The radar data used in this paper is provided by DWD, which operates a radar network of 17 dual-polarization weather radars, covering the entire landmass of Germany. These radars operate in the STAR mode as described above, where H and V polarized pulses are transmitted simultaneously and where the power and phase of the received signal are recorded simultaneously for H and V polarizations. The recorded signals are acquired in sweeps, each containing the data from one 360° revolution of the antenna, with the antenna first pointing north and then rotating clockwise. More precisely, every five minutes, each of the radars performs a volume scan consisting of 10 sweeps acquired at different elevation angles, as well as a terrain-following sweep , which measures precipitation as closely to the ground as possible. In the following, we utilize only these terrain-following sweeps. If the radar view is unobstructed, the elevation angle at which the electromagnetic waves are sent out for such sweeps is set to 0.8°. In cases where orography or obstacles obstruct the view, the elevation is raised accordingly.

The radars scan at a range resolution of 250m and an azimuthal resolution of 1°, with a maximum range of 150km, resulting in 360 rays of 600 radar gates each. Each of these radar gates is sampled by 50 pulses of electromagnetic waves, which serve as input to compute various radar moments for this radar gate. An important step after collecting the radar measurements is quality control of the radar data, which provides a solid data base for subsequent quantitative precipitation estimation, hydrometeor classification and thunderstorm detection. One main goal of this process is to identify and subsequently filter out, or correct for, non-meteorological echoes, that is, the signals returned by non-meteorological scatterers. Typical non-meteorological scatterers include ground clutter (trees, mountains), biological scatterers (birds, insects), wind turbines, towers, ships, airplanes, external signals (e.g. wifi), and chaff. In contrast, meteorological scatterers are any hydrometeors, e.g., rain, snow, hail, or drizzle. The signals returned by meteorological scatterers are called meteorological echoes.

The various radar moments are particularly useful for this purpose of identifying and filtering out non-meteorological echoes, as they provide insight into different qualities of the detected scatterers. The most widely used radar moment is the radar reflectivity factor , which quantifies the strength of the returned signal. It is measured separately at horizontal and vertical polarization, yielding Zh and Zv, respectively. Due to variations in hydrometeor type (liquid, frozen), size and number concentration, the radar reflectivity factor can vary by several orders of magnitude. Hence, it is usually expressed in logarithmic units (dBZ) and denoted by DBZH and DBZV, respectively, where the minimum detectable value increases with range. For example, at a distance of 1km from the radar, the minimum detectable reflectivity factor is around -38dBZ, whereas at ranges beyond 25km, signals below -10dBZ cannot be detected by DWD radars , i.e., they cannot be distinguished from noise.

The differential reflectivity ZDR contains information about the shape of the scatterers and is commonly used, e.g., to discriminate between liquid and frozen hydrometeors. In combination with other radar moments, it is also useful for identifying clutter.

Finally, because the linear depolarization ratio LDR cannot be measured directly by DWD radars, an estimated depolarization ratio (denoted by UDR) is deduced from the differential reflectivity ZDR and the co-polar cross-correlation coefficient ρHV . This radar moment is a measure of how homogeneous and spherical the scatterers are within a radar gate, and thus serves as a good discriminator between clutter and meteorological echoes , with small values (≪0) indicating weather and values closer to 0 indicating clutter or biological signals. In the available DWD data, the reflectivity factors DBZH and DBZV, and the differential reflectivity ZDR have been filtered by a Doppler filter  aiming to remove any stationary non-meteorological scatterers, whereas no such filter has been applied to the depolarization ratio UDR.

The DWD provided all terrain-following sweeps measured at the 17 different dual-polarization weather radars for three one-hour time periods: 09:00–10:00 UTC on 16 June 2022, 10:00–11:00 UTC on 18 June 2022, and 17:00–18:00 UTC on 9 January 2025. Radar sweeps collected in January 2025 are referred to as winter sweeps, and radar sweeps collected in June 2022 are referred to as summer sweeps. Moreover, the radar sweeps collected on 16 June feature both meteorological and non-meteorological echoes and are referred to as mixed summer sweeps. In contrast, the radar sweeps collected on 18 June were collected during a time period when no precipitation was measured, indicating that only non-meteorological echoes were detected. Therefore, these sweeps are referred to as cluttered summer sweeps. For the winter sweeps, the specific time frame was chosen with the goal of selecting sweeps featuring a minimum amount of non-meteorological echoes. However, even for the winter sweeps, a certain amount of non-meteorological echoes cannot be avoided. Figure  shows examples of the radar moments DBZH, ZDR and UDR obtained from different sweeps measured during these time periods.

