and environment. These characteristics include: the length of the section under consideration, the relief of the surrounding area, airflow velocity profiles, the value of humidity and temperature depending on the distance above the ground, the thermal conductivity of cables, the temperature of individual surfaces, etc.

Creation of a complete mathematical model capable of describing the processes of icing and aerodynamics of an iced body is an important and extremely complex engineering task. Today, many of the existing mathematical models are built on the basis of simplified methods, where certain restrictions are deliberately introduced or some of the influencing parameters are not taken into account. In most cases, such models are based on statistical and experimental data (including SNIP standards) obtained in the course of laboratory studies and long-term field observations.

Setting up and conducting numerous and multivariate experimental studies of the icing process requires significant financial and time costs. In addition, in some cases it is simply not possible to obtain experimental data on the behavior of an object, for example, under extreme conditions. Therefore, more and more often there is a tendency to supplement the full-scale experiment with numerical simulation.

The analysis of various climatic phenomena using modern methods of engineering analysis became possible both with the development of the numerical methods themselves and with the rapid development of HPC technologies (High Performance Computing technologies), realizing the possibility of solving new models and large-scale problems in adequate time frames. Engineering analysis, carried out with the help of supercomputer simulation, provides the most accurate solution. Numerical simulation allows you to solve the problem in a complete formulation, conduct virtual experiments with varying various parameters, study the influence of many factors on the process under study, simulate the behavior of an object under extreme loads, etc.

Modern high-performance computing systems, with the proper use of engineering analysis calculation tools, make it possible to obtain a solution in adequate time frames and track the progress of the problem solution in real time. This significantly reduces the cost of conducting multivariate experiments, taking into account multicriteria settings. A full-scale experiment, in this case, can only be used at the final stages of research and development, as a verification of the numerically obtained solution and confirmation of individual hypotheses.

Computer simulation of the icing process

A two-stage approach is used to model the icing process. Initially, the parameters of the carrier phase flow (velocity, pressure, temperature) are calculated. After that, the icing process is calculated directly: modeling the deposition of liquid drops on the surface, calculating the thickness and shape of the ice layer. As the thickness of the ice layer grows, the shape and dimensions of the streamlined body change, and the flow parameters are recalculated using the new geometry of the streamlined body.

The calculation of the flow parameters of the working medium occurs due to the numerical solution of the system of nonlinear differential equations describing the main conservation laws. Such a system includes the equation of continuity, the equation of momentum (Navier-Stokes) and energy. To describe turbulent flows, the package uses the Reynolds-averaged Navier-Stokes (RANS) equations and the LES large eddy method. The coefficient in front of the diffusion term in the momentum equation is found as the sum of the molecular and turbulent viscosity. To calculate the latter, in this paper, we use the Spallart-Allmaras one-parameter differential turbulence model, which is widely used in external flow problems.

Modeling of the icing process is carried out on the basis of two embedded models. The first of these is the model of melting and solidification. It does not explicitly describe the evolution of the liquid-ice interface. Instead, the enthalpy formulation is used to define the portion of the liquid in which a solid phase (ice) forms. In this case, the flow must be described by a two-phase flow model.

The second model that makes it possible to predict the formation of ice is the thin film model, which describes the process of droplet deposition on the walls of a streamlined body, thereby making it possible to obtain a wetting surface. According to this approach, consideration includes a set of Lagrangian fluid particles that have mass, temperature, and velocity. Interacting with the wall, the particles, depending on the balance of heat fluxes, can either increase the ice layer or reduce it. In other words, both the icing of the surface and the melting of the ice layer are modeled.

As an example illustrating the capabilities of the package for modeling the icing of bodies, the problem of air flow around a cylinder with a speed U=5 m/s and a temperature T=-15 0C was considered. The cylinder diameter is 19.5 mm. To partition the computational domain into control volumes, a multifaceted type of cells was used, with a prismatic layer near the surface of the cylinder. In this case, for a better resolution of the trace after the cylinder, local mesh refinement was used. The problem was solved in two stages. At the first stage, using the model of a single-phase liquid, the fields of velocities, pressures and temperatures for "dry" air were calculated. The results obtained are in qualitative agreement with numerous experimental and numerical studies on single-phase flow around a cylinder.

