Sky View Factor and Screening Impacts on the Forecast Accuracy of Road Surface Temperatures in Finland

Virve Karsisto aFinnish Meteorological Institute, Helsinki, Finland

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Matti Horttanainen aFinnish Meteorological Institute, Helsinki, Finland

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Abstract

Forecasting road conditions is important, especially in areas with wintry conditions and rapidly changing weather. Accurate forecasts help authorities keep roads safe and optimize maintenance. Considering local features is important when making the forecast because the road surface temperature can vary significantly depending on the road surroundings. For example, in a shadowed location, the road surface temperature can be significantly lower than in open surroundings. A road weather model developed at the Finnish Meteorological Institute is used to forecast the road surface temperature and road conditions. However, the model still assumes open road surroundings. In this study, sky view factor and screening are included in the model, and their effects on the forecast road surface temperature is tested. Road surface temperature hindcasts were performed for 23 selected road weather stations in Finland for three winter periods (October–March) between 2018 and 2021. The results were location dependent, and even changing the lane had a great effect on the verification results in some cases. At best, the screening considerably decreased RMSE values during the day. However, there were many cases in which the screening increased RMSE. In general, the used shadowing algorithm increased the already negative bias during the day. Nevertheless, there were also cases in which the shadowing algorithm improved the bias, especially in February. During the night, the sky view factor made the forecast generally a little warmer, which often slightly decreased the negative bias in the forecast.

Significance Statement

The screening caused by objects surrounding a road has a great effect on the road surface temperature. Recently, a screening algorithm was added to the Finnish Meteorological Institute’s model that forecasts road conditions. The purpose of this study was to test how the algorithm affects the accuracy of road surface temperature forecasts. According to the results, the screening greatly improved the forecast accuracy in some cases. However, in some cases, the screening made the already overly cold forecast even colder. The study has increased our understanding of the effect of shadowing in the modeled road surface temperatures and helps to create more accurate forecasts in the future.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Virve Karsisto, virve.karsisto@fmi.fi

Abstract

Forecasting road conditions is important, especially in areas with wintry conditions and rapidly changing weather. Accurate forecasts help authorities keep roads safe and optimize maintenance. Considering local features is important when making the forecast because the road surface temperature can vary significantly depending on the road surroundings. For example, in a shadowed location, the road surface temperature can be significantly lower than in open surroundings. A road weather model developed at the Finnish Meteorological Institute is used to forecast the road surface temperature and road conditions. However, the model still assumes open road surroundings. In this study, sky view factor and screening are included in the model, and their effects on the forecast road surface temperature is tested. Road surface temperature hindcasts were performed for 23 selected road weather stations in Finland for three winter periods (October–March) between 2018 and 2021. The results were location dependent, and even changing the lane had a great effect on the verification results in some cases. At best, the screening considerably decreased RMSE values during the day. However, there were many cases in which the screening increased RMSE. In general, the used shadowing algorithm increased the already negative bias during the day. Nevertheless, there were also cases in which the shadowing algorithm improved the bias, especially in February. During the night, the sky view factor made the forecast generally a little warmer, which often slightly decreased the negative bias in the forecast.

Significance Statement

The screening caused by objects surrounding a road has a great effect on the road surface temperature. Recently, a screening algorithm was added to the Finnish Meteorological Institute’s model that forecasts road conditions. The purpose of this study was to test how the algorithm affects the accuracy of road surface temperature forecasts. According to the results, the screening greatly improved the forecast accuracy in some cases. However, in some cases, the screening made the already overly cold forecast even colder. The study has increased our understanding of the effect of shadowing in the modeled road surface temperatures and helps to create more accurate forecasts in the future.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Virve Karsisto, virve.karsisto@fmi.fi

1. Introduction

The surroundings of a road point can have a significant effect on the road surface temperature (RST). Mountains, buildings, and trees block direct solar radiation and cause the RST to be lower than in open surroundings. On the other hand, they also emit longwave radiation and have a warming effect on the surface on clear nights. Taking these features into account is important when forecasting the RST. According to Bogren et al. (2000), the surface temperature variations between screened and sun-exposed sites can be of considerable magnitude. There can be severe forecast error on the shadowed parts of the road network if the forecast is made with an assumption about open surroundings. Timely and spatially accurate RST forecasts are important for road maintenance action optimization. For example, salt should be spread on the road before the RST drops below 0°C to prevent ice formation. This keeps road friction at a safe level and lowers maintenance costs and environmental impacts, as more salt would be needed to melt the ice when it has already formed (Thornes 1991). In addition, the treated road stretches can be selected more carefully with accurate forecasts to avoid salting locations that are not likely to freeze.

Numerical weather prediction (NWP) models produce large-scale weather forecasts. However, their grid size can be several kilometers and only account for large-scale terrain effects. Road condition forecasts are made with specialized 1D road weather models (RWMs). They use data from NWP models as input and include detailed heat-balance calculations to determine the RST and the amount of water, ice, and snow on the road. One such model is the Finnish Meteorological Institute (FMI) RWM (Kangas et al. 2015). Thus far, the physics considering road surroundings have not been included in the operational FMI RWM, although there have been some experiments. The terrain in Finland is relatively flat, so there is no need to consider effects caused by mountains or deep valleys. However, smaller-scale features like buildings and trees should be included in the model to obtain better forecast accuracy.

In this study, two parameters were used to modify the radiation received by the road surface. Sky view factor (SVF) is defined as the fraction of the radiation flux reaching the surface from the radiation flux of the entire hemisphere (Johnson and Watson 1984). SVF is 0 when the sky is fully obscured and 1 if the sky is fully visible. The second parameter is local horizon angle (LHA), which means the angle between the flat surface at the observer’s location and the visible horizon. If the solar elevation angle is lower than the LHA in the direction of the sun, the point is in shadow.

There are several approaches to determine SVF and LHA. The traditional method is to use photographs that are taken with a fish-eye lens and show a 360° view of the location. First, the pixels presenting the sky are delineated from the image. Then, SVF and local horizon angles are calculated based on the derived horizon. Several techniques have been developed for this process (Steyn 1980; Holmer 1992; Chapman et al. 2001a). In recent years, machine learning methods have also been used to delineate the sky pixels from the image (Liang et al. 2017). A disadvantage of fish-eye photographs is that they are not always available at the location of interest. However, Google Street View (Anguelov et al. 2010) provides an interesting option to get fish-eye images from road points. Determining SVF from Google Street View images has been studied by Liang et al. (2017) and Middel et al. (2018), for example, with positive results. Using the Google Street View images would be a feasible solution in Finland, where data coverage is high. However, the images are taken from the top of the vehicle rather than at road level, which might cause some inaccuracy because the local horizon angles are lower than at the road surface.

