text:
[ Research Article ]
Asian Journal of Atmospheric Environment - Vol. 16, No. 1, pp.14-23
ISSN: 1976-6912 (Print) 2287-1160 (Online)
Print publication date 31 Mar 2022
Received 03 Nov 2021 Revised 28 Dec 2021 Accepted 06 Jan 2022

# Wind and Gust Forecasts Assessment of Weather Research and Forecast (WRF) Model in Córdoba, Argentina

Matías Suárez1), 2), 3), 4), * ; Denis Poffo2), 3), 4) ; Edgardo Pierobon3), 4) ; Agustín Martina3), 4) ; Jorge Saffe3), 4) ; Andrés Rodríguez1), 3), 4)
1)Instituto de Estudios Avanzados en Ingeniería y Tecnología, CONICET, UNC, Av. Vélez Sarsfield 1611, Córdoba, X5016GCA, Córdoba, Argentina
2)Facultad de Matemática, Astronomía, Física y Computación, UNC, Av. Medina Allende s/n, Córdoba, X5016HUA, Córdoba, Argentina
3)Laboratorio de Hidráulica, Facultad de Ciencias Exactas, Físicas y Naturales, UNC, Dr. Juan Filloy s/n, Córdoba, X5016GCA, Córdoba, Argentina
4)Observatorio Hidrometeorológico de la Provincia de Córdoba, Ministerio de Servicios Públicos, Ituzaingó 1400, Córdoba, X5000IKB, Córdoba, Argentina

Correspondence to: * Tel: +54 351 3971254 E-mail: matias.suarez@mi.unc.edu.ar

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

## Abstract

WRF wind forecasts from four operative schemes used by OHMC (Observatorio HidroMeteorológico de Córdoba), a test scheme (WRF-E) and two daily runs with 4 km horizontal resolution were analyzed. Wind simulations were compared with measurements from eight ground stations with anemometers at 10 m high during the period from June, 2019 to June, 2020. WRF-E incorporates more vertical levels, and an activated topo_wind option. The wind speed results show that WRF overestimates wind speed at most stations and the WRF-E model reduces the BIAS and the RMSE when compared with the operational models. The wind direction analysis shows that the higher the wind speed is, the more accurate the models are. In addition, a wind gust forecasting has been implemented and evaluated in this work. Wind gust correlation coefficient values are between 0.3 and 0.6, RMSE is between 3 and 5 m/s, and a positive BIAS (<2 m/s) at most stations.

## Keywords:

WRF model, Wind speed, Wind gust, Wind direction, Topo wind, Weather forecast

## 1. INTRODUCTION

Extreme hydrometeorological phenomena which take place on our planet result in great human loss and important damage in infrastructure and personal properties, which implies economic setbacks that may last for a long time (Bronstert et al., 2018; Manuel-Navarrete, 2007). To lessen this impact, international institutions use global climatic models such as GFS (Global Forecast System), ECMWF (European Centre for Medium-Range Weather Forecasts), ICON (Icosahedral Non-Hydrostatic), and JMA (Global weather forecast model from the “Japan Meteorological Agency”) as input for models of limited area (LAM). These high-resolution models, which are used for short term forecasting, have the advantage of being more precise in the reproduction of small-scale phenomena. In fact, LAM description of the passage of cold fronts, convective cells, and the orographic influence are better than the description provided by the global models (Politi et al., 2018).

Since Argentina extends from latitude 21°46′52″S to 55°03′21″S, it is affected by a wide variety of weather phenomena (Le Favi, 2020). In particular the province of Córdoba is an inland province with a complex orographic system which causes extreme weather conditions. It is important to stress that these meteorological phenomena, which have a variety of space-time scales, are frequent hazards in the province. The study of these events gave rise to several research works including project RELAMPAGO campaign carried out recently in Córdoba (Casanovas et al., 2021; Schumacher et al., 2021; Singh et al., 2019). This context led to the creation of the Hydrometeorologial Observatory of the Province of Córdoba (OHMC) in March, 2017. OHMC is an institution which provides early warning services by means of several products obtained through satellite information, automatic weather stations, and weather radar data. The latter are provided by SINARAME (National System of Weather Radars). Additionally, OHMC runs a numerical model called WRF-OHMC (Weather Research and Forecast). The products mentioned before are published and updated daily at a specific website (https://ohmc.ar/, last accessed on October 14th, 2021). The information is provided by graphs, maps, weather charts and tables. The WRF-OHMC model renders meteorological information at regional level, which is used by different governmental and private organizations. This model has two daily runs (06 and 18 UTC) that provide four forecasts labeled WRF-A, WRF-B, WRF-C and WRF-D. The meteorological information includes hourly precipitation, accumulated precipitation, temperature, atmospheric pressure, wind speed, and wind direction.

Information obtained from LAMs models such as WRF is useful to study the energetic behavior of wind farms (Jacondino et al., 2021; Prosper et al., 2019; Wang et al., 2019), their optimal placement (Feroz et al., 2021; Dhunny et al., 2020), and as a tool for wind resource assessment. Additionally, the information allows collaboration with local or regional institutions for emergency management such as forest fires, flooding, and strong winds (Patel et al., 2019; Rodriguez et al., 2018).

This work presents a statistical analysis of the wind variable from the four operative forecasts of the WRF-OHMC model using data from eight automatic weather stations (AWS) distributed throughout the province of Córdoba. Results of this analysis will be of vital importance for wind risk management in Córdoba.

The used database includes information about wind speed and direction from June 1, 2019 to June 1, 2020. In this work, WRF assessment will be carried out for measured wind speed and wind gust greater than 2.77 m/s or 10 km/h since slower winds are not considered relevant by the civil defense authorities and wind risk management of Córdoba.

This paper also analyses the performance of a new forecast scheme, WRF-E, which includes more vertical levels than previous ones, and a better representation of the roughness of the terrain and it analyses a new product used to determine wind gusts.

## 2. STUDY REGION AND WRF-OHMC MODEL

### 2. 1 Study Region

In this work the study region is the province of Córdoba, located in the center of Argentina, with a surface area of 165,321 km2, is a large territory with plains, mountain ranges and valleys, which gives the province a unique landscape identity. The East of the province consists of an extensive plain with a gently slope down towards the East. Over the West, there are three mountain ranges known as Sierras de Córdoba. The easternmost range (Sierras Chicas) starts at about 20 km west of the city of Córdoba with altitudes ranging from around 1,000 m in the south end to 1,950 m at Cerro Uritorco. To the west of this chain, there are two important valleys: the Calamuchita valley to the south, and the Punilla Valley to the north. Both valleys are economically important because of the tourist industry. The next mountain range to the west includes the Champaqui Hill (2,880 m), which is the highest mountain in the province.

