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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.

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.

Fig. 1. 
WRF domain used in this work (D01), the region topography and the location of automatic weather stations.

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.

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.

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:

where Δw_i=W_sim,i-W_obs,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:

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

where variables with over bar indicate average value.

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):

where θ_sim , θ_obs 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°.

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).

An important objective of this paper is the implementation and evaluation of a wind gust forecast W_G. 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).

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

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%.

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. 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.

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.

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.

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.

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.

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.

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.