The winter sweeps contain a variety of precipitation features (Fig. a), with isolated showers over north-western Germany, widespread stratiform precipitation in north-eastern Germany, a convective line over southern Germany, and some very light precipitation similar to insect signatures. The cluttered summer sweeps show different insect signatures for different radars (Fig. b): the radars in the south and east of Germany show strong insect signatures, whereas the radars in the north and north-west show lighter signatures.

For each radar station, a single sweep consists of the measured values of the radar moments at the radar gates covered by the radar. These radar gates partition the scanned area into a polar grid defined by the radar's number of rays na∈N={1,2,…} and the number of range bins nr∈N. More specifically, the radar gate corresponding to the ith range bin of the jth ray is defined as the set 1gi,j={wrsin⁡αcos⁡α:r∈(i-1,i],α∈(2πna(j-1),2πnaj]}⊂R2, where w=250 denotes the range resolution of the radar in meters, r is the distance from the radar site in units of the range resolution w, and the azimuthal angle α is measured clockwise from north.

Let M denote the set of radar moments available for a given sweep. Then, for each radar moment m∈M, its measured values from the sweep can be represented by a single-channel image Am=(Ai,jm)∈Rnr×na. For each pixel (i,j)∈Ω={1,…,nr}×{1,…,na}, the entry Ai,jm corresponds to the value of the radar moment m at the associated radar gate gi,j. Single-channel images can be combined into a multi-channel image A=(Am)m∈M′∈RC×nr×na, where M′⊆M is the subset of included radar moments and C=|M′| is the number of channels. In the following, we refer to these multi-channel images as radar images. Moreover, the provided data also contains information on which radar gates had already been identified as non-meteorological during the preprocessing performed by DWD. For these radar gates, the corresponding pixels of the DBZH image are assigned a placeholder value p=-40dBZ, which lies far below the reflectivity range of meteorological echoes. Pixels with a horizontal reflectivity value of -40dBZ are referred to as excluded pixels, as they conclusively do not correspond to meteorological echoes. All other pixels are referred to as included pixels. A Cartesian representation of a DBZH image is shown in Fig. a. Most of the radar images still contain pixels that likely correspond to non-meteorological echoes, even for radar images measured in winter. To filter some of these pixels out, we apply further preprocessing steps.

For example, as depicted in Fig. a, the DBZH images show weak signals with horizontal reflectivity values below -10dBZ near the radar. However, only very light drizzle could produce reflectivity values of that magnitude. That is, thresholding at -10dBZ most likely removes noise and clutter, and does not remove any convectively significant weather. Therefore, pixels with lower horizontal reflectivity values are considered to correspond to non-meteorological echoes and are thus excluded as potential meteorological echoes (Fig. b). Their DBZH values are then also set to -40dBZ to mark them as excluded pixels.

Moreover, meteorological echoes observed in the radar images typically form connected components consisting of several pixels (Fig. ). In contrast, isolated included pixels are assumed to correspond to non-meteorological echoes. For this reason, each DBZH image is further processed by a despeckle filter consisting of two steps. First, we use the Hoshen-Kopelman algorithm  to identify all connected components of included pixels. More specifically, we apply the algorithm to the binarized image obtained by thresholding at -40dBZ, separating the excluded pixels from the included ones. Here, we use the 4-neighborhood, which means that two pixels (i1,j1),(i2,j2)∈Ω with (i1,j1)≠(i2,j2) are neighboring if their associated radar gates gi1,j1,gi2,j2 share a common edge. Note that the DBZH image is periodic in the second component, see Eq. (), since each index j∈{1,…,na} represents the azimuthal angle of a ray, and the image corresponds to a sweep. Consequently, pixels corresponding to the first and last ray are neighboring if they have the same range index i∈{1,…,nr}. More precisely, for each pixel (i,j)∈Ω, the set N(i,j)⊂Ω of neighboring pixels can be written as N(i,j)=(k,ℓ)∈Ω:|i-k|+d(j,ℓ)=1, where d:{1,…,na}×{1,…,na}→N0 denotes the periodic distance measure, given by 2d(j,ℓ)=min⁡{|j-ℓ|,na-|j-ℓ|}. for each ℓ∈{1,…,na}. After identifying the connected components, those consisting of less than six undetermined pixels are selected. Then, the DBZH values of pixels (i,j)∈Ω in these components are set to -40dBZ, indicating that they do not correspond to meteorological echoes. The result of the despeckling process is shown in Fig. c.