The climate of Córdoba is temperate and subtropical with a marked dry season. Temperatures, as well as rainfall, decrease from North to South and from East to West, except in the eastern slopes of the mountains, where the humid winds from the East deposit more rain. In this area, the regime is 1,100-1,300 mm per year. Precipitation has a seasonal character, mainly between October and April, and the provincial average is close to 800 mm per year.

Temperatures usually oscillate between 8°C and 30°C. Summer in Córdoba is generally warm. Average maximums are around 30°C, although there are peaks that can reach 40°C. In January, the warmest month, the average maximum is 31°C and the minimum is 17°C. Winter is mild and quite dry. The average temperature is around 10-12°C with maximum temperatures around 18°C, and minimum temperatures between 4 and 5°C. Another characteristic of winter is the occurrence of snowfalls in the highest locations of the province.

Electrical storms frequently occur throughout the province in the spring and summer months, especially in the area of highest mountains of the Sierras de Córdoba. The east province area has a higher frequency of storms, some of which can be severe. Hail is also a fairly common phenomenon in the province.

In this region, the prevailing winds, which come from the North and Northeast, are associated with advection of warm and humid air in spring and summer. Winds from the South and South West are associated with the passage of cold fronts, and the entry of cold and dry air masses to the province. Winds from the east and west are infrequent, short and relatively weak.

### 2. 2 Description of the WRF Model and Domain

Numerical simulations were performed using WRF model (Skamarock et al., 2019), version 4.1.1. Initial and boundary conditions are supplied by data from the Global Forecast System (GFS) with a horizontal resolution of 0.25°. Several numerical experiments were conducted using different parameterization schemes (WRF-A, WRF-B, WRF-C, WRF-D, WRF-E). WRF model domain consists of 270×270 grid points with a 4 km horizontal resolution. Table 1 shows the physical configurations of WRF-OHMC used in this work. Fig. 1 shows WRF domain D01 (physical map at middle), Córdoba topography and AWS locations used in this paper (upper right square). This figure shows a plain on the east, and a region with a complex topography on the west with mountains along the south-north direction.

Description of parameterization schemes used operationally by WRF-OHMC.

WRF domain used in this work (D01), the region topography and the location of automatic weather stations.

### 2. 3 Database

Wind speed forecasts at 10 m height from five models were used. The dataset used span the period between June 1, 2019 and June 1, 2020. Simulations were performed during 33 hours beginning at 06 and 18 UTC every day. The first 9 hours were discarded because of the model spin up time, and then the subsequent 24 hours were considered. WRF-E simulations were performed only for 06 UTC run due to limited storage resources.

In this work, eight automatic weather stations (AWS) were used:

• • 30253 - Los Reartes
• • 30350 - Arroyo Algodon
• • 30349 - Bell Ville
• • 30167 - Cruz del Eje
• • 30168 - La Rinconada
• • 30137 - Laboratorio de Hidraulica
• • 30254 - Las Varillas
• • 30231 - Villa Dolores

These AWS are capable of measuring wind speed, wind gusts and wind direction at 10 m above ground level with a frequency of one measurement each 10 minutes. Wind direction is measured with a resolution of 22.5°.

It is important to remark that stations 30350 and 30349 (Arroyo Algodon and Bell Ville) have data from March 5, 2020 to June 1, 2020.

### 2. 4 Filters Applied to Database

Since low wind intensity are not considered relevant by the wind risk management of Córdoba, winds below 2.77 m/s (10 km/h) were removed and were not included in the analysis.

In order to detect and remove repeated wind direction measurements during long intervals, a filter was applied to the dataset. Through this filter we were able to detect unusual measurements in some stations. The affected AWS were Laboratorio de Hidraulica (30137) and Las Varillas (30254) where the reported wind direction remained constant (90°) for a couple of months, probably as a result of wind vanes malfunctioning. On the other hand, since the stations measure wind direction with a resolution of 22.5°, it is necessary to adapt the WRF wind direction forecast to this coarse resolution, which was carried out by considering intervals of ±11.25° around the values that the stations can measure. Then, each of the WRF wind direction forecasted value within one of the intervals is associated to the value that the station measures within that interval.

## 3. STATISTICAL METRICS FOR WIND FORECASTS VALIDATION AND WIND GUST PARAMETERIZATION

A particular value of wind velocity depends on two variables: wind intensity and wind direction. WRF model calculates wind velocity forecast in each grid point. Each point has an associated area of 16 km2, and a variable h that changes with elevation.

Components U and V are used to specify the wind velocity at any given location of latitude (i), longitude (j) and height (k). U and V are associated with directions x (west-east direction), and y (south-north direction) respectively. To determine wind direction for each time step t, from the velocity components U and V, the fourquadrant inverse tangent function is used. In turn, wind speed Wijk in a grid point (i, j, k) is given by Eq. (1) (Dzebre et al., 2019).

 ${W}_{ijk}=\sqrt{{\left(\frac{{U}_{i,j,k}+{U}_{i+1,j,k}}{2}\right)}^{2}+{\left(\frac{{V}_{i,j,k}+{V}_{i,j+1,k}}{2}\right)}^{2}}$ (1)

In this work, WRF forecasts at 10 m above ground were used. At present, the WRF-OHMC uses a set of levels that covers most of the weather active atmosphere (see Table 2).

Height of 34 levels used by WRF-OHMC.

### 3. 1 Statistical Metrics for Wind Speed and Wind Gust Validation

Hourly forecasted wind speeds at 10 m above ground (U10, V10) were compared with hourly AWS data measured at 10 m above ground. The forecasts from different parameterization schemes and measured data were analyzed by using several statistical metrics. This procedure allows the assessment of the WRF model for the forecast of both wind speed and wind direction. The statistical coefficients are the following:

• • Root Mean Square Error (RMSE),
• • BIAS,
• • Pearson Correlation Coefficient (CC)

RMSE represents the difference between forecasted and measured data, and is given by:

 $RMSE=\sqrt{\frac{1}{N}{\sum }_{i=1}^{N}{\left(\Delta {w}_{i}\right)}^{2},}$ (2)

where Δwi=Wsim,i-Wobs,i are the difference between simulated and observed wind speed and N is the number of data. BIAS is another measure of error, which allows one to determine if the model overestimates or underestimates measured wind speed. BIAS is defined by the following equation:

 $BIAS=\frac{1}{N}{\sum }_{i=1}^{N}\Delta {w}_{i}.$ (3)

The linear dependency between forecasted and measured data was assessed using Pearson Correlation Coefficient (CC). It is defined as:

 $CC=\frac{{\sum }_{i=1}^{N}\left({W}_{sim,i}-\overline{{W}_{sim}}\right)\left({W}_{obs,i}-\overline{{W}_{obs}}\right)}{\sqrt{{\sum }_{i=1}^{N}\left({W}_{sim,i}-\overline{{W}_{sim}}\right)\left({W}_{obs,i}-\overline{{W}_{obs}}\right)}},$ (4)

where variables with over bar indicate average value.