At the second stage, Lagrangian particles were injected into the flow, simulating the presence of finely dispersed water droplets in the air flow, the trajectories of which, as well as the field of the absolute air velocity, are shown in Fig. 2. The distribution of ice thickness over the surface of the cylinder for different times is shown in Fig.3. The maximum thickness of the ice layer is observed near the flow stagnation point.

Fig.2. Drop Trajectories and the Scalar Field of Absolute Air Velocity

Fig.3. The thickness of the ice layer at different times

The time spent on the calculation of the two-dimensional problem (physical time t=3600s) was 2800 core hours, using 16 computing cores. The same number of kernel hours is needed to calculate only t=600 s in the three-dimensional case. Analyzing the time spent on calculating test models, we can say that for the calculation in the full formulation, where the computational domain will already consist of several tens of millions of cells, where a larger number of particles and complex geometry of the object will be taken into account, a significant increase in the required hardware computing power will be required. In this regard, to carry out a complete simulation of the problems of three-dimensional icing of bodies, it is necessary to use modern HPC technologies.

Method for forecasting areas of possible aircraft icing

General information

In accordance with the Test Plan for 2009, the State Hydrometeorological Center of Russia conducted operational tests of the method for forecasting areas of possible icing of aircraft (AC) using the SLAV and NCEP models in the period from April 1 to December 31, 2009. The method is integral part technologies for calculating the map of special phenomena (SP) at the middle levels of the atmosphere (Significant Weather at the Middle levels - SWM) for aviation. The technology was developed by the Division of Aeronautical Meteorology (OAM) in 2008 under R&D Theme 1.4.1 for implementation in the Area Forecast Laboratory. The method is also applicable to the prediction of icing at the lower levels of the atmosphere. The development of the technology for calculating the prognostic map of the OH at the lower levels (Significant Weather at the Low levels - SWL) is scheduled for 2010.

Aircraft icing can occur under the necessary condition of the presence of supercooled cloud droplets in the right amount. This condition is not sufficient. Sensitivity various types aircraft and helicopters to icing is not the same. It depends both on the characteristics of the cloud and on the flight speed and aerodynamic characteristics of the aircraft. Therefore, only “possible” icing is predicted in layers where its necessary condition is met. Such a forecast should ideally be made up of a forecast of the presence of clouds, their water content, temperature, and also the phase state of cloud elements.

In the early stages of the development of computational methods for icing forecasting, their algorithms were based on temperature and dew point forecasts, synoptic cloud forecasts, and statistical data on cloud microphysics and aircraft icing frequency. Experience has shown that such a forecast at that time was ineffective.

However, even subsequently, up to the present time, even the best world-class numerical models did not provide a reliable forecast for the presence of clouds, their water content and phase . Therefore, the forecast of icing in the world centers (to build maps of the EP; we do not touch here on the ultra-short-range forecast and nowcasting, the state of which is characterized in ) is currently still based on the forecast of air temperature and humidity, as well as, if possible, on the simplest characteristics of cloudiness ( layered, convective). The success of such a forecast, however, turns out to be practically significant, since the accuracy of the prediction of temperature and air humidity has greatly increased compared to the state corresponding to the time of writing.

In the main algorithms of modern methods of icing forecasting are presented. For the purpose of constructing SWM and SWL maps, we have selected those that are applicable to our conditions, i.e., are based only on the output of numerical models. Algorithms for calculating the “icing potential”, combining model and real data in the nowcasting mode, are not applicable in this context.

Development of a forecast method

As samples of aircraft icing data used to assess the relative success of the algorithms listed in , as well as previously known ones (including the well-known Godske formula), the following were taken:
1) data from the TAMDAR system installed on aircraft flying over the territory of the United States within the lower 20 thousand feet,
2) a database of aircraft sounding over the territory of the USSR in the 60s. of the twentieth century, created in 2007 in the OAM under the theme 1.1.1.2.

Unlike the AMDAR system, the TAMDAR system includes icing and dew point sensors. TAMDAR data could be collected from August to October 2005, all of 2006 and January 2007 from the website http:\\amdar.noaa.gov. Since February 2007, access to the data has been closed to all users, except for US government organizations. The data was collected by OAM staff and presented in a computer-readable database by manually extracting the following information from the site mentioned above: time, geographic coordinates, GPS altitude, air temperature and humidity, pressure, wind, icing and turbulence.