For the excluded pixels (i,j)∈Ω, their corresponding entries in the DBZH image were set to -40dBZ to indicate that they conclusively do not correspond to meteorological echoes (Fig. d). For the other radar moments, ZDR and UDR, we also assign specific placeholder values p∈R to the entries of their single-channel images. Similar to the horizontal reflectivity, these placeholder values are chosen to lie outside the range of typical values for meteorological echoes in our dataset. More specifically, for the differential reflectivity, the placeholder value is set to p=20dB. This particular value was chosen since it lies above typical values for meteorological echoes (around 0dB), but within the range for non-meteorological echoes (between 5 and 20dB) in our data, as can be seen in Fig. b and c. Furthermore, as described in , except for some special cases such as hail, the depolarization ratio of meteorological scatterers is typically below -12 dB. In contrast, the depolarization ratio of non-meteorological scatterers typically ranges between -12 and 0dB. Therefore, we chose a placeholder value of p=0dB for the depolarization ratio.

The presented preprocessing steps remove most of the clutter with low reflectivity values. However, many mixed summer radar images contain much larger connected components corresponding to more reflective non-meteorological scatterers, as can be seen in Fig. b. Detecting such echoes presents a challenging task for conventional methods such as fuzzy logic filtering or depolarization ratio thresholding .

The task of detecting non-meteorological echoes can be viewed as a segmentation task of multi-channel two-dimensional (2D) radar image data. Each pixel of the image is classified as corresponding to meteorological or non-meteorological echoes, that is, each pixel is assigned a binary class label c∈{0,1}. In , the so-called U-net architecture, a fully convolutional neural network, has been introduced to address similar segmentation tasks of 2D images.

A U-net has an encoder-decoder architecture with skip connections, consisting of a so-called contracting path that downsamples the spatial resolution of the features and an expansive path that upsamples it again. Both the downsampling and the upsampling paths consist of several levels. The network considered in the present paper is an adapted version of the U-net architecture comprising five levels, with the fifth level acting as a bottleneck. Consequently, the network performs four downsampling steps and four upsampling steps. Each downsampling step consists of two convolution blocks and a 2×2 max-pooling layer for downsampling the spatial resolution of the feature map . A convolution block contains a padded 3×3 convolutional layer, followed by a batch normalization layer and a rectified linear unit (ReLU) activation function, which is given by ReLU:R→R0+=[0,∞), ReLU(x)=max⁡(x,0). The convolution blocks of the first downsampling step produce nf∈N feature channels, and each further downsampling step doubles the number of feature channels. The bottleneck at the fifth layer consists of two such convolution blocks. For each of the subsequent upsampling steps, the spatial resolution of the feature channels is increased using bilinear interpolation . The resulting channels are then concatenated with the feature channels of the corresponding level of the downsampling path. Two convolutional blocks following the concatenation of those feature channels divide the number of feature channels by three and complete the upsampling step. Here, the number of feature channels is divided by three since the concatenated channels consist of the channels of the downsampling path and twice as many interpolated channels from the level below. After the final upsampling step, the sigmoid activation function σ:R→[0,1], given by σ(x)=11+e-x, is applied to the output.

Compared to the original U-net architecture presented in , we use padded convolutional layers with a padding of 1 in each step, preserving the image size throughout the network. Since the network input is periodic in the second component, we use periodic padding  in this direction, while the padding in the direction of the first component is reflective. Moreover, the spatial resolution of the features is upsampled using bilinear interpolation instead of an up-convolution. Furthermore, the network does not include a final 1×1 convolution. Instead, the output of the final convolution block is already a single-channel map to which the sigmoid activation function is applied directly. A sketch of the network architecture described above is shown in Fig. .