### 3. 2 Statistical Metrics for Wind Direction Validation

Hourly forecasted wind direction at 10 m above ground were compared with the measured wind direction at 10 m above ground level. In order to make these comparisons, the already defined RMSE and BIAS through Eq. (2) and (3) respectively were used, although in this case, the variable Δθ must be used instead. Δθ is defined by (Dzebre et al., 2019):

 (5)

where θsim , θobs are the simulated and observed wind direction respectively. Eq. (5) assigns a positive/negative difference if the wind direction given by WRF is rotated clockwise/anticlockwise with respect to the direction measured by the AWS. Δθ ranges from -180° to 180°.

### 3. 3 WRF-E Forecast Model

This work proposes a new scheme oriented to improve wind speed forecasting (See Table 3). This scheme is based on a sensitivity study carried out in Andalusia, Spain (Santos-Alamillos et al., 2013). In that study, 32 parameterization schemes were analyzed with different choices of microphysics, cumulus, planetary boundary layer, shortwave, and longwave radiation. Their conclusion was used to determine the physical configuration of the WRF-E model. Furthermore, the number of vertical levels of WRF-E was increased from 34 to 50. The new levels were distributed in order to increase the model resolution near ground. Ten levels were added to the first 100 meters of height, and three levels were added between 100 and 200 meters (See Table 4). In addition, to reduce the high wind BIAS seen in WRF, the option topo_wind=1 was enabled. This option is based on the concept of a momentum sink term, which makes use of the standard deviation of the subgrid scale orography as well as the Laplacian of the topographic field (Jiménez, 2012).

Description of parametrization schemes used by WRF-E.

Height of the first 14 levels used by WRF-E.

### 3. 4 Wind Gust Parameterization

An important objective of this paper is the implementation and evaluation of a wind gust forecast WG. Eq. (6) will be used to perform this calculation. This equation was utilized in the former NOAA RUC20 (Rapid Update Cycle) of Post-Processing Diagnosed Variables (Benjamin et al., 2002).

 (6)

where v10 is the simulated wind speed at 10 m above ground level, vPBL is the simulated wind speed at the top of the planetary boundary layer, and hPBL is the height of this layer in meters. According to RUC20 documentation (Benjamin et al., 2020), hPBL in Eq. (6) is equal to 1,000 m for any height greater than 1,000 m.

## 4. RESULTS AND DISCUSSION

### 4. 1 Wind Speed WRF-OHMC Operative and WRF-E

Preliminary statistical performance analysis of the operational forecasts of WRF-OHMC and the new model WRF-E can be seen in Figs. 2, 3, and 4. These figures show the statistical measures CC, RMSE and BIAS calculated at 06 UTC from section 3 for each AWS represented by their numerical code in the abscissa. The color coded bars A to E correspond to the five WRF models (WRF-A, WRF-B, WRF-C, WRF-D and WRF-E). The lower panel in these figures represents the difference between runs at 06 UTC and at 18 UTC. The top panel in Fig. 2 shows that the operative forecasting WRF models have a similar behavior for each AWS. Likewise, the bottom panel shows slight differences between runs delayed by twelve hours. In Fig. 2 the CC highest bars with values above 0.7 correspond to Arroyo Algodón (30350) AWS, which is located in a plain region. On the other hand, the correlation coefficient has the lowest values for the stations Los Reartes (30253), Villa Dolores (30231), and La Rinconada (30168) while the rest of the stations have CC above 0.5. It should be noticed that stations 30253 and 30231 are both in mountainous terrain. Interestingly, the new model (WRF-E, brown bars) does not present significant differences in CC with the other operative WRF models, except for Cruz del Eje (30167) station where the difference is close to 50%.

Pearson correlation coefficient calculated at 06 UTC (upper panel) and difference CC 06 UTC-CC 18 UTC (lower panel).

Root mean square error (RMSE) calculated at 06 UTC (upper panel) and difference RMSE 06 UTC-RMSE 18 UTC (lower panel).

BIAS calculated at 06 UTC (upper panel), and difference BIAS 06 UTC-BIAS 18 UTC (lower panel).

Fig. 3 shows the RMSE in the top panel, and the difference between runs 12 hours apart in the bottom panel. Clearly, the WRF-A model gives the worst performance for the majority of stations while the WRF-E shows an improvement with respect to the other models in at least half of the stations (30253, 30167, 30137 and 30231). For the rest of them, WRF-E has a similar performance to that of the other models.

The BIAS given by Eq. (3) is positive, which indicates that the wind speed is overestimated except when the equation is applied to stations 30350 and 30349. As seen in Fig. 4, the WRF-A model has the worst performance except for stations 30350 and 30349. In general, the WRF-E model reduces the positive BIAS when compared with the operational models, as seen for stations 30253, 30167, 30137 and 30231. However, when operative model BIAS is negative, WRF-E model tends to increase the negative BIAS, as seen for stations 30350, 30349 and 30254. This behavior could be due to topo_wind option in WRF-E. In Figs. 2, 3 and 4, the lower panel shows negligible changes in the statistical parameters of wind speed forecasted by the operational models between runs at 06 UTC and 18 UTC.

It is interesting to note that the forecasted wind speed statistical performance is related to the kind of terrain where the AWS stations are. In fact, the best performance seen in Figs. 2, 3 and 4 correspond to stations 30350, 30349, 30137, and 30254 which are on a plain. Conversely, the worst statistical performance is for stations 30253, 30167, and 30231 with BIAS larger than 2 m/s (models WRF-B, WRF-C, WRF-D), and above 3 m/s for model WRF-A. The latter stations are located in the mountainous region.

### 4. 2 Wind Direction Forecasted by Operative WRF-OHMC and WRF-E

The hourly wind direction predictions were compared with the ground data measured hourly at a height of 10 m above ground level. The statistical measures used in this analysis are RMSE and BIAS for Δθ, which represents the angular difference between forecasts and measurements. Fig. 5 shows wind direction variation as a function of measured wind speed for each AWS. The red dots correspond to the 06 UTC run and blue dots to the 18 UTC run. There is a clear indication that the angular variation decreases with wind speed. This is not observed for station 30231, where Δθ has a tendency to ~-90° for high wind speed. This fact suggests that there is a negative BIAS in the model forecast i.e. WRF shows an anticlockwise rotation with respect to the wind measured in Villa Dolores. This could be due to the difficulty to simulate wind direction in complex terrain or perhaps an incorrect operation of the station wind vane. Moreover, Fig. 2 shows a low correlation for this particular station.

Difference between forecasted and measured wind direction vs measured wind speed. Each column of four scatter plots correspond to stations and rows correspond to models WRF-A, WRF-B, WRF-C, WRF-D and WRF-E. Red dots correspond to 06 UTC run and blue dots to 18 UTC run.