Let us dwell briefly on the features of the TAMDAR system, compatible with international system AMDAR and operational on US civil aviation aircraft since December 2004. The system was developed in accordance with the requirements of WMO, as well as NASA and US NOAA. Sensor readings are made at predetermined pressure intervals (10 hPa) in climb and descent modes and at predetermined time intervals (1 min) in level flight mode. The system includes a multifunctional sensor mounted on the leading edge of the aircraft wing and a microprocessor that processes signals and transmits them to a data processing and distribution center located on the ground (AirDat system). An integral part is also the GPS satellite system, which operates in real time and provides spatial reference of data.

Keeping in mind the further analysis of the TAMDAR data together with the OA and numerical forecast data, we limited ourselves to extracting the data only in the vicinity of ± 1 h from 00 and 12 UTC. The data array collected in this way includes 718417 individual readings (490 dates), including 18633 readings with icing. Almost all of them refer to the period of 12 UTC. The data were grouped according to the squares of the latitude-longitude grid 1.25x1.25 degrees in size and according to the height in the vicinity of the standard isobaric surfaces of 925, 850, 700 and 500 hPa. Layers 300 - 3000, 3000 - 7000, 7000 - 14000 and 14000 - 21000 f., respectively, were considered as neighborhoods. The sample contains 86185, 168565, 231393, 232274 counts (cases) in the vicinity of 500, 700, 850, and 925 hPa, respectively.

To analyze TAMDAR data on icing, it is necessary to take into account the following feature of them. The icing sensor detects the presence of ice with a layer of at least 0.5 mm. From the moment the ice appears until the moment it completely disappears (i.e. during the entire period of icing), the temperature and humidity sensors do not work. The dynamics of deposits (rate of rise) is not reflected in these data. Thus, not only are there no data on the intensity of icing, but there are also no data on temperature and humidity during the icing period, which predetermines the need to analyze the TAMDAR data together with independent data on the indicated values. As such, OA data from the base of the State Institution “Hydrometeorological Center of Russia” on air temperature and relative humidity were used. A sample that includes TAMDAR data on the predictor (icing) and OA data on the predictors (temperature and relative humidity) will be referred to in this report as the TAMDAR-OA sample.

The sample of airborne sounding data (SS) over the territory of the USSR included all readings containing information on the presence or absence of icing, as well as on air temperature and humidity, regardless of the presence of clouds. Since we do not have reanalysis data for the period 1961–1965, there was no point in limiting ourselves to the neighborhoods of 00 and 12 UTC or the neighborhoods of standard isobaric surfaces. Airborne sounding data were thus used directly as in situ measurements. The SZ data sample included more than 53 thousand readings.

As predictors from the numerical forecast data, the predictive fields of the geopotential, air temperature (Т) and relative humidity (RH) were used with a lead time of 24 hours of global models: semi-Lagrangian (at grid nodes 1.25x1.25°) and the NCEP model (at grid points 1x1° ) for the periods of information collection and comparison of models in April, July and October 2008 (from the 1st to the 10th day of the month).

Results of methodological and scientific importance

1 . Air temperature and humidity (relative humidity or dew point temperature) are significant predictors of areas of possible aircraft icing, provided that these predictors are measured in situ (Fig. 1). All tested algorithms, including the Godske formula, on a sample of aircraft sounding data showed quite practically significant success in separating the cases of the presence and absence of icing. However, in the case of TAMDAR icing data supplemented with objective temperature and relative humidity data, separation success is reduced, especially at the 500 and 700 hPa levels (Figures 2–5), due to the fact that the predictor values ​​are spatially averaged (within the square grids 1.25x1.25°) and can be vertically and temporally separated from the moment of observation by 1 km and 1 h, respectively; moreover, the accuracy of objective relative humidity analysis decreases significantly with altitude.

2 . Although aircraft icing can be observed in a wide range of negative temperatures, its probability is maximum in relatively narrow temperature and relative humidity ranges (-5…-10°C and > 85%, respectively). Outside these intervals, the probability of icing decreases rapidly. At the same time, the dependence on relative humidity seems to be stronger: namely, at RH > 70%, 90.6% of all cases of icing were observed. These conclusions were obtained on a sample of aircraft sounding data; they find complete qualitative confirmation in the TAMDAR-OA data. The fact of good agreement between the results of the analysis of two data samples obtained by different methods in very different geographic conditions and at different time periods shows the representativeness of both samples used to characterize the physical conditions of aircraft icing.