The network outputs are images of the same spatial dimensions as each of the input channels. More specifically, the network architecture stated above with parameter constellation θ∈Θ⊂Rq is given by a function fθ:Rk×h×w→[0,1]h×w, with spatial dimensions h,w∈N and the number of input channels k=3. Here, θ denotes the vector of trainable parameters of the network, and Θ⊂Rq is the network's parameter space for some q∈N depending on the number of feature channels nf. Each input channel corresponds to a single-channel image of a radar moment, as described in Sect. , allowing the network to combine information about different radar moments to detect non-meteorological echoes.

The goal is then to perform supervised training of the network to assign binary labels to each pixel (i,j)∈Ω, describing which pixels correspond to meteorological and non-meteorological echoes, respectively. This training process requires pixel-wise labeled training data, that is, each pixel (i,j)∈Ω must be assigned a ground truth class label ci,j∈{0,1}. However, mixed radar images containing both meteorological and non-meteorological echoes lack pixel-wise ground truth labels, and generating such labels by hand is very costly. Therefore, we propose a method to generate synthetic multi-channel images and corresponding pixel-wise ground truth labels for training the network.

As outlined in Sect. , the network architecture considered in this paper can utilize radar images as input, where each channel corresponds to a single-channel image of a specific radar moment. The training samples consist of such radar images and corresponding binary ground truth images indicating whether each pixel corresponds to a meteorological or a non-meteorological echo. We generate synthetic radar images by combining radar images corresponding to winter sweeps (featuring meteorological echoes) and radar images corresponding to cluttered summer sweeps (featuring non-meteorological echoes). For brevity, we refer to these as winter radar images and cluttered summer radar images, respectively. This approach is motivated by the observation that the horizontal reflectivity (DBZH) values in mixed summer radar images often have the appearance of a combination of (scaled) DBZH values from winter and from cluttered summer radar images, as illustrated in Fig. b. In this way, we can generate labeled training samples where the contributions of meteorological and non-meteorological echoes are explicitly known, addressing the challenge of difficult labeling in mixed radar images. However, the meteorological echoes in the synthetic radar images are exclusively those of the winter radar images. Consequently, precipitation structures that occur in summer only are not represented in the training data.

More specifically, we generate a realistic mixed (synthetic) DBZH image by combining two DBZH images AH,w,AH,s∈Rnr×na from a winter and a cluttered summer radar image, respectively, in the following manner. Since the horizontal reflectivity is measured in decibels, which is a logarithmic unit of measurement, we first transform the entries of the DBZH images into linear scale using the transformation Φ:R→R+=(0,∞) , which is given by Φ(x)=10x/10. The transformed reflectivity values are scaled by suitable weighting factors λw>0 and λs>0 for the DBZH images from the winter and the cluttered summer radar image, respectively. For each pixel, the scaled reflectivity values are summed up and transformed back into decibels to obtain the synthetic DBZH image AH,m∈Rnr×na with entries Ai,jH,m=Φ-1(λwΦ(Ai,jH,w)+λsΦ(Ai,jH,s)),if Ai,jH,w>-40dBZ or Ai,jH,s>-40dBZ,-40,otherwise, for each (i,j)∈Ω.

Similarly to the placeholder values described in Sect. , we assign the entry of the synthetic DBZH image Ai,jH,m a placeholder value p=-40dBZ if the pixel is excluded for both radar images. To find appropriate weighting factors λw and λs, we consider the difference in horizontal reflectivity values observed in Fig. . Since the range of the horizontal reflectivity values corresponding to non-meteorological echoes is almost identical for cluttered summer radar images (Fig. c) and mixed summer radar images (Fig. b), the choice of λs=1 is suitable. However, the horizontal reflectivity values corresponding to meteorological echoes are substantially lower for winter radar images (Fig. a) compared to mixed summer radar images. Since the resulting synthetic DBZH image should resemble the typical DBZH images from mixed summer radar images, a weighting factor λw>1 is necessary. In order to determine a suitable choice, four representative mixed summer radar images were chosen. For each of them, a winter radar image with precipitation areas of similar size was assigned. Then, for different weighting factors λw∈{1.5,3,5,8,15}, we compared the DBZH values of manually sampled pixels within similar meteorological structures of both images. As a result, a weighting factor λw between 5 and 8 was deemed appropriate. Note that the weighting factors determined in this way are specific to the considered time periods, though the considered range for the weighting factor allows for calibration differences of up to 3dB. Figure  shows how a synthetic DBZH image is generated by combining a winter and a cluttered summer radar image using a weighting factor λw=6.5. The resulting synthetic DBZH image (Fig. c) is then compared with one from a mixed summer radar image (Fig. d).