There are not noticeable differences between forecasts run in the morning versus forecasts run in the evening for all the operative schemes (WRF-A, WRF-B, WRF-C and WRF-D).

Fig. 6 shows RMSE in the top panel, and BIAS in the bottom panel, for the AWS used. Values are presented in color circles (06 UTC) and crosses (18 UTC) for the four operative forecasts. The values of the new WRF-E model are represented by black squares, but only for 06 UTC. RMSE has a dispersion below 60° for all the stations except for 30231 station. Moreover, for all stations there are negligible differences for runs twelve hours apart. The BIAS in the wind direction is lower than 20° anticlockwise for six stations. Station 30254 presents a positive BIAS of about 35°, and station 30231 a BIAS between 70° and 80°. The latter is consistent with the column labeled 30231 in Fig. 5. The new WRF-E shows only a slight BIAS improvement for all cases.

Wind direction RMSE (upper panel) and BIAS (lower panel) for operative models WRF-A, WRF-B, WRF-C, WRF-D and test model WRF-E.

### 4. 3 Wind Gust Forecasted by Operative WRF-OHMC and WRF-E

In this section, wind gusts measured by the stations were compared with those wind gusts forecasted by models WRF- A, WRF-B, WRF-C, WRF-D and WRF-E. To evaluate the wind gust estimation proposed in Eq. (6), it is better to consider only forecasted wind speeds that have a good correlation with measured wind speeds. This is the reason why a filter was applied to the wind speed to keep only the data that meet the condition CC≥0.5 for 6 hs time intervals. The results of the comparisons with the filtered data are presented in Fig. 7.

Wind gust Pearson correlation coefficient (upper panel), RMSE (middle panel) and BIAS (lower panel) for OHMC operative models WRF- A, WRF-B, WRF-C, WRF-D and test model WRF-E.

The top panel of Fig. 7 shows that the range of CC of wind gust forecasted by operative models WRF-A, WRF-B, WRF-C and WRF-D is between ~0.3 for station 30254 (Las Varillas) and ~0.6 for stations 30349 and 30167 (Bell Ville and Cruz del Eje). WRF-A model has a slightly greater CC than the other operative models. Regarding model WRF-E, it has lower CC values than operative models in most stations except for station 30168 (La Rinconada) where CC is approximately equal.

RMSE is shown in the middle panel of Fig. 7. RMSE values are between ~3 m/s for station 30349 (Bell Ville) and ~5 m/s for stations 30167 (Cruz del Eje), 30168 (La Rinconada), 30254 (Las Varillas) and 30231 (Villa Dolores). There are no significant differences of RMSE among operative models WRF-A, WRF-B, WRF-C and WRF-D. However, model WRF-E has slightly greater RMSE than operative models in most stations.

The lower panel of Fig. 7 shows BIAS for all stations. From this panel it is possible to notice that all stations have a positive BIAS except for station 30349 (Bell Ville). In addition, models WRF-B, WRF-C and WRF-D have a similar BIAS in most stations. Instead, model WRF-A has a greater BIAS in stations 30253 (Los Reartes), 30350 (Arroyo Algodón), 30168 (La Rinconada), 30137 (Laboratorio de Hidraulica), and 30254 (Las Varillas) than models WRF-B, WRF-C, WRF-D, and WRF-E. In contrast, WRF-A has a lower BIAS in station 30349 (Bell Ville) than the same models.

On the other hand, model WRF-E has a significantly lower BIAS than operative models in all stations except 30349 (Bell Ville), 30167 (Cruz del Eje), and 30231 (Villa Dolores). It is important to note that models WRF-B, WRF-C and WRF-D have a similar performance in most stations possibly because these models have a common planetary boundary layer, and land surface parameterization schemes (YSU PBL and Unified Noah LSM, respectively). Despite the use of the same planetary boundary layer and land surface parameterization schemes, model WRF-E has a different performance in most stations, probably as a result of both, more vertical levels in this scheme (50 vs. 34 levels), and the use of the topo_wind option.

## 5. CONCLUSION

In this paper, an evaluation of WRF 10 m wind speed, wind gust and wind direction forecasts were performed by comparing them with data from eight automatic weather stations widely spread across the province of Córdoba (Argentina). The stations dataset used span a whole year from June 1, 2019 to June 1, 2020. The WRF forecasts used in this work correspond to four operative models (WRF-A, WRF-B, WRF-C and WRF-D), and a test model named WRF-E that aims to correct the high wind speed BIAS seen in WRF. This new model implements more vertical levels than the operative models (50 vs. 34 levels), and activates the topo_wind option.

The correlation coefficient showed a similar behavior among operative models. The RMSE shows that model WRF-A has a higher value than the other models (Fig. 3) in almost all stations. The analysis of BIAS shows that the simulated wind speeds have positive BIAS with respect to the wind measured in most stations. Model WRF-A presents a greater positive BIAS than the other models used in this work including WRF-E. It is important to note that the new model WRF-E produces less biased wind speeds, which is an objective of this work, however when the BIAS of operative models is negative, WRF-E tends to increase the negative BIAS. The similarities in RMSE and BIAS observed in models WRF-B, WRF-C and WRF-D are probably a consequence of the physical configuration used in these models. In fact, they use Yonsei University PBL scheme while model WRF-A uses MYJ PBL scheme. Results suggest that there is no significant difference in wind speed statistical parameters between 06 and 18 UTC runs.

The analysis performed in wind direction shows that WRF has a higher forecast accuracy when wind speed is high (≥ 5 m/s). In contrast, the forecast quality is worse for low wind speeds (Fig. 5). The values of wind direction RMSE range from 40° to 60° for most stations. The BIAS analysis indicates that WRF has a counterclockwise BIAS in wind direction forecast (~-20°). There are no significant differences in RMSE and BIAS between operative models and test model WRF-E. This fact could indicate that wind direction forecast is insensitive to the different parameterization schemes. Possibly, the wind direction forecast may be more dependent on model representation of topography rather than on model physical configuration. The WRF-E model improves the wind speed forecast compared to the operative models because there is a significant reduction of positive BIAS and RMSE in wind speed forecast in most stations. Unfortunately, the correlation results of WRF-E are generally worse than those presented by the operational model forecasts.

In this work, a gust wind forecast algorithm was implemented and subsequently evaluated. In order to perform a statistical analysis of wind gust forecast, Eq. (6) was applied to the 1-year dataset of WRF operative models and WRF-E test model. Results show that the correlation coefficient values associated with the wind gust forecasts are between 0.3 and 0.6. RMSE values associated with WRF-E model are between 3 and 5 m/s and does not show significant variations with respect to the operational models. Model WRF-E shows a significant improvement of BIAS with respect to the operational models for most stations possibly due to the use of topo_wind option.