3 . Based on the results of testing various algorithms for calculating icing zones and taking into account the available data on the dependence of icing intensity on air temperature, the most reliable algorithm that has previously proven itself in international practice (the algorithm developed at NCEP) was selected and recommended for practical use. This algorithm turned out to be the most successful (the values ​​of the Piercy-Obukhov quality criterion were 0.54 on the airborne sounding data sample and 0.42 on the TAMDAR-OA data sample). In accordance with this algorithm, the forecast of zones of possible icing of aircraft is a diagnosis of these zones according to the forecast fields of temperature, Т°C, and relative humidity, RH %, on isobaric surfaces of 500, 700, 850, 925 (900) hPa at the nodes of the model grid .

The nodes of the grid belonging to the zone of possible icing of aircraft are the nodes in which the following conditions are met:

Inequalities (1) were obtained at NCEP within the framework of the RAP program (Research Application Program) on a large sample of measurement data using aircraft sensors for icing, temperature, air humidity and are used in practice to calculate forecast maps of special phenomena for aviation. It is shown that the frequency of aircraft icing in the zones where inequalities (1) are satisfied is an order of magnitude higher than outside these zones.

Specifics of operational testing of the method

The program for operational testing of the method for forecasting areas of possible icing of aircraft using (1) has certain features that distinguish it from standard programs for testing new and improved forecast methods. First of all, the algorithm is not an original development of the Hydrometeorological Center of Russia. It has been sufficiently tested and evaluated on different data samples, see .

Further, the success of separating the cases of the presence and absence of aircraft icing cannot be the object of operational tests in this case, due to the impossibility of obtaining operational data on aircraft icing. Single, irregular pilot reports received by the Air Traffic Control Center cannot in the foreseeable future form a representative sample of data. There are no objective data of the TAMDAR type over the territory of Russia. It is also not possible to obtain such data over the territory of the United States, since the site from which we obtained the data that made up the TAMDAR-OA sample, information on icing is now closed to all users, except government organizations USA.

However, taking into account that the decision rule (1) was obtained on a large data archive and implemented in NCEP practice, and its success has been repeatedly confirmed on independent data (including within the framework of topic 1.4.1 on the S3 and TAMDAR-OA samples), we can to believe that in diagnostic terms, the statistical relationship between the probability of icing and the fulfillment of conditions (1) is sufficiently close and sufficiently reliably estimated for practical application.

It remains unclear the question of how correctly the zones of fulfillment of conditions (1), identified according to the data of objective analysis, are reproduced in the numerical forecast.

In other words, the object of testing should be a numerical prediction of zones in which conditions (1) are satisfied. That is, if in the diagnostic plan the decision rule (1) is effective, then it is necessary to evaluate the success of the prediction of this rule by numerical models.

The author's tests within the framework of topic 1.4.1 showed that the SLAV model quite successfully predicts the zones of possible aircraft icing, determined through conditions (1), but is inferior in this respect to the NCEP model. Since at present the operational data of the NCEP model are received by the Hydrometeorological Center of Russia quite early, it can be assumed that, given a significant advantage in the accuracy of the forecast, it is advisable to use these data to calculate the EP maps. Therefore, it was considered expedient to evaluate the success of forecasting the zones of fulfillment of conditions (1) both by the SLAV model and by the NCEP model. In principle, the T169L31 spectral model should also be included in the program. However, serious shortcomings in the forecast of the humidity field do not yet allow us to consider this model as promising for forecasting icing.

Methodology for evaluating forecasts

The fields of the results of calculations on each of the four indicated isobaric surfaces in dichotomous variables were recorded in the database: 0 means non-fulfillment of conditions (1), 1 means fulfillment. In parallel, similar fields were calculated according to objective analysis data. To assess the accuracy of the forecast, it is necessary to compare the results of calculation (1) at the grid nodes for the prognostic fields and for the fields of objective analysis on each isobaric surface.

As actual data on the zones of possible icing of the aircraft, the results of calculations of ratios (1) according to the data of an objective analysis were used. As applied to the SLAV model, these are the results of calculations (1) at grid nodes with a step of 1.25 deg; with respect to the NCEP model, at grid nodes with a step of 1 deg; in both cases, the calculation is made on isobaric surfaces of 500, 700, 850, 925 hPa.