Digital elevation models (DEMs) and digital surface models (DSMs) are other widely used data sources to determine SVF and LHA. DEM and DSM are raster formats, in which each pixel represents height. The DEM presents bare terrain without buildings and vegetation, whereas they are included in the DSM (Jiao et al. 2019). The resolution of the DSM needs to be high to present trees and buildings with sufficient accuracy (Matzarakis and Matuschek 2011). The LHA can be simply determined from the raster data by finding the point in the given range that produces the highest horizon angle (Böhner and Antonić 2009). This is dependent on the search radius, which should be long enough to include all the relevant terrain features. There are several analytical equations to calculate SVF based on LHA (Jiao et al. 2019). An alternative method to determine SVF from the raster data is a shadow-casting algorithm (Ratti and Richens 1999; Gál et al. 2009). The SVFs calculated using DEM and DSM are not as accurate as those acquired with fish-eye photographs, but using the raster enables fast SVF calculation for large areas.

Some previous studies exist in which SVF and/or LHAs have been used to model the RST. Chapman et al. (2001b) and Kršmanc et al. (2014) used LHAs to determine whether the road point receives direct solar radiation. The direct solar radiation was set to zero if the road point was determined to be in shadow. Chapman et al. (2001b) determined LHAs from fish-eye photographs. They implemented the SVFs in an RWM by simply multiplying the radiation emitted by the road by the SVF. According to their study, the usage of geographical parameters improved the model ability to explain the RST differences along the route. However, the study included only 1 route and 20 thermal mapping surveys. Also, the study by Kršmanc et al. (2014) included only a few stations. Their study used a DEM to determine LHAs. Neither Chapman et al. (2001b) nor Kršmanc et al. (2014) implemented the effect of SVFs on incoming diffuse shortwave radiation.

Whereas the studied time periods have been short and the number of studied sites small in all the previous studies, the current effort covers 3 winters and 23 test sites. The main questions are: How does the use of SVF and LHA affect forecast RST at different times of the year, and do they improve the forecasts?

2. Data and methods

a. RWM

The purpose of the FMI road weather model is to predict road weather conditions by simulating the state of the surface. The surface state includes temperature and the amounts of water, ice, snow, and frost on the road. The model is one dimensional and calculates heat exchange between its 16 ground layers and heat balance at the surface. A detailed description of the model physics is given in appendix A, and additional information is provided by Kangas et al. (2015), Karsisto et al. (2017), and Karsisto and Lovén (2019).

As a 1D ground surface model, the FMI RWM does not calculate large-scale variations in weather. It requires atmospheric values as inputs to calculate energy fluxes. These values are air temperature, humidity, wind speed, precipitation, and incoming longwave (LW) and shortwave (SW) radiation (Table 1), which can be obtained either from observations or from a forecast made by NWP. Road surface temperature observations and precipitation phase values can also be used as input when available. Road surface temperature observations are used so that the temperature of the topmost layer in the RWM is set to the observed value at each time step during the initialization. In this study, net longwave radiation and direct shortwave radiation were also used as input values to take the screening and the sky visibility into account. Figure 1 shows different input data sources used in the study as a flowchart. The forecast air temperature and humidity values were from a 2-m model level, wind speed was from a 10-m model level, and precipitation and radiation values were from a 0-m model level.

Fig. 1.
Fig. 1.

Flowchart of different data sources and processes used in the study.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Table 1

FMI RWM input parameters and their units, data sources, and input frequencies used in this study. MEPS refers to the NWP model explained in more detail in section 2b.

Table 1

One road weather model run consists of two phases. The first is a two-day initialization phase where observations are used as input data sources. The meaning of the initialization phase is to get a good starting state for the ground temperature profile. In this study, the observations were obtained from selected road weather stations. Exceptions are radiation values and precipitation phase, which were obtained from NWP model data. After the initialization phase, there is a forecast phase that uses data from the NWP model as inputs. As the time step of the RWM is 30 s; all of the input values are interpolated to each time step. NWP forecast data are given as hourly values, so the model uses interpolated values to cover all 30-s time steps between the given input data points. In case of radiation, this is a little problematic because the input values describe the average radiation intensity over the previous hour. The raw NWP model radiation output consists of cumulative values (J m−2) for each hour, and the average intensity (W m−2) for the last hour is calculated by subtracting the current value from the previous value and dividing this by the number of seconds in the hour. Keeping the radiation value constant during each hour would lead to abrupt changes at the changing of the hour. Instead, the full-hour radiation values are set as the previous half-hour’s values, and interpolation is done after that. Precipitation values from the model were also considered as half-hour values.

The basic outputs of the model are road surface temperature (°C) and the storage terms (amounts of ice, snow, water, and deposit on the road as water-equivalent mm). The output surface temperature is calculated as the average of the two uppermost model layers. Based on these outputs, the model determines road conditions that can be, for example, dry, wet, or icy. The model also estimates overall driving conditions (normal, difficult, very difficult) and friction (Juga et al. 2013). The output values are calculated for every time step (30 s) in the model, and the user can define the output frequency. An output frequency of 1 h was used in this study as hourly values were used in the verification.

The model’s sensitivity to radiation was tested by Karsisto et al. (2016). They found that reducing incoming longwave radiation by 20 W m−2 over 1 h caused the road surface temperature to be about 0.36°C lower at the end of the hour. The change in road surface temperature was found to be rather linear when longwave radiation was altered within range from −100 to 100 W m−2. More sensitivity tests are presented in appendix B.

b. MEPS

MetCoOp Ensemble Prediction System (MEPS) is an ensemble prediction system developed by the High Resolution Limited Area Model (HIRLAM) consortium and is run in cooperation with the National Meteorological Institutes of Finland, Norway, and Sweden (Frogner et al. 2019). Ensemble prediction means that multiple different forecasts are generated to forecast the probability of events. Multiple forecasts are produced by running an NWP model several times with different settings and/or input datasets. These perturbations account for uncertainties, for example, for the initial conditions and model physics (Frogner et al. 2019). MEPS has a horizontal resolution of 2.5 km. Five ensemble forecasts with 66-h forecast length are produced each hour. Only data from the main forecast called the “control member” were used in this study. The control member is run eight times per day. In this study, the atmospheric variables from the control member runs launched at 0000, 0600, 1200, 1800 UTC were used as input data for the RWM. The local time in Finland is UTC + 2 h in winter and UTC + 3 h when daylight saving time is in effect. In Finland, daylight saving time starts on the last Sunday of March and ends on the last Sunday of October. The data were interpolated to the selected road weather station (RWS) points from the four surrounding grid points using bilinear interpolation, except for the precipitation phase, which was taken from the nearest grid point instead. Exceptions were Huittinen Korvenmaa RWS (Table 2; station 11) and Ranua Portimo RWS (Table 2; station 22), where interpolation points were a few kilometers off for forecasts done between 5 October 2018 and 26 January 2020 (10 km off for Huittinen RWS and 6 km off for Ranua RWS).

Table 2

Forecast points and the calculated SVFs.

Table 2

c. Road weather observations

In Finland there are about 400 RWSs. The stations are manufactured by Vaisala and maintained by Intelligent Traffic Management Finland Oy. The stations measure air temperature, humidity, wind speed, precipitation, road surface temperature, amounts of water ice and snow on the road, road state (e.g., dry, moist, ice), and friction. Instrumentation on the stations vary, but most measure road surface temperature with asphalt-embedded DRS511s (Vaisala 2021). The instrument consists of a solid block with properties that match the surface thermal conductivity and emissivity. A sensor measuring road surface temperature is located at the top of the block, flush with the surface. Optical Vaisala DST111s are used at some stations to measure road surface temperature (Vaisala 2021). It is often paired with optical DSC111s or DSC211s that measure friction (Vaisala 2017, 2021). Some stations have multiple road surface temperature sensors located on different lanes. Twenty-three RWSs were included in this study (Fig. 2; Table 2). RWSs in obscured locations were selected, as SVF has no effect in open surroundings. The observations from stations were used as RWM input and in the verification of the simulations. However, the same observations were not used to verify and initialize the same simulation.

Fig. 2.
Fig. 2.

Locations of studied RWSs (Table 2). Made with Natural Earth (https://www.naturalearthdata.com/).

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Some error is involved in RWS measurements, which is not considered in forecast verification. The reported accuracy of DRS511 surface temperature measurements is ±(0.1 + 0.001 67 × temperature) °C. The resolution of DST111 surface temperature measurements is 0.1°C, and they have an RMSE of 0.3°C (Vaisala 2021). This causes a small error in the verification results. Some quality checks were done for road surface temperature measurements before using them in forecast verification. First, unnatural spikes were removed from the data. If the temperature changed by 5°C or more within 20 min, the values were removed 1 h before and 1 h after the occurrence. Second, cases for which the road surface temperature was unnaturally constant were removed. The condition for this was that the temperature remained the same for more than four hours and there were at least five measurements. Last, values warmer than 50°C and colder than −50°C were removed from the data.

A time series with 1-h intervals was formed from the road weather station measurements for the forecast verification. Each value was selected by taking the nearest observation for each time step in case the time difference was not more than 15 min. Note that unmodified road weather observation data were still used in the initialization of the road weather model, because the model gets the observations directly from the FMI database.

d. Laser scanning data and DSM

DSMs of the road weather stations’ surroundings were created from laser scanning data (National Land Survey of Finland 2021a,b), which are freely available from the National Land Survey of Finland. The data were collected between 2008 and 2020, and there is an ongoing process of renewing the data for the whole of Finland at 5-yr intervals. The scans were done either in early spring when there was only a little snow and no leaves on the trees or in summer when the leaves were at full size. The mean distance between laser points is generally 1.4 m. The data are automatically classified by land use, but that information was not used in the calculation process. The data were downloaded from the IT Center for Science, Ltd. (CSC), Paituli data portal (https://paituli.csc.fi/download.html).

The laser data were processed using LAStools software (Isenburg 2020), created by M. Isenburg. The data were clipped around each road weather station as 250 m × 250 m squares to make the calculation faster. A method documented on the Rapidlasso website (Rapidlasso 2016) was used to produce smooth DSMs by removing possible errors and artificial spikes resulting from sparse lidar data. For example, flying objects like birds could cause errors in the DSM. In some cases, powerlines, roadside poles, or traffic signs caused unnaturally bulky shapes in the DSM, because the resolution was too coarse to present them accurately. If this kind of structure happened to be just next to the point where LHAs were calculated, even one-quarter of the horizon could be covered by it. Every DSM produced was manually checked, and these overly bulky features were smoothed from the vicinity of the forecast points to avoid erroneous shadowing.

e. SVFs and LHAs

Before SVFs and LHAs were calculated, the exact coordinates for the simulation points were determined. Unfortunately, the reported coordinates of RWSs were often vague and not always even on the road. Even if the coordinates were right, they were often located at the side of the road where the measurement pole is installed. The SVFs and LHAs are highly dependent on the location, so the selected coordinates should ideally present the point of the road surface temperature sensor. Usually at least one sensor is located on the road next to the measurement pole, so simulation points were manually selected to be in line with the pole across the road. For large roads, two simulation points were selected on different sides of the road, but for small roads only one point was determined. Exact coordinates are given with the used data in the FMI data repository “METIS” (Karsisto and Horttanainen 2022). As an example, Fig. 3 shows the DSM and the selected coordinate points at Espoo Kolmiranta RWS (Table 2; site 4).

Fig. 3.
Fig. 3.

The DSM determined from laser scanning data around Espoo Kolmiranta RWS and the selected coordinate points for the simulations.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Local horizon angles were determined using Grass software (Huld et al. 2007). The algorithm starts at a low angle and progresses along a line of sight, step by step. If the line of sight hits the terrain, the angle is increased so that the line of sight passes just above the terrain. This is continued until a predetermined maximum distance is reached or the line of sight reaches a height that is higher than any point in the region. The local horizon angles were determined this way using 1° steps in every direction.

Figure 4 shows an example of calculated local horizon angles for Espoo Kolmiranta RWS. The results for both lanes are shown separately. The terms “southern” and “northern” are used for simplicity, although “southwestern” and “northeastern” would be more accurate. The horizon angles in the road direction to the southeast and northwest are clearly lower than in the other directions for both points. In the southern lane, the trees are closer to the southwest, so the horizon angles are higher in that direction. In the northern lane, the trees are closer to the northeast, so the horizon angles are higher in that direction. The figure also shows the sun paths for 1 January, 1 February, and 1 March. In January and early February, the sun is not visible in either lane for most of the day. However, in early March, the sun is visible for much longer on the northern lane than on the southern lane. This causes considerable RST differences between the lanes.

Fig. 4.
Fig. 4.

LHAs at Espoo Kolmiranta RWS (Table 2; site 4) on the (left) southern and (right) northern lanes. The direction is shown on the outer perimeter so that north is at 0°. The inner circles show the angle between a flat horizon and the top of the sky. LHAs are shown as a blue line, and the visible sky is shown in light-blue color. Brown, red, and yellow lines show the sun elevation angles throughout the first days of March, February, and January, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

The SVFs were calculated with the equation proposed by Helbig et al. (2009) by assuming an isotropic diffuse radiation environment,
SVF=12π02πcos2ϑh(ϕ)dϕ1Ni=1Ncos2ϑh,i(ϕi),
where ϕ is the azimuth angle, ϑh(ϕ) is the angle between the inclined surface and the horizon direction at the azimuth angle, and N = 360. The summation was done in 1° steps, so inaccuracies caused by it are small. An isotropic radiation environment means that diffuse radiation is uniform across the sky. In reality this is not the case, but as the grid size of the input radiation data is just 2.5 km, the differences in diffuse radiation across the sky cannot be determined. Equation (1) is defined in a sloped coordinate system, but in this study, it has been simplified so that ϑh is redefined as the angle between the horizontal plane and the horizon direction, following the example of Jiao et al. (2019). Most of the studied points were not located on slopes, so this is a suitable assumption. Only Ikaalinen Teikangas (Table 2; site 13) was located on a slope, which might cause small errors in SVF. The calculated SVFs are presented in Table 2. The flowchart of the process to calculate local horizon angles and sky view factors is presented in Fig. 1. The SVFs determined from DSMs are not as accurate as what could be achieved with fish-eye photographs. However, calculating SVFs with DSMs is fast and easy for the whole road network, whereas taking fish-eye photographs would be time consuming. DSMs are thus used to calculate SVFs as a more suitable operational solution.

f. Radiation modification

The equations in this section describe how SVF and screening were implemented in the FMI RWM. The modeled radiation fluxes by the NWP were modified based on the SVF. The net shortwave radiation was calculated as (Senkova et al. 2007)
Snet=(1ar)[SVF×Sdif+(1SVF)Sref+Sdir],
where αr is the road surface albedo, δ is the sky view factor, Sdif is the diffuse shortwave radiation, Sref is the reflected shortwave radiation from surroundings, and Sdir is the direct solar radiation. The direct solar radiation was set to zero if the sun elevation was lower than the LHA in the direction of the sun. The road surface is assumed to be flat, so surface inclination was not taken into account. Most of the studied points were not located on slopes, so it did not cause much error. The assumption might have caused a small error in net shortwave radiation for the one station located on slope rising from northwest to southeast (Table 2; site 13, Ikaalinen Teikangas). The FMI RWM uses the albedo value of 0.1 for bare road surfaces, 0.6 for snow, and for ice it varies between 0.1 and 0.6 depending on the ice thickness. The age of the asphalt and moisture on the road were not taken into account, which causes some uncertainty in the albedo value. The reflected shortwave radiation means radiation that is reflected by the road surroundings and is calculated as
Sref=αs(Sdif+Sdir),
where αs is the albedo of the surroundings. In this study, αs was set to 0.15 as a suitable value for both deciduous and coniferous forest (Buchdahl 1999). At many of the studied stations this is a good approximation, as the reduced SVF was mostly due to vegetation, but, for example, at road points surrounded by rock cuttings with high albedo, this might cause underestimation of the SW radiation. Snow cover on trees during wintertime was not taken into account, which also causes some underestimation.
The net longwave radiation was calculated as (Senkova et al. 2007)
Lnet=SVF×Ld+(1SVF)LsLr,
where Ld is the downwelling longwave radiation from the atmosphere, Ls is the longwave radiation emitted by the road surroundings (buildings, vegetation, etc.), and Lr is the longwave radiation emitted by the road. The radiation emitted by the road is calculated as blackbody emission,
Lr=εσTr4,
where ε is emissivity, σ is the Stefan–Boltzmann constant, and Tr is the road surface temperature. In the RWM, radiative skin temperature has been approximated by thermodynamic temperature. This may cause an error of some tens of watts per square meter, especially when the road is covered with ice or snow. The used emissivity value was 0.95 (Kangas et al. 2015). In this study, the radiation from surroundings is obtained from the NWP model forecast as the average longwave radiation emitted by the surface. This causes some inaccuracies as the road surroundings might not match the average land use of the grid cell in the NWP. However, the variations in emissivity for different typical land covers in Finland are not very large. For example, the typical value for asphalt and concrete is 0.94 and for pine trees it is 0.98 (Wittich 1997). If the radiation from surroundings is not known, Ls could be roughly approximated to be equal to Lr so that the latter part of Eq. (4) becomes simply SVF × Lr as in Chapman et al. (2001b). However, this is not a good approximation in sunny situations, for example, where the RST is much higher than the temperature from the surroundings.

Note that if the NWP model used as an input data source for the RWM already takes into account the orographic effects they should not be included again in the RWM. The forecast atmospheric variables in this study (Table 1) were obtained from the MEPS model (Frogner et al. 2019), which does not include orographic effects in radiation calculation.

g. Model simulations

The FMI RWM was run both with and without SVF and LHA to study their effects on the forecast. The simulations that were done with SVF and LHA are thereafter referred to as “test” simulations and the simulations without them “reference” simulations. The model simulations were made to resemble real forecasts. The simulations consisted of a 48-h initialization phase where the model was forced with observations and a 24-h forecast phase where the forcing came from the MEPS forecast. Four separate RWM runs started each day. The forecast start times were 0300, 0900, 1500, and 2100 UTC. These used data from the 0000, 0600, 1200, and 1800 UTC MEPS runs, respectively. The simulations were done for three winter periods (October–March) starting October 2018 and ending in March 2021 for 23 selected RWSs in Finland (Table 2). In case the station had multiple RST sensors, the RWM was run multiple times using each of their data as forcing separately. As the exact locations of the RST sensors are not known and are not easily obtainable, the simulations were done separately for both sides of the road, except on the smaller roads where only one point was selected. For example, if a station had three sensors, this would mean six different forecasts in total. Although this makes interpreting the verification results more complicated, it also makes it possible to study how the results behave when the forecast point is in the wrong lane.

The coupling method was used before the forecast phase to adjust the radiation balance in the model (Karsisto et al. 2016). The aim of the coupling method is to make the modeled RST match the latest observed RST. A 3-h period at the end of the initialization phase is run iteratively using different correction coefficients for either short- or longwave radiation. The radiation correction coefficient is greater than 1 if the RST in the model is too low relative to the observed RST and is smaller than 1 if the RST is too high. The process is continued until the RST in the model is within 0.1°C of the observed RST. The radiation correction coefficient is used at the forecast phase so that it gradually approaches one as the forecast advances. Generally, the correction is used for the radiation variable that has the higher value at the start of the coupling period. Because the shadowing algorithm can cause abrupt changes in the shortwave radiation, the correction was always given to the longwave radiation in the simulations using SVFs and LHAs. The coefficient was applied to the total incoming longwave radiation after the SVF-related modifications. A detailed description of the coupling method is given by Karsisto et al. (2016).

h. Bootstrap method

The same bootstrap method as used by Karsisto and Lovén (2019), Efron and Tibshirani (1993), and Hogan and Mason (2011) was used to find if the difference between the forecast errors in the simulations were statistically significant. First, a sample of the dataset was generated with replacement, which means that the original dataset was sampled randomly so that original values could occur multiple times in the sample. The dataset in this case means the RST forecast observations pairs. The RMSE values were calculated separately for each station, each hour of the day, and each month over three winters (see section 3), so the number of pairs was about 90. The size of the generated sample was the same as that of the dataset. RMSE was calculated from each sample separately for test and reference simulations. The samples for these simulations contained the same forecast times to make the results comparable. After calculating the RMSE for the test and reference simulations, the difference between those values was calculated. The sampling process was repeated 1000 times, which is an appropriate number considering the dataset size. Then, 95% confidence intervals were calculated from the RMSE difference value distributions. The differences between the simulations were considered to be statistically significant with 95% confidence if zero was not in the obtained range.

3. Results

a. Example station

Figures 5 and 6 show examples of how RST verification results behave on different lanes at the Salo Lakiamäki station. The station is located on a four-lane motorway with rock cuttings on both sides of the road. Bias means the systematic error in the forecast and is calculated as
bias=i=1N(xf,ixo,i)N,
where xf,i is the forecast value, xo,i is the observed value, and N is the number of forecast cases. RMSE contains information of both random and systematic errors and is calculated as
RMSE=i=1N(xm,ixo,i)2N.
If there is no bias, then the RMSE is equal to the standard deviation. The results for the reference simulations are naturally the same for both lanes as they have the same input values. As the reference simulations do not take screening into account, the solar radiation causes the RST to increase too much during the daytime (Fig. 5). In the evening, the model cools too quickly, which causes negative bias. The positive bias is clearly reduced when SVFs and LHAs are included. However, most test simulations have negative bias instead. The northern lane is more exposed to solar radiation from the south, which causes the forecasts to be warmer during the day than on the southern lane. The verification results differ considerably between the sensors. It seems that sensor 1 is most exposed to the sun as it has the smallest positive bias during the daytime for the reference run and the most negative bias for the test run. Conversely, sensor 4 seems to be in the most shadowed location. It is difficult to say which sensors are the closest to the forecast point as the forecast error is caused by many factors. At later forecast hours during the nighttime, all the simulations have negative bias, but the test simulations have slightly more positive values. This indicates that the radiation from the surroundings causes the surface to be a little warmer at night, as expected.
Fig. 5.
Fig. 5.

Bias for the test (continuous lines) and the reference (dashed lines) simulations for 0300 UTC–started runs for Salo Lakiamäki station (Table 2; station 5) October 2018–20 for the (left) southern lane and (right) northern lane. The x axis shows time of day in Finnish wintertime (UTC + 2). Brown lines show results for simulations initialized and verified with RST sensor 1, light-brown lines show results with sensor 2, light-turquoise lines show results with sensor 3, and darker-turquoise lines show results with sensor 4.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Like bias, the RMSE varies considerably between lanes and sensors (Fig. 6). During the day, the test runs give lower RMSE values because of the screening algorithm in all cases expect for sensor 1 on the southern lane. As mentioned earlier, sensor 1 seems to be the most exposed to the sun, so reducing radiation caused the surface to be too cold. The forecasts using sensors 2 and 4 had lower RMSE values during the day for the southern lane than for the northern lane, but the forecasts using sensors 1 and 3 had better values for the northern lane. It seems that sensors 2 and 4 are in more shadowed locations than sensors 1 and 3. At the end of the forecast during the night, the test simulations give slightly lower RMSE values than the reference simulations, which might be because the radiation from the surroundings is included in the test simulations. As the bias values are in many cases more than 50% of the RMSE, a considerable part of the RMSE is caused by systematic error. If the systematic error were corrected using statistical methods, for example, the RMSE values would be considerably lower.

Fig. 6.
Fig. 6.

As in Fig. 5, but for RMSE.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

b. Bias

Figure 7 shows bias values of the test simulations started at 0300 UTC. The results are calculated using data from the three studied years for each month. The panels in Fig. 8 have scatterplots with results for the reference simulation on the x axis and for the test simulations on the y axis. In October and March, the test simulations have negative bias during the daytime (Fig. 7) for most of the stations. The daytime bias is clearly more negative for the test simulations than for reference simulations (Fig. 8). It appears that the use of SVFs and LHAs make what is already an overly cold daytime forecast even colder. However, during the daytime in February, the reference simulations often had positive bias, which was considerably reduced when SVFs and LHAs were used. Still, the difference varies considerably between stations. There is also variation between lanes, although at many stations both lanes behave rather similarly. During November, December, and January there is not much shortwave radiation, so the difference between simulations during the daytime is also smaller, but the test simulations still have more negative bias than the reference simulations (results from December and January are not shown).

Fig. 7.
Fig. 7.

Bias °C for the test simulations started at 0300 UTC in October, November, February, and March. The values are calculated over three winter periods from October 2018 to March 2021. The y axis shows for which station the simulation is performed (Table 2). The results are grouped so that the values for different stations are separated with continuous lines and values for different sensors are separated with dashed lines. The simulations for different lanes are on top of one another without a line. The x axis shows time of day in Finnish wintertime (UTC + 2).

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Fig. 8.
Fig. 8.

Scatterplots of bias °C values for the reference (x axis) and the test (y axis) simulations for (top left) October, (top right) November, (bottom left) February, and (bottom right) March. The values are calculated over three winter periods from October 2018 to March 2021. Each point represents data for one station–lane–sensor combination at a certain time of day. Different colors represent different times, given in Finnish wintertime (UTC + 2). The black line shows where the points would be if the values were equal. White background shows the area where the test simulation has a smaller absolute bias, and light-pink background shows the area where the reference simulation has a smaller absolute bias.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Åland Åva station (Table 2; station 9) stands out from the others by having positive bias values for the whole simulation during each month (Fig. 7). The station is located on a small island off the southwestern coast of Finland. The resolution of the MEPS model is too large to distinguish such small features, and the presence of the sea probably causes the forecast to be too warm at the RWS in the middle of the island. The station at the entrance of a tunnel at Vuosaari (station 2) also has distinguishable bias values from the rest of the stations with strong positive biases during the daytime in October and March. The station was selected because of the interesting location from the perspective of LHAs and SVFs, but the presence of the tunnel entrance probably affects the measurements. In addition, the tunnel leads to Vuosaari harbor, so heavy traffic can also disturb the measurements. According to the calculated LHAs, the forecast locations receive shortwave radiation for some time in the morning, but the actual sensors can be located so that it does not receive that much radiation, which would lead to positive bias in the simulations.

The test simulations have mostly negative bias during the nighttime in October, but there are also stations with slightly positive bias (Fig. 7). In November, many of the stations have positive bias during the night. The rest of the studied months have more variation between the stations. At station 2, the negative bias is much stronger than at other stations, but the entrance to the tunnel probably causes the measurements to be warmer than otherwise. During the night, the difference between the test and the reference simulations is much smaller than during the day because there is no shortwave radiation (Fig. 8). The size of the difference is similar for all the stations, causing points in Fig. 8 to fall on a diagonal line. At the start of the forecast, the values are almost equal, but later in the forecast during the night, the bias for the test simulations is slightly more positive. The reason for this is that the test simulations take the radiation from the surroundings into account, which causes the surface to be warmer in the simulation.

The daytime bias in the test simulations behaved similarly with all simulation start times, except with simulations starting at 0900 UTC in October, when the values were more positive than the others. During the nighttime, many simulations that started at 1500 and 2100 UTC had more positive bias than the corresponding 0300 UTC simulations (not shown). Verification separately for each year showed that while the general behavior of the results was similar for each year, there were also some differences. In October 2019, the test simulations had more negative bias than in October 2018 and 2020 as there happened to be several cases in October 2019 where the forecast was too cold at night. In December 2019, January 2020, and February 2020, there was more positive bias than in other years.

c. RMSE

Figure 9 shows the RMSE difference between the reference and test simulations started at 0300 UTC. Positive values mean that the test simulation has lower RMSE, and negative values mean that test simulation has greater RMSE. Times when the difference between the simulations was not statistically significant according to the bootstrap method have been grayed out. As for bias, the results are highly dependent on station and lane. The largest differences occur during the day in February and March. In February, many of the test simulations have lower RMSE values than the reference simulations during the day because the shadowing is taken into account. However, there are some cases in which the reference run performs better. It might be that these sensors are located on lanes exposed to radiation. The results have more variation in March. At some locations, the test simulations give clearly better results, but there are also many where the reference simulation is better. The lane where the forecast point is located has a great effect in March at some stations. For example, the differences in simulations are large at station 7 (Lakiamäki) on the southern lane, while on the less-obscured northern lane, the differences are much smaller. The results are also sensor dependent. The test simulations produce better RMSE values than the reference simulations with two of the sensors, but the reference simulations give better values when using the other two. As already stated in section 3a, some of the sensors are probably more exposed to the sun than others. The results behave similarly at station 5 (Karnainen) in February.

Fig. 9.
Fig. 9.

As in Fig. 7, but for RMSE difference between reference simulations and test simulations. The cases in which the difference was not statistically significant according to the bootstrap method are shown in gray.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

During the night, the differences are smaller in February and March than during the day because there is no shortwave radiation, and in many cases the difference is not statistically significant. However, at many stations, the test simulation has slightly lower RMSE values, which might be because the radiation from the surroundings is taken into account. The differences are also small in November, December, and January when the shortwave radiation is low. At some stations, the test simulations give slightly greater RMSE values during the day than the reference simulations, but at some stations, the test simulations give better results. During the night the difference is mostly in favor of the test simulation when the difference is statistically significant, but there are also few exceptions.

The daily behavior of the RMSE differences is similar for the simulations started at 1500 and 2100 UTC and for the 0300 UTC simulations. The results also look rather similar for the simulations started at 0900 UTC, but there are some differences. In some cases in which the test simulations have greater RMSE values during the day, the difference between the simulations is smaller. In addition, there are more cases in January during the day where the test simulations have lower RMSE values. As for bias, the results for separate years have similar general behavior. However, in October 2019, the improvement gained by using LHAs and SVFs was not that large as in October 2018 and 2019 during the day. Also, in December 2019 and January 2020 during the night, the improvement was not as large either. The test simulations even gave greater RMSE values at some stations.

d. Type-1 and type-2 errors

One of the most important features of a good road weather forecast is that it estimates correctly when the RST drops below 0°C. Therefore, we studied which simulation better predicts that the road surface temperature is below 0°C. This was done by comparing the number of type-1 and type-2 errors. Type-1 errors are defined as cases in which the observed temperature was below 0°C but the forecast temperature was above 0°C. Type-2 errors are defined as cases in which the forecast temperature was below 0°C but the observed temperature was above 0°C. Figure 10 shows the differences in type-1 errors and Fig. 11 shows type-2 errors between the test and reference simulations started at 0300 UTC. The test simulations have clearly fewer type-1 errors during the day in all months except December. The difference is large, especially in February and March. However, the test simulations also clearly had more type-2 errors during the day. This is in line with the fact that the test simulations had more negative bias values during the day. Since the test simulations are colder, the RST is more often below 0°C. However, the test simulations were often warmer than the reference simulations during the night. This causes them to have fewer type-2 errors than the reference simulations, but it also increased the number of type-1 errors during the night. The daily behavior of type-1 and type-2 errors was also similar for other forecast start times. Many kinds of verification scores could be calculated for binary events (Mason and Graham 1999; Ferro and Stephenson 2011). However, the total number of simulations for one station–lane–sensor combination in Figs. 10 and 11 was only about 90. Even small changes in the number of hits and misses could have a great effect on the scores, so only the results for type-1 (misses) and type-2 errors (false alarms) are presented to avoid misinterpretation of the results.

Fig. 10.
Fig. 10.

As in Fig. 7, but for the difference between type-1 errors in the reference and test simulations. The simulation case was considered to have a type-1 error when the observed temperature was below 0°C but the modeled temperature was above 0°C. Note that some values exceed the upper value of the color bar. It would have been too hard to distinguish smaller values if the color bar limit had been set to the maximum difference between the simulations.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Fig. 11.
Fig. 11.

As in Fig. 7, but for the difference between type-2 errors in the reference and test simulations. The forecast case was considered to have a type-2 error when the modeled temperature was below 0°C but the observed temperature was above 0°C. Note that some values exceed the lower value of the color bar. It would have been too hard to distinguish smaller values if the color bar limit had been set to the maximum difference between the simulations.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

4. Conclusions

In this study, the FMI RWM including SVFs and LHAs was used to produce road weather forecasts for three winter periods between 2018 and 2021. The study covered 23 selected RWSs in Finland, with the SVFs varying between 0.72 and 0.98. The SVFs and LHAs were determined from the DSM that was generated from the National Land Survey of Finland’s laser scanning data. The forecast errors were compared with the error of the reference simulations that assumed open surroundings. The results provide insight into how SVFs and LHAs affect forecast accuracy, which is important, as the quality of the model must be assessed before operational implementation.