According to results, WRF-E model reduces BIAS of wind speed and wind gust forecasts compared to operative models. Therefore, its use is recommended to achieve wind speed and wind gust simulations less biased. However, it is necessary to study whether the computing time demanded on the WRF-E simulation justifies the less biased results achieved. On the other hand, it is advisable to explore finer horizontal resolutions and better terrain representation in order to reduce wind speed, wind gust and wind direction RMSE in the province of Córdoba.

## DECLARATION OF COMPETING INTEREST

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

The authors would like to thank OHMC (Observatorio Hidrometeorológico de la Provincia de Córdoba) for providing the necessary resources to carry out this research.

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• Feroz, R.M.A., Javed, A. (2021) Forecasting of wind resources using the weather research and forecasting software. 2021 International Bhurban Conference on Applied Sciences and Technologies (IBCAST), IEEE, pp. 726-729. [https://doi.org/10.1109/IBCAST51254.2021.9393212]
• Jacondino, W.D., da Silva Nascimento, A.L., Calvetti, L., Fisch, G., Beneti, C.A.A., da Paz, S.R. (2021) Hourly day-ahead wind power forecasting at two wind farms in northeast brazil using WRF model. Energy, 230, 120841. [https://doi.org/10.1016/j.energy.2021.120841]
• Jiménez, P.A., Dudhia, J. (2012) Improving the representation of resolved and unresolved topographic effects on surface wind in the WRF model. Journal of Applied Meteorology and Climatology, 51(2), 300-316. [https://doi.org/10.1175/JAMC-D-11-084.1]
• Le Favi, D.N. (2020) Atlas climatico digital de la República Argentina. Temas de Biologia y Geologia del NOA, 9(3), 64-67.
• Manuel-Navarrete, D., Gomez, J.J., Gallopín, G. (2007) Syndromes of sustainability of development for assessing the vulnerability of coupled human-environmental systems. the case of hydrometeorological disasters in Central America and the Caribbean. Global Environmental Change, 17(2), 207-217. [https://doi.org/10.1016/j.gloenvcha.2006.07.002]
• Patel, P., Ghosh, S., Kaginalkar, A., Islam, S., Karmakar, S. (2019) Performance evaluation of WRF for extreme flood forecasts in a coastal urban environment. Atmospheric Research, 223, 39-48. [https://doi.org/10.1016/j.atmosres.2019.03.005]
• Politi, N., Nastos, P., Sfetsos, A., Vlachogiannis, D., Dalezios, N. (2018) Evaluation of the AWR-WRF model configuration at high resolution over the domain of Greece. Atmospheric Research, 208, 229-245. [https://doi.org/10.1016/j.atmosres.2017.10.019]
• Prósper, M.A., Otero-Casal, C., Fernández, F.C., Miguez-Macho, G. (2019) Wind power forecasting for a real onshore wind farm on complex terrain using WRF high resolution simulations. Renewable Energy, 135, 674-686. [https://doi.org/10.1016/j.renene.2018.12.047]
• Rodriguez, H., Lighezzolo, A., Martina, A., Zigarán, G., Viscardi, D.A.V., Rodriguez, A., Baudo, F., Scavuzzo, C.M., Bellis, L.M., Arganaraz, J.P. (2018) Towards the operational implementation of the fire weather index FWI based on the highresolution WRF model. 2018 IEEE Biennial Congress of Argentina (ARGENCON), IEEE, pp. 1-6. [https://doi.org/10.1109/ARGENCON.2018.8645974]
• Santos-Alamillos, F., Pozo-Vázquez, D., Ruiz-Arias, J., Lara-Fanego, V., Tovar-Pescador, J. (2013) Analysis of WRF model wind estimate sensitivity to physics parameterization choice and terrain representation in Andalusia (southern Spain). Journal of Applied Meteorology and Climatology, 52(7), 1592-1609. [https://doi.org/10.1175/JAMC-D-12-0204.1]
• Schumacher, R.S., Hence, D.A., Nesbitt, S.W., Trapp, R.J., Kosiba, K.A., Wurman, J., Salio, P., Rugna, M., Varble, A.C., Kelly, N.R. (2021) Convective-storm environments in subtropical South America from high-frequency soundings during RELAMPAGO-CACTI. Monthly Weather Review, 149(5), 1439-1458. [https://doi.org/10.1175/MWR-D-20-0293.1]
• Singh, I., Nesbitt, S.W., Davis, C.A. (2019) Initiation of deep moist convection over the sierras de Córdoba mountains in Argentina. AGU Fall Meeting Abstracts, 2019, A53U-3043.
• Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Liu, Z., Berner, J., Wang, W., Powers, J.G., Duda, M.G., Barker, D.M., Huang, X.Y. (2019) A description of the advanced research WRF model version 4. National Center for Atmospheric Research: Boulder, CO, USA 145.
• Wang, Q., Luo, K., Yuan, R., Zhang, S., Fan, J. (2019) Wake and performance interference between adjacent wind farms: Case study of Xinjiang in China by means of mesoscale simulations. Energy, 166, 1168-1180. [https://doi.org/10.1016/j.energy.2018.10.111]

### Fig. 1.

WRF domain used in this work (D01), the region topography and the location of automatic weather stations.

### Fig. 2.

Pearson correlation coefficient calculated at 06 UTC (upper panel) and difference CC 06 UTC-CC 18 UTC (lower panel).

### Fig. 3.

Root mean square error (RMSE) calculated at 06 UTC (upper panel) and difference RMSE 06 UTC-RMSE 18 UTC (lower panel).

### Fig. 4.

BIAS calculated at 06 UTC (upper panel), and difference BIAS 06 UTC-BIAS 18 UTC (lower panel).

### Fig. 5.

Difference between forecasted and measured wind direction vs measured wind speed. Each column of four scatter plots correspond to stations and rows correspond to models WRF-A, WRF-B, WRF-C, WRF-D and WRF-E. Red dots correspond to 06 UTC run and blue dots to 18 UTC run.

### Fig. 6.

Wind direction RMSE (upper panel) and BIAS (lower panel) for operative models WRF-A, WRF-B, WRF-C, WRF-D and test model WRF-E.

### Fig. 7.

Wind gust Pearson correlation coefficient (upper panel), RMSE (middle panel) and BIAS (lower panel) for OHMC operative models WRF- A, WRF-B, WRF-C, WRF-D and test model WRF-E.

### Table 1.

Description of parameterization schemes used operationally by WRF-OHMC.

Parameterization scheme References
A B C D
Micro Physics 8 4 6 5 4: Single Moment 5-class
5: Eta (Ferrier)
6: Single M. 6-c.
8: Thompson
Planetary
Boundary Layer
2 1 1 1 1: Yonsei University (YSU)
Shortwave
2 1 4 1 1: Dudhia Shortwave
2: Goddard Shortwave
4: RRTMG Sw and Lw
Longwave
1 1 4 1 1: RRTM Longwave
4: RRTMG Sw and Lw
Land Surface 2 2 2 2 2: Unified Noah LS Model
Surface Layer 2 1 1 1 1: Revised MM5
2: Eta Similarity

### Table 2.

Height of 34 levels used by WRF-OHMC.

 Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 24.1 m 79.1 m 149.2 m 238.4 m 351 m 491.5c Level 7 Level 8 Level 9 Level 10 Level 11 Level 12 664.8 m 875.8 m 1,129.0 m 1,427.9 m 1,774.6 m 2,169.7 m Level 13 Level 14 Level 15 Level 16 Level 17 Level 18 2,611.7 m 3,097.1 m 3,624.7 m 4,196.3 m 4,814.1 m 5,481.9 m Level 19 Level 20 Level 21 Level 22 Level 23 Level 24 6,205.4 m 6,987.6 m 7,829.2 m 8,731.5 m 9,657.9 m 10,570.2 m Level 25 Level 26 Level 27 Level 28 Level 29 Level 30 11,472.8 m 12,375.9 m 13,285.9 m 14,200.4 m 15,114.3 m 16,024.4 m Level 31 Level 32 Level 33 Level 34 16,927.5 m 17,822.9 m 18,714.7 m 19,607.6 m

### Table 3.

Description of parametrization schemes used by WRF-E.

WRF-E
Micro Physics 10 (Morrison 2-moment Scheme)
Planetary Boundary Layer 1 (Yonsei University)


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# 3rd order Runga Kutta method agrees with Taylor Series up to terms of order $h^3$?

Consider the initial value problem: $$y(0) = 1, y ′ (t) = λy(t)$$

Using that the solution is $y(t) = e^{λt}$, write out a Taylor series for $y(t_{i+1})$ about $y(t_i)$ up to terms of order $h^4$ (note: use that $h = t_{i+1} − t_i$).

Write out what the RK32 method would be for this problem. Show that it agrees with the Taylor Series expansion up to terms of order $h^3$.

I have determined the Taylor series for $y(t_{i+1})$ about $y(t_i)$ as

$$y(t_i) + \lambda y(t_i)h + \frac{1}{2}\lambda^2 y(t_i)h^2 + \frac{1}{3!}\lambda^3 y(t_i)h^3 + \cdots$$

But I am not able to write out the equation in RK3-2 form

RK3-2 is defined as

$k_1 = f(t_i, y_i)$

$k_2 = f(t_i + \frac{1}{2}h, y_i + \frac{1}{2}hK_1)$

$k_3 = f(t_i + h, y_i - hk_1 + 2hK_2)$

$y_{i+1} = y_i + h(\frac{1}{6}k_1 + \frac{4}{6}k_2 +\frac{1}{6}k_3)$

How can I show that the RK3-2 method agrees with the Taylor expansion up to terms of order $h^3$?

-

In your case $f(t,y)=\lambda y$ so

$k_1 = \lambda y_i$

$k_2 = \lambda (y_i+\frac{1}{2}h \lambda y_i)$

$k_3 = \lambda (y_i-h\lambda y_i+2h \lambda (y_i+\frac{1}{2}h \lambda y_i))$

Expand the formula for $y_{i+1}$ and you'll get exactly the Taylor expansion in $y_i$ up to order 3.

-

Let's compute what $k_i$ are in terms of $y$ and $t$:

$$k_1 = \lambda y(t_i)$$ $$k_2 = \lambda \left(y\left(t_i\right)+\frac{h}{2} k_1\right) = \lambda \left(y\left(t_i\right)+\frac{h}{2}\lambda y\left(t_i\right)\right)$$ $$\vdots$$

Plug these into your RK formula $y_{n+1} = y_n +\sum_{i=1}^k b_ik_i$ and you should be able to show agreement (it's a bunch of tedious algebra, mostly).

-
This agrees with Beni's answer, who got it right much faster than me! –  Arkamis Nov 16 '12 at 17:31
But in $k_2$, the $t_i$ term is actually $t_i + \frac{1}{2}h$. So why have you got $y(t_i)$ instead of $y(t_i + \frac{1}{2}h)$? –  sonicboom Nov 16 '12 at 17:34
No, you only replace $t$ with $t_i+\frac{1}{2}h$ when $t$ appears explicitly. In $k_2$, you replace $y$ with $y_i+\frac{1}{2}hk_1$. The important thing to note is you replace it with a $y_i$, and $y_i = y(t_i)$. –  Arkamis Nov 16 '12 at 17:42

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4.1k views

Let $G=(V,E)$ be a directed graph where $V$ is the set of vertices and $E$ the set of edges. Then which one of the following graphs has the same strongly connected components as $G$ ?

1. $G_1$ = $(V,E_1)$ where $E_1 = \left\{(u,v) \mid (u,v) \notin E\right\}$
2. $G_2$ = $(V,E_2)$ where $E_2 = \left\{(u,v) \mid (v,u) \in E \right\}$
3. $G_3$ = $(V,E_3)$ where $E_3 = \{(u,v) \mid$ there is a path of length $\leq2$ from $u$ to $v$ in $E\}$
4. $G_4$ = $(V_4,E)$ where $V_4$ is the set of vertices in $G$ which are not isolated
in DS
recategorized | 4.1k views
+4
Both B & C seem true.
0

0
Updated ..that was a typo
0
What is strongly connected component?
0

strongly connected component means, if there is a path exists between all the vertices of the component

https://www.geeksforgeeks.org/strongly-connected-components/

(A) is false. Consider just two vertices connected to each other. So, we have one SCC. The new graph won't have any edges and so $2$ SCC.

(B) is true. In a directed graph an SCC will have a path from each vertex to every other vertex. So, changing the direction of all the edges, won't change the SCC.

(D) is false. Consider any graph with isolated vertices- we loose those components.

(C) is a bit tricky. Any edge is a path of length $1$. So, the new graph will have all the edges from old one. Also, we are adding new edges $(u,v)$. So, does this modify any SCC? No, because we add an edge $(u,v)$, only if there is already a path of length $<= 2$ from $u$ to $v$- so we do not create a new path.  So, both (B) and (C) must answer, though GATE key says only B.

by Veteran (420k points)
edited by
0
@arjun sir

When the original graph has a strongly connected component which includes isolated vertex

then option C fails

because length <=2 and therefore also includes path length =0 and will give rise to a path which is not there in the original, thereby changing the number of strongly connected components
+2

@A_i_\$_h : If the oath do not exist then path length would be undefined/infinity. If we take zero then shortest path wont work.

Remember ,if we apply dijkstra/bellman ford on graph and it has isolated vertex,then path would be not defined.If you define it as zero then it would report 0 length path,which is wrong

0
@rahul

yea valid one :)
+7

@From cormen

0

@Arjun Sir
Pls check: If there is a path of length ≤ 1 from u to v in E, still the SCC will be same as in G right?