The predictions were assessed using the scoring technique for dichotomous variables. The estimates were carried out and analyzed at the Laboratory for Testing and Evaluation of Forecast Methods of the State Institution Hydrometeorological Center of Russia.

To determine the success of forecasts for possible aircraft icing zones, the following characteristics were calculated: the feasibility of forecasts for the presence of the phenomenon, the absence of the phenomenon, the overall accuracy, the warning of the presence and absence of the phenomenon, the Piercey-Obukhov quality criterion and the Heidke-Bagrov reliability criterion. Estimates were made for each isobaric surface (500, 700, 850, 925 hPa) and separately for forecasts starting at 00 and 12 UTC.

Operational test results

The test results are presented in Table 1 for three forecast areas: for the northern hemisphere, for the territory of Russia and its European territory (ETR) with a forecast lead time of 24 hours.

It can be seen from the table that the frequency of icing according to an objective analysis of both models is close, and it is maximum on the surface of 700 hPa, and minimum on the surface of 400 hPa. When calculating for the hemisphere, the surface of 500 hPa ranks second in terms of the frequency of icing, followed by 700 hPa, which is obviously due to the large contribution of deep convection in the tropics. When calculating for Russia and European Russia, the 850 hPa surface is in second place in terms of the frequency of icing, and on the surface of 500 hPa, the frequency of icing is already half as much. All characteristics of the justification of forecasts turned out to be high. Although the success rates of the SLAV model are somewhat inferior to the NCEP model, however, they are quite practically significant. At levels where the frequency of icing is high and where it poses the greatest danger to aircraft, success rates should be considered very high. They noticeably decrease at the surface of 400 hPa, especially in the case of the SLAV model, remaining significant (the Pearcey criterion decreases to 0.493 for the northern hemisphere, and to 0.563 for Russia). According to ETP, test results at the 400 hPa level are not given due to the fact that there were very few cases of icing at this level (37 grid points of the NCEP model for the entire period), and the result of evaluating the success of the forecast is statistically insignificant. At other levels of the atmosphere, the results obtained for the ETR and Russia are very close.

conclusions

Thus, operational tests have shown that the developed method for forecasting areas of possible aircraft icing, which implements the NCEP algorithm, provides a sufficiently high forecast success, including on the output data of the global SLAV model, which is currently the main prognostic model. By the decision of the Central Methodological Commission for Hydrometeorological and Heliogeophysical Forecasts of Roshydromet dated December 1, 2009, the method was recommended for implementation in the operational practice of the Laboratory of Area Forecasts of the State Institution Hydrometeorological Center of Russia for the construction of maps of special phenomena for aviation.

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Aircraft icing intensity in flight(I mm/min) is estimated by the rate of ice growth on the leading edge of the wing - the thickness of the ice deposition per unit time. Intensity is distinguished:

A) light icing - I less than 0.5 mm / min;

B) moderate icing - I from 0.5 to 1.0 mm / min;

C) heavy icing - I more than 1.0 mm / min;

When assessing the risk of icing, you can use the concept of the degree of icing. Degree of icing - total ice deposition for the entire time the aircraft has been in the icing zone. The longer the flight of an aircraft in icing conditions, the greater the degree of icing.

For a theoretical assessment of the factors affecting the intensity of icing, the following formula is used:

Icing intensity; - aircraft airspeed; - water content of the cloud; - integral capture coefficient; - freezing factor; - the density of the growing ice, which ranges from 0.6 g/cm 3 (white ice); up to 1.0 g/cm 3 (clear ice);

The intensity of icing of the aircraft increases with an increase in the water content of the clouds. The values ​​of the water content of clouds vary in wide aisles - from thousandths to several grams per cubic meter of air. The water content of clouds is not measured at AD, but it can be indirectly judged by the temperature and shape of the clouds. When the water content of the cloud is 1 g/cm3, the strongest icing is observed.

A prerequisite for aircraft icing in flight is the negative temperature of their surfaces (from 5 to -50 degrees C). Icing of aircraft with gas turbine engines can occur at positive air temperatures. (from 0 to 5 degrees C)

As the airspeed of the aircraft increases, the intensity of icing increases. However, at large airspeeds, kinetic heating of the aircraft occurs, which prevents icing.

The intensity of aircraft icing in different forms is different.