The two chosen winter and cluttered summer radar images are then also used to generate synthetic single-channel images for the other radar moments considered in Sect. . In addition to the horizontal reflectivity, which is proportional to the particle concentration and the particle's horizontal cross-section within the radar gate, the differential reflectivity (ZDR) primarily reflects the mean axis ratio of the particles . Since differential reflectivity is defined as the difference between horizontal and vertical reflectivity in decibels, synthetic values can be generated by taking the difference between synthetic horizontal and vertical reflectivity values. Similarly to the synthetic DBZH image AH,m, a synthetic DBZV image AV,m∈Rnr×na is also generated. Then, the corresponding synthetic ZDR image is denoted by AZDR,m∈Rnr×na, and its entries are given by Ai,jZDR,m=Ai,jH,m-Ai,jV,m,if Ai,jH,m>-40 and Ai,jV,m>-40,20,if Ai,jH,m=-40 or Ai,jV,m=-40, for each (i,j)∈Ω, see Fig. . Following Sect. , a placeholder value of p=20dB is assigned to all entries of the synthetic ZDR image for which at least one of the corresponding synthetic DBZH and DBZV values is a placeholder value.

In addition to describing the size and shape of particles using DBZH and ZDR, we also use the depolarization ratio UDR to quantify the homogeneity of the detected particles' shapes within a radar gate. To generate a synthetic UDR image AUDR,m∈(-∞,0]nr×na, we use the property that pixels (i,j)∈Ω included in the winter radar image are assumed to correspond to meteorological echoes. The corresponding entries from the synthetic UDR image are assigned the depolarization ratio values AUDR,w∈(-∞,0]nr×na from the winter radar image. Pixels excluded from the winter radar image are assigned the values AUDR,s∈(-∞,0]nr×na from the cluttered summer radar image if they are included in this radar image. Otherwise, they are assigned a placeholder value. More precisely, the entries of AUDR,m are given by Ai,jUDR,m=Ai,jUDR,w,if AH,w>-40dBZ,Ai,jUDR,s,if AH,w=-40dBZ and AH,s>-40dBZ,0,otherwise, for each (i,j)∈Ω, see Fig. . For pixels included in both radar images, the synthetic DBZH value combines both DBZH values. However, the synthetic UDR value for these pixels is taken from the winter radar image alone, since there is no physically obvious way of combining the two depolarization ratios.

Alongside the synthetic radar image Am=(AH,m,AZDR,m,AUDR,m)∈R3×nr×na, we generate a corresponding ground truth image G∈{0,1}nr×na. Its values indicate which pixels of the synthetic radar image correspond to meteorological (Gi,j=0) and non-meteorological echoes (Gi,j=1), respectively. Pixels included in the winter radar image AH,w are assumed to correspond to meteorological echoes, as described in Sect. . Since the synthetic image is generated in such a way that these pixels also correspond to meteorological echoes in the synthetic image, they are assigned a ground truth label of 0. In particular, pixels that are also included in the cluttered summer radar image, and whose synthetic reflectivity values therefore contain both a meteorological and a non-meteorological contribution, are labeled as meteorological. In this way, every pixel corresponding to meteorological echoes is labeled as such. All of the other pixels, i.e., those excluded from the winter radar image, are labeled 1. More precisely, for each pixel (i,j)∈Ω, the ground truth label Gi,j is given by Gi,j=0,if AH,w>-40dBZ,1,otherwise. Generating synthetic radar images in this way provides mixed radar images with pixel-wise ground truth labeling, assigning each pixel as either meteorological or non-meteorological echoes. This ground truth allows the three synthetic channels to serve as training samples for the neural network.