0

G3 = (V,E3) where E3={(u,v)∣ there is a path of length ≤2  from u to v in E}

What is options are like

G3 = (V,E3) where E3 = {(u,v) such that there is A PATH from u to v in E}

as in original G ..u and v are connected ..here in G3 also they will be connected and does it add any new SCCs in G3 ???

0
yes of course. SSC won't change here..
0

@sushmita....how can C true they already mentioned it is directed graph....if you add atmost 2 length path from U to V  then how can you say that it is also V to U.....if it is corrected then i am missing something.

0

Arjun sir...

the explaination you have given in proving the option A) is false is true iff G is an undirected graph...

But G is directed..

i am not saying option A) is the answer...its obviously B)..but the reason you have written for A) is wrong i think..

SORRY IT HAS BEEN UPLOADED UPSIDE DOWN..

THANKS..

+1

@blackcloud

Arjun sir's explanation is correct, he has considered a graph which is different from your example, in which there is an edge from vertex 1 to vertex 2, as well as from 2 to 1, that's how there's only 1 SCC in G, and then applying option A gives 2 SCCs

Also, even a directed graph can have 2 edges between 2 vertices (from 1 to 2 and from 2 to 1). Even though it's equivalent to an undirected graph with vertices 1 and 2, it can still be considered as a directed graph.

A. Can be eliminated as if the component is strongly connected in E then it will not be strongly connected in E's complement.

B.This is reversing the directions of the edges. When a triangle is considered for instance, where the directions are such that it will form a cycle, on reversing these directions the triangle will no more be strongly connected as there will be a vertex from which we cant reach out to any other vertex.

C.This is mostly the answer as according to the condition the number of edges in E3 will be those present in E and also additional edges which connect all U to all V such that UV<=2. Hence the connected component will stay connected.

D.V4 has only single vertices ,i.e those which were isolated in G and no edges will be present between them.
by Active (1.2k points)
+7
Your counter example for (B) is not correct. When we reverse the direction of all edges, it again forms a cycle rt- in reverse direction?
0
doubt: (D) also seems correct.. V4 is set of of vertices which in G which are not isolated. Anyways those isolated vertices makes no contribution in strongly connected component.. so even if we choose  those or not the graph gonna  have the same connected component as that of G... Isn't it..??

So (B) and (D) both seems correct..??
+1
As per official answer GATE 2014 answer key it is B. Also counter example for B is incorrect.
0
Consider the graph G to be containing 3 nodes, wherein we have 2 edges - 1 between the 1st and the 2nd nodes and the other edge between the 2nd and the 3rd nodes.

Now, for (C), we'll get a graph wherein, an edge has been constructed between the 1st and the 3rd nodes, thus we will be getting a SCC in this modified graph, whereas we didn't have any in the origina graph.

Hence, (C) can be eliminated.

1
2


text:
## Pragmatic Semiotic Information • Discussion 8

Re: Ontolog ForumJS

The concept of a triadic sign relation, in typical form $L \subseteq O \times S \times I,$ where $O$ is the object domain (think universe of discourse) and $S$ and $I$ are domains of signs (think channels or languages) being used to talk and think about $O,$ is most often applied in one of two ways.

1. $S$ and $I$ are really the same channel, language, medium, set of signs, or state space of a system we are using to convey information about $O.$  In cases where $S = I$ we are often concerned with transformations taking place within a single set of signals and we may write $I = S^\prime$ to signify our focus on sign relational triples of the form $(o, s, s^\prime)$ where $s^\prime$ is a sign that follows $s$ in a logical or temporal sequence, in short, where $s^\prime$ is contemplated as a next state of $s.$
2. $S$ and $I$ are two different channels, languages, media, sets of signs, or state spaces of systems being used to convey information about $O.$  In this case the issue is one of translation or interoperability.

### Reference

• Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

## Pragmatic Semiotic Information • Discussion 7

Re: Ontolog ForumJS

JS:
It appears to me that it is very difficult to fully grasp the fundamental issues associated with pragmatic semiotic information when the natural language of the individual conducting the inquiry is the main object of study.

That one took me a double take but if I take the when clause as a hypothetical condition and not the assertion of a fixed intention then I’d naturally agree:

IF
The natural language of the individual conducting the inquiry is the main object of study
THEN
It is very difficult to fully grasp the fundamental issues associated with pragmatic semiotic information.

It is well worth the candle to reflect on the properties of our embedding languages but we normally meet with limited, partial, and well-circumscribed success on any given trial.  That is why we study formalized object languages as microcosms of our yet unformalized semiotic contexts.

### Reference

• Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

## Where Is Fancy Bred? • Comment 1

A species in progress, with its naturally evolved organs of sensitivity, effectivity, and discernment, in its trials to learn the properties of its environment, cannot be expected to know in advance the full dimensionality of the space it inhabits on a mundane basis and through which it charts its eventual evolution.

An adaptive mutation in one of those capacities will expand its grasp of its environment into a larger space of states.

## Pragmatic Semiotic Information • Discussion 6

Re: Ontolog ForumJS

The subject of natural languages and their relation to formal languages, for example, logical calculi, logical graphs, mathematical formalisms, and programming languages, has come up periodically in our discussions and I’ve been struggling to arrive at something both cogent and coherent to say about it.  But what the heck, here’s a few thoughts off the cuff.

We naturally use our mother tongues as metalanguages to talk among ourselves in fora like these, not only about well-formalized object languages but also about the object domains that supply them with semantic substance, in a word, “meaning”.  Nothing about that makes “the natural language of the individual conducting the inquiry … the main object of study”.  At least, that is not how I’d personally understand the task at hand.

I began using the run-on formula “pragmatic-semiotic point of view” during a few exchanges with Bruce Schuman and John Sowa as a way of alluding to the line of thinking about signs stretching from Aristotle to Peirce, Dewey, and pragmatists of that stripe.  Here’s a link to my blog rehash of that episode:

To be continued …

### Reference

• Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

## Pragmatic Semiotic Information • Discussion 5

Re: Ontolog ForumAA

Of course it’s not that simple.  I called it a cornerstone not a whole building but it gives us a starting point and a first approach to a pragmatic semiotic architecture still being built as we speak.

There is more detail and a trace of semiotic’s later development in this paper:

• Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

We began by quoting the founding paragraph from Aristotle:

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche);  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the mental affections themselves, of which these words are primarily signs (semeia), are the same for the whole of mankind, as are also the objects (pragmata) of which those affections are representations or likenesses, images, copies (homoiomata).  (Aristotle, De Interp. i. 16a4).