In cumulonimbus and powerful cumulus clouds, at negative air temperatures, heavy icing of the aircraft is almost always possible. These clouds contain large droplets with a diameter of 100 µm or more.

In an array of stratus rain and altostratus clouds, with increasing height, a decrease in the size of drops and their number is observed. Heavy icing is possible when flying in the lower part of the cloud mass. Intramass stratus and stratocumulus clouds are most often water clouds and are characterized by an increase in water content with height. At temperatures from -0 to -20 in these clouds, light icing is usually observed, in some cases icing can be severe.

When flying in altocumulus clouds, light icing is observed. If the thickness of these clouds is more than 600 meters, icing in them can be severe.

Flights in areas of heavy icing are flights in special conditions. Heavy icing is a meteorological phenomenon dangerous for flights.

Signs of heavy icing of the aircraft are: rapid ice buildup on the windshield wipers and windshield; a decrease in the indicated speed 5-10 minutes after entering the clouds by 5-10 km/h.

(There are 5 types of icing in flight: clear ice, frosted ice, white ice, frost and hoarfrost. The most dangerous species icing is transparent and frosted ice, which are observed at air temperatures from -0 to -10 degrees.

Transparent ice- is the densest of all types of icing.

frosted ice has a rough bumpy surface. Strongly distorts the profile of the wing and aircraft.

white ice- coarse ice, porous deposits, adheres loosely to the aircraft, and easily falls off when vibrated.)

Icing intensity aircraft in flight (I, mm/min) is estimated by the rate of ice growth on the leading edge of the wing - the thickness of the ice deposit per unit time. By intensity, weak icing is distinguished - I less than 0.5 mm / min; moderate icing - I from 0.5 to 1.0 mm / min; heavy icing - I more than 1.0 mm / min.

When assessing the risk of icing, the concept of the degree of icing can be used. The degree of icing - the total deposition of ice for the entire time the aircraft has been in the icing zone.

For a theoretical assessment of the factors affecting the intensity of icing, the following formula is used:

where I is the intensity of icing; V is the airspeed of the aircraft; ω - cloud water content; E - integral coefficient of capture; β - freezing coefficient; ρ is the density of growing ice, which ranges from 0.6 g/cm 3 (white ice) to 1.0 g/cm 3 (clear ice).

The intensity of aircraft icing increases with an increase in the water content of clouds. The water content of clouds varies widely - from thousandths to several grams per 1 m3 of air. When the water content of the cloud is 1 g/m 3 or more, the strongest icing is observed.

Capture and freezing coefficients are dimensionless quantities that are practically difficult to determine. The integral capture coefficient is the ratio of the mass of water actually settled on the wing profile to the mass that would have settled in the absence of curvature of the trajectories of water droplets. This coefficient depends on the size of the droplets, the thickness of the wing profile and the airspeed of the aircraft: the larger the droplets, the thinner the wing profile and the higher the airspeed, the greater the integral capture coefficient. The freezing coefficient is the ratio of the mass of ice that has grown on the surface of an aircraft to the mass of water that has settled on the same surface in the same time.

A prerequisite for aircraft icing in flight is the negative temperature of their surface. The ambient air temperature at which aircraft icing was noted varies widely - from 5 to -50 °C. The probability of icing increases at air temperatures from -0 to -20 °C in supercooled clouds and precipitation.

With an increase in the airspeed of the aircraft, the intensity of icing increases, as can be seen from the formula. However, at high airspeeds, kinetic heating of aircraft occurs, which prevents icing. Kinetic heating occurs due to the deceleration of the air flow, which leads to air compression and an increase in its temperature and the temperature of the surface of the aircraft. Due to the effect of kinetic heating, aircraft icing occurs most often at airspeeds below 600 km/h. Aircraft are typically exposed to icing during takeoff, climb, descent, and approach when speeds are slow.

During flights in the zones of atmospheric fronts, icing of aircraft is observed 2.5 times more often than during flights in homogeneous air masses. This is due to the fact that frontal cloudiness is, as a rule, more powerful vertically and more extended horizontally than intramass cloudiness. Strong icing in homogeneous air masses is observed in isolated cases.

The intensity of aircraft icing during flights in clouds of various forms is different.

In cumulonimbus and powerful cumulus clouds at negative air temperatures, heavy icing of aircraft is almost always possible. These clouds contain large droplets with a diameter of 100 µm or more. The water content in clouds increases with altitude.