The SVF and LHA effect on road weather forecasts varied a lot, depending on the location, month, and the time of day. At best, their use considerably decreased the positive bias in the forecast during the day and improved the forecast during the night. However, there were many cases in which they had no statistically significant effect on the RMSE or even increased it. The use of SVFs and LHAs often made the already overly cold forecast even colder during the day in October and March. Despite that, one notable finding was that the simulations for different lanes on the same road were considerably different in some cases. For example, if there is a rock cutting on the southern side of the road and the sun is low, the northern lane can be exposed to direct solar radiation in the simulation while the southern lane remains in shadow. Also, the verification results varied significantly in many cases depending on the RST sensor used. The exact locations of the RST sensors were unknown, which made the verification of the forecasts challenging. However, studying how the results varied depending on the used sensor in the initialization and verification provided insight into how sensitive the forecast is to sensor location at each station.

The screening algorithm has the greatest effect on the daytime temperatures, while for road maintenance purposes, the nighttime temperatures are often seen as the most important, as there is a greater risk for the RST going below 0°C. Nevertheless, the accuracy of the daytime temperature forecasts is also important, as the heat is stored in the asphalt and it warms the surface during the night. However, this effect is not seen in the results. On the contrary, despite the strong positive bias during the day, the reference simulations had more negative bias during the night than the simulations using SVFs and LHAs. Either the effect of the radiation from the surroundings is stronger at night or the effect of stored heat is not modeled accurately in the RWM. This topic would need further research.

One error source for the simulations is the resolution of the DSM. Some objects like electricity poles and trees can be too bulky in the DSM and thus cause overly long blocking of the direct solar radiation in the simulation. In addition, the laser scanning data were rather old in some cases and the road surrounding might have changed. Another option to determine SVFs and LHAs would be to use Google Street View imagery. However, the images are taken from the top of the car and not at the road surface, which would cause some error. In addition, SVFs and LHAs can only be determined at the points where the images are taken, while the points can be chosen more freely from the DSM. For future research, it would be useful to take fish-eye images at the RST sensor locations. This would enable comparison of SVFs and LHAs calculated from DSM with those calculated from the image.

In many cases, SVFs and LHAs failed to improve the simulation because of the other forecast errors, which made the simulation too cold. In addition to the inaccuracies of the RWM itself, the input forecast from the NWP is not perfect, either. Without these other errors, the performance of the test simulations would have been better in relation to the reference simulations. Adjusting the degree of direct radiation blocking from 100% to 60%, for example, would improve the verification results in cases in which the forecast was too cold during the day. However, this would reduce the improvement in cases in which the reference simulation was considerably too warm. Heating caused by traffic was not taken into account in the simulations, which might have increased the negative bias in the results.

The results of this study show that it is advisable to do a separate forecast for different lanes when the forecasts are required with high resolution. If a DSM is used to determine the SVFs and LHAs, it should be ensured that the forecast points coincide with the road in the DSM, because even a small location error has a large effect on the values. The locations in this study were mostly on major roads, and the screening was mainly caused by trees or rocks. An interesting topic for further research would be to study the behavior of the model using SVFs and LHAs in different environments, like in an urban area or in more mountainous terrain. Studying the model behavior in lower-latitude regions would be interesting as well. In Finland, the angle of the sun is quite low in winter, early spring, and late fall, so even low obstacles cause screening. At lower-latitude regions, the sun is higher and low obstacles cause screening only in early morning and late evening. On the other hand, at lower latitudes, the days are longer in winter, so the screening can be effective for longer periods at road points with low SVFs.

Acknowledgments.

The support provided by the following projects is gratefully acknowledged: Winter Premium, funded by the European Regional Development Fund, the Arctic Airborne 3D project by Interreg Nord, and the 5G-Safe-Plus project, which is part of the Eureka Cluster Celtic-NEXT initiative, funded in Finland by Business Finland.

Data availability statement.

Calculated local horizon angles, road weather station observations, MEPS forecasts, road weather model output road surface temperature, and verification results are openly available from the FMI research data repository METIS (Karsisto and Horttanainen 2022).

APPENDIX A

Model Physics

The FMI RWM is one dimensional, and the ground is divided into 16 layers. The model calculates the heat exchange between the layers at each time step. The calculation is based on the following equation (Patankar 1980):
ρgcgδT(z,t)δt=δδzKδT(z,t)δz,
where T is thermodynamic temperature, z is vertical distance in the ground, t is time, K is heat conductivity, ρg is density, and cg is specific heat capacity of the ground. The equation used to calculate the temperature for the next time step is obtained by integrating Eq. (A1) over the time step and the volume of the layer and solving it using the forward-difference explicit method,
Tij+1=Ti+1ρgcgzi+1zi12Δt(KiTi+1jTijzi+1ziKi1TijTi1jzizi1),
where index i refers to ground layer and index j to time, Δt is model time step, and Ki means heat conductivity between layers i + 1 and i.
In addition to the heat exchange with deeper ground layers, the model calculates the heat exchange between the surface and the atmosphere. A schematic presentation of energy fluxes is given in Fig. A1. The heat flux to the ground G is affected by net radiation Inet, sensible heat flux H, and latent heat flux LE following the surface energy balance equation (Brutsaert 1984),
G=InetHLE.
The calculation of Inet is explained in section 2f. Flux H is calculated as (Campbell 1985, 1986)
H=BLC(TsTa),
where BLC is boundary layer conductance, Ts is surface temperature, and Ta is air temperature. Boundary layer conductance is calculated as (Campbell 1985, 1986)
BLC=caρakufln(zTd+zhzh)+Ψh,
where ca is the specific heat of air, ρa is the density of air, k is von Kármán’s constant, uf is the friction velocity, zT is the temperature measurement height, d is the zero-displacement height, zh is the roughness length for heat, and Ψh is the stability correction factor for heat. Friction velocity uf is calculated as (Campbell 1985, 1986)
uf=kuln(zwd+zmzm+Ψm),
where zW is the wind speed measurement height, zm is the roughness length for momentum, and Ψm is the stability correction factor for momentum. In stable conditions, Ψh and Ψm are calculated as 4.7ζ (Campbell 1985, 1986), where ζ is the stability parameter and is calculated as (Campbell 1985, 1986)
ζ=kzTgHcaρaTauf3,
where g is the gravitational constant. In unstable conditions, Ψh and Ψm are calculated as (Campbell 1985, 1986)
Ψh=2ln(1+116ζ2) and
Ψm=0.6Ψh.
Because ζ is function of H, H must be solved iteratively. At the first iteration round, Ψh and Ψm are set to zero and values for BLC, H, and ζ are calculated. Then Ψh and Ψm are calculated using the obtained values for BLC, H, and ζ. The new values for Ψh and Ψm are then used to calculate BLC, H, and ζ again. This is repeated until the absolute difference in the BLC values between subsequent iteration rounds is smaller than 0.001 or the maximum number of iterations (i.e., 40) is reached.
Fig. A1.
Fig. A1.