We used the following Figure to highlight the structure of the triadic relation among objects (pragmata), affections or impressions (pathemata), and symbols or signs (symbola, semeia) as given in Aristotle’s account:

Figure 1.  The Sign Relation in Aristotle

The triadic nexus marked “R” in the Figure is what graph theorists call a node or point of degree 3 and it provides a graphical picture of a relational triple that may be taken in any convenient order so long as we keep it constant throughout a given discussion.  For example, we could take Aristotle’s object, sign or symbol, and impression in the order $(o, s, i),$ mostly just because I find that convenient in later developments.

Diagrams of that sort, whether triangular or tri-radial in form, have long been in common use for conveying the properties of triadic sign relations.  But I have discovered to my dismay over the intervening years that people tend to be led astray by pictures like that, often getting stuck on square one, or rather triangle one.  That is, they get stuck on single triples of sign relations rather than grasping them as they should, as prototypical examples of a whole class of ordered triples.

## Pragmatic Semiotic Information • Discussion 4

Measurement is an extension of perception.  Measurement gives us data about an object system the way perception gives us percepts, which we may consider just a species of data.

If we ask when we first became self-conscious about this whole process of perception and measurement, I don’t know, but Aristotle broke ground in a very articulate way with his treatise On Interpretation.  Sense data are impressions on the mind and they have their consensual, communicable derivatives in spoken and written signs.  This triple interaction among objects, ideas, and signs is the cornerstone of our contemporary theories of signs, collectively known as semiotics.

## Differential Logic, Dynamic Systems, Tangent Functors • 1

People interested in category theory as applied to systems may wish to check out the following article, reporting work I carried out while engaged in a systems engineering program at Oakland University.

The problem addressed is a longstanding one, that of building bridges to negotiate the gap between qualitative and quantitative descriptions of complex phenomena, like those we meet in analyzing and engineering systems, especially intelligent systems endowed with a capacity for processing information and acquiring knowledge of objective reality.

One of the ways this problem arises has to do with describing change in logical, qualitative, or symbolic terms, long before we grasp the reality beneath the appearances firmly enough to cast it in measured, quantitative, real number form.

Development on the quantitative shore got no further than a Sisyphean beachhead until the discovery/invention of differential calculus by Leibniz and Newton, after which things advanced by leaps and bounds.

And there’s our clue what we need to do on the qualitative shore, namely, to discover/invent the missing logical analogue of differential calculus.

With that pre-ramble …

• Differential Logic and Dynamic Systems

This article develops a differential extension of propositional calculus and applies it to a context of problems arising in dynamic systems.  The work pursued here is coordinated with a parallel application that focuses on neural network systems, but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.


text:
## Borisov, V. M.

Compute Distance To:
 Author ID: borisov.v-m Published as: Borisov, V. M.
 Documents Indexed: 23 Publications since 1964 Co-Authors: 8 Co-Authors with 18 Joint Publications 29 Co-Co-Authors
all top 5

### Co-Authors

 4 single-authored 7 Mikhajlov, I. E. 4 Ivankov, A. A. 4 Litvinovich, A. S. 2 Finchenko, V. S. 1 Bosov, Alexey V. 1 Golomazov, M. M. 1 Kurilenko, Yu. V. 1 Lyul’ka, V. A. 1 Shipilin, A. V. 1 Stefanovich, Aleksei Igorevich
all top 5

### Serials

 7 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 6 U.S.S.R. Computational Mathematics and Mathematical Physics 3 Computational Mathematics and Mathematical Physics 1 Fluid Dynamics 1 Automation and Remote Control 1 PMM, Journal of Applied Mathematics and Mechanics
all top 5

### Fields

 19 Fluid mechanics (76-XX) 5 Numerical analysis (65-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Optics, electromagnetic theory (78-XX) 1 Partial differential equations (35-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

7 Publications have been cited 11 times in 7 Documents Cited by Year
On maximum thrust nozzles with arbitrary isoperimetric conditions. Zbl 0133.20001
Borisov, V. M.; Shipilin, A. V.
1964
The optimization of the supersonic parts of three-dimensional nozzles. Zbl 0527.76052
Borisov, V. M.; Mikhajlov, I. E.
1981
Calculation of radiation heat transfer in problems of flow past bodies with account for heat-shield coating mass loss. Zbl 1184.76709
Borisov, V. M.; Golomazov, M. M.; Ivankov, A. A.; Finchenko, V. S.
2004
Calculation of radiative-energy transfer in hypersonic flow round blunt bodies using $$P_ 1$$- and $$P_ 2$$-approximations of the method of spherical harmonics. Zbl 0777.76066
Borisov, V. M.; Ivankov, A. A.
1992
The method of characteristics for calculating three-dimensional supersonic irrotational flows. Zbl 0457.76048
Borisov, V. M.; Mikhajlov, I. E.
1979
Computation of the radiative heat flux for a reentry vehicle flying in Venus atmosphere. Zbl 1078.85502
Borisov, V. M.; Ivankov, A. A.; Finchenko, V. S.
2002
Minimax estimation in systems of observation with Markovian chains by integral criterion. Zbl 1231.93109
Borisov, V.; Bosov, A. V.; Stefanovich, A. I.
2011
Minimax estimation in systems of observation with Markovian chains by integral criterion. Zbl 1231.93109
Borisov, V.; Bosov, A. V.; Stefanovich, A. I.
2011
Calculation of radiation heat transfer in problems of flow past bodies with account for heat-shield coating mass loss. Zbl 1184.76709
Borisov, V. M.; Golomazov, M. M.; Ivankov, A. A.; Finchenko, V. S.
2004
Computation of the radiative heat flux for a reentry vehicle flying in Venus atmosphere. Zbl 1078.85502
Borisov, V. M.; Ivankov, A. A.; Finchenko, V. S.
2002
Calculation of radiative-energy transfer in hypersonic flow round blunt bodies using $$P_ 1$$- and $$P_ 2$$-approximations of the method of spherical harmonics. Zbl 0777.76066
Borisov, V. M.; Ivankov, A. A.
1992
The optimization of the supersonic parts of three-dimensional nozzles. Zbl 0527.76052
Borisov, V. M.; Mikhajlov, I. E.
1981
The method of characteristics for calculating three-dimensional supersonic irrotational flows. Zbl 0457.76048
Borisov, V. M.; Mikhajlov, I. E.
1979
On maximum thrust nozzles with arbitrary isoperimetric conditions. Zbl 0133.20001
Borisov, V. M.; Shipilin, A. V.
1964
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### Cited by 8 Authors

 2 Kraiko, A. N. 2 Tillyaeva, N. I. 1 Ivankov, A. A. 1 Krajko, A. A. 1 Krajko, Aleksandr Nikolaevich 1 Mikhailov, I. E. 1 Osipov, Alexander A. 1 P’yankov, K. S.

### Cited in 3 Serials

 4 Journal of Applied Mathematics and Mechanics 2 Fluid Dynamics 1 Computational Mathematics and Mathematical Physics

### Cited in 4 Fields

 7 Fluid mechanics (76-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX)