TMY

Interpolation

As a first step, Meteonorm calculates monthly average values for six key climate parameters for a target location (latitude, longitude, and altitude):

• Global horizontal irradiance
• Air temperature
• Dew point temperature
• Wind speed
• Precipitation
• Number of days with precipitation

A standardized interpolation method is applied for all parameters, blending quality-controlled measurements from ground weather stations with high-resolution gridded data.

Measurements from ground weather stations provide local accuracy while gridded data provides global coverage. In non-polar regions, satellite data is used for global horizontal irradiance. In polar regions, and for the other parameters, ERA5 reanalysis data is used.

Distance-Based Blending

The core of the interpolation is a distance-based blending strategy. The influence of ground stations versus gridded data depends on the 3D weighted distance between the target location and the nearest station.

• Nearest station is closer than $d_1$ km: only data from the nearest station is used.
• Nearest station is between $d_1$ and $d_2$ away: data from up to six nearby stations is blended using the inverse distance weighting method described below.
• Nearest station is between $d_2$ and $d_3$ km away: station data is blended with gridded data. The weight of the station data decreases as the distance increases.
• Nearest station is more than $d_3$ km away: only gridded data is used.

Parameter	$d_1$	$d_2$	$d_3$
Global horizontal irradiance	2	10	50
Temperature	2	20	100
Dew point temperature	2	20	100
Wind speed	2	20	100
Precipitation	2	20	100
No. of days with precipitation	2	20	100

Table 1: Distance thresholds (in km) used for blending gridded and ground station data.

The following schema illustrates the blending logic:

Figure 1: A visual representation of the blending logic based on the distance to the nearest station.

Inverse Distance Weighting

When multiple ground stations are used, a target time series is interpolated using a modified inverse distance weighting (IDW) method. This method takes into account both the horizontal distances between target and stations, and the differences in altitude, applying a parameter-specific vertical scale factor and gradient. For $N$ stations, the target value $Y_x$ is the weighted average of the station values $Y_i$:

$$Y_x = \frac{ \sum_i^N w_i \cdot \bigl(Y_i + (z_i - z_x) \cdot g_v \bigr) }{ \sum_i^N w_i }$$

where

• $w_i = \frac{1}{\biggl(\frac{d_i}{R}\biggr)^2 + v^2 \cdot (z_i - z_x)^2}$
  is the weight for station $i$ (note that we only consider stations with $d_i \lt R$),
• $d_i$ is the horizontal distance between the target and station $i$,
• $R$ is the maximum search radius (see Table 2),
• $v$ is the vertical scaling factor ("altitude penalty", see Table 2),
• $z_i - z_x$ is the difference in altitude between the target and station $i$,
• $g_v$ is the vertical gradient (see Table 2).

Parameter	Vertical Gradient ( $g_v$ )	Vertical Scaling Factor ( $v$ )	Max. Search Radius ( $R$ )
Global horizontal irradiance	0	100	150 km
Temperature	-0.5 °C / 100m	200	300 km
Dew point temperature	-0.4 °C / 100m	200	300 km
Wind speed	+0.2 m/s / 100m	200	300 km
Precipitation	0	200	300 km
No. of days with precipitation	0	200	300 km

Table 2: Parameter-specific factors for the IDW interpolation.