Schematic presentation of the energy fluxes in the FMI RWM.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

Latent heat flux is calculated as (Calder 1990)
LE=ρmcaγesearo,
where ρm is the density of moist air, γ is the psychrometric constant, es is the surface vapor pressure, ea is the air vapor pressure, and ro is the aerodynamic resistance. Aerodynamic resistance is calculated as (Tourula and Heikinheimo 1998)
ro=[ln(zW+zmzm)+Ψm][ln(zW+zhzh+Ψh)]k2u,
The maximum value for ra is set to 30.0 s m−1. The amount of evaporated water in a time step EVw is calculated as
EVw=LELvapρwδt,
where Lvap is the latent heat of water vaporization and ρw is the density of water. If the temperature is below 0°C, the Lvap is replaced with latent heat of fusion. If there is no water on the surface, LE and EVw are set to zero.

APPENDIX B

Sensitivity Tests

Some sensitivity tests were performed on the road weather model to find out how changing input atmospheric values changes the road surface temperature. The model was fed with input data where all input variables remained constant. Air temperature was set to 5°C, wind speed was set to 3 m s−1, relative humidity was set to 70%, precipitation was set to 0 mm h−1, incoming shortwave radiation was set to 0 W m−2, and incoming longwave radiation was set to 300 W m−2. The test was repeated multiple times by slightly changing one input value. The results are shown in Fig. B1. The surface temperature is set to the value of air temperature at the beginning of the simulation. The surface energy balance seems to reach an equilibrium a few hours after the simulation starts, after which the surface temperature remains fairly constant. Reducing the incoming longwave radiation by 10 W m−2 results in about 0.3°C lower road surface temperature relative to the original simulation. Decreasing wind speed by 1 m s−1, decreasing air temperature by 1.0°C, and increasing precipitation by 1 mm h−1 causes 0.4°, 0.9°, and 2.3°C lower road surface temperatures, respectively. In the last case, the evaporation caused the very low surface temperature. If relative humidity is increased by 10% while the precipitation is kept at 1 mm h−1, the resulting surface temperature is only about 1.3°C lower when compared with the original simulation. Although keeping the input values constant differs much from real forecast cases, the results of sensitivity tests show that the FMI RWM is very sensitive to input data.

Fig. B1.
Fig. B1.

Results of sensitivity tests. The simulation length in hours is shown on the x axis, and RST is shown on the y axis. The red line shows surface temperature for the simulation in which air temperature Ta was kept at 5°C, wind speed υ was kept at 3 m s−1, relative humidity RH was kept at 70%, precipitation (prec) was kept at 0 mm h−1, incoming SW radiation Sd was kept at 0 W m−2, and incoming LW radiation Ld was kept at 300 W m−2. Other lines show surface temperature from simulations in which these values are slightly altered. The alterations are stated in the legend.

Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0026.1

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    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
  • Fig. 1.

    Flowchart of different data sources and processes used in the study.

  • Fig. 2.

    Locations of studied RWSs (Table 2). Made with Natural Earth (https://www.naturalearthdata.com/).

  • Fig. 3.

    The DSM determined from laser scanning data around Espoo Kolmiranta RWS and the selected coordinate points for the simulations.

  • Fig. 4.

    LHAs at Espoo Kolmiranta RWS (Table 2; site 4) on the (left) southern and (right) northern lanes. The direction is shown on the outer perimeter so that north is at 0°. The inner circles show the angle between a flat horizon and the top of the sky. LHAs are shown as a blue line, and the visible sky is shown in light-blue color. Brown, red, and yellow lines show the sun elevation angles throughout the first days of March, February, and January, respectively.

  • Fig. 5.

    Bias for the test (continuous lines) and the reference (dashed lines) simulations for 0300 UTC–started runs for Salo Lakiamäki station (Table 2; station 5) October 2018–20 for the (left) southern lane and (right) northern lane. The x axis shows time of day in Finnish wintertime (UTC + 2). Brown lines show results for simulations initialized and verified with RST sensor 1, light-brown lines show results with sensor 2, light-turquoise lines show results with sensor 3, and darker-turquoise lines show results with sensor 4.

  • Fig. 6.

    As in Fig. 5, but for RMSE.

  • Fig. 7.

    Bias °C for the test simulations started at 0300 UTC in October, November, February, and March. The values are calculated over three winter periods from October 2018 to March 2021. The y axis shows for which station the simulation is performed (Table 2). The results are grouped so that the values for different stations are separated with continuous lines and values for different sensors are separated with dashed lines. The simulations for different lanes are on top of one another without a line. The x axis shows time of day in Finnish wintertime (UTC + 2).

  • Fig. 8.

    Scatterplots of bias °C values for the reference (x axis) and the test (y axis) simulations for (top left) October, (top right) November, (bottom left) February, and (bottom right) March. The values are calculated over three winter periods from October 2018 to March 2021. Each point represents data for one station–lane–sensor combination at a certain time of day. Different colors represent different times, given in Finnish wintertime (UTC + 2). The black line shows where the points would be if the values were equal. White background shows the area where the test simulation has a smaller absolute bias, and light-pink background shows the area where the reference simulation has a smaller absolute bias.

  • Fig. 9.

    As in Fig. 7, but for RMSE difference between reference simulations and test simulations. The cases in which the difference was not statistically significant according to the bootstrap method are shown in gray.

  • Fig. 10.

    As in Fig. 7, but for the difference between type-1 errors in the reference and test simulations. The simulation case was considered to have a type-1 error when the observed temperature was below 0°C but the modeled temperature was above 0°C. Note that some values exceed the upper value of the color bar. It would have been too hard to distinguish smaller values if the color bar limit had been set to the maximum difference between the simulations.

  • Fig. 11.

    As in Fig. 7, but for the difference between type-2 errors in the reference and test simulations. The forecast case was considered to have a type-2 error when the modeled temperature was below 0°C but the observed temperature was above 0°C. Note that some values exceed the lower value of the color bar. It would have been too hard to distinguish smaller values if the color bar limit had been set to the maximum difference between the simulations.

  • Fig. A1.

    Schematic presentation of the energy fluxes in the FMI RWM.

  • Fig. B1.

    Results of sensitivity tests. The simulation length in hours is shown on the x axis, and RST is shown on the y axis. The red line shows surface temperature for the simulation in which air temperature Ta was kept at 5°C, wind speed υ was kept at 3 m s−1, relative humidity RH was kept at 70%, precipitation (prec) was kept at 0 mm h−1, incoming SW radiation Sd was kept at 0 W m−2, and incoming LW radiation Ld was kept at 300 W m−2. Other lines show surface temperature from simulations in which these values are slightly altered. The alterations are stated in the legend.

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