The available winter dataset Dw={Anw}n=1180⊂D=R3×nr×na consists of 180 radar images Anw=(AnH,w,AnV,w,AnUDR,w), where the radar moments present in the data are horizontal reflectivity, vertical reflectivity, and the depolarization ratio. Similarly, the available cluttered summer dataset is given by Ds={Ans}n=1180⊂D. We partition each of these datasets into two disjoint subsets. One subset of radar images is used for generating the training samples, while the other subset is reserved for generating the validation samples, which are used for model selection, see Sect. . For this purpose, we partition the index set I={1,…,180} into two disjoint subsets Itrain,Ival⊂I, i.e., Itrain∪Ival=IandItrain∩Ival=∅. The index sets Itrain,Ival⊂I are chosen so that all winter and cluttered summer radar images from a single radar station (radar Essen) are used for the generation of validation samples, while the radar images from other radar stations are used for the generation of training samples.

We use the methodology described in Sect.  to generate synthetic training samples by combining radar images from the winter and cluttered summer datasets. Each synthetic training sample consists of a synthetic radar image A∈D and a corresponding ground truth image G∈{0,1}nr×na. The synthetic radar image comprises the radar moments of horizontal reflectivity, differential reflectivity, and the depolarization ratio, i.e., A=(AH,AZDR,AUDR). Before generating the synthetic training samples, we apply various data augmentation steps to increase their diversity. More precisely, as described in Sect. , the DBZH and DBZV images from the winter and cluttered summer datasets are scaled by reflectivity weighting factors λw,λs>0, respectively. In addition, we apply a rotation and a possible inversion of orientation.

Specifically, we introduce a parametric mapping gψ,ψ′:D×D→D×{0,1}nr×na that combines two radar images to generate a synthetic radar image and a corresponding ground truth image. The space of admissible parameters for data augmentation is given by Ψ=R+×{1,…,na}×{-1,1}. Each parameter vector ψ=(λ,φ,o)∈Ψ contains the reflectivity weighting factor λ>0, the rotation angle φ∈{1,…,na}, and the orientation flag o∈{-1,1}. Here, a rotation angle of φ∈{1,…,na} indicates a rotation by φ rays. Hence, a shift of φ rows is applied to the radar image. An orientation flag of o=-1 indicates an inverted orientation. In that case, the radar image is flipped along the x-axis. To distinguish the transformations we apply to winter and cluttered summer radar images, we introduce restricted admissible parameter spaces Ψw,Ψs⊂Ψ. They only differ in the admissible range of the reflectivity weighting factor, which is given by the interval [5,8] for Ψw and by [0.9,1.1] for Ψs. The set of synthetic training samples generated by combining two radar images is then denoted by Dtrainm={gψw,ψs(Anww,Anss):ψw∈Ψw,ψs∈Ψs,nw,ns∈Itrain}. Note that, in order to make use of as many different combinations as possible, the indices nw,ns∈Itrain of the winter and the cluttered summer radar image of a training sample are not matched by radar station or measurement time. In particular, radar images from different radar stations are combined for the generation of synthetic radar images.

These synthetic training samples feature both meteorological and non-meteorological echoes. However, in the training process, the network should be provided with training samples from various scenarios. Since the radar images from the winter and cluttered summer datasets, Dw and Ds, are used to represent meteorological and non-meteorological echoes, respectively, it is possible to generate synthetic radar images that feature only one type of echo. To this end, we introduce a radar image Aexc∈D in which all pixels are excluded, i.e., all of its entries are assigned the corresponding placeholder values. A synthetic radar image that features only meteorological echoes is then generated by combining a winter radar image and the radar image Aexc. In particular, the set of training samples featuring only meteorological echoes is given by Dtrainw={gψw,ψ(Anww,Aexc):ψw∈Ψw,ψ∈Ψ,nw∈Itrain}. Analogously, the set of synthetic radar images featuring only non-meteorological echoes is given by Dtrains={gψ,ψs(Aexc,Anss):ψ∈Ψ,ψs∈Ψs,ns∈Itrain}. Note that the validation dataset Dvalm, comprising radar images featuring both meteorological and non-meteorological echoes, and the validation datasets Dvalw and Dvals, comprising radar images featuring only one type of echo, are generated analogously using the index set Ival instead of Itrain.

As stated in Sect. , the network can be described by its vector of trainable parameters θ∈Θ using a function fθ:Rk×h×w→[0,1]h×w. Here, h=nr and w=na denote the image dimensions of a single-channel image, and k=3 is the number of input channels. Then, for a given radar image A∈D, the output fθ(A) of the network represents the matrix of probabilities (fθ(A))i,j that a pixel (i,j) corresponds to a non-meteorological echo for each (i,j)∈Ω.

The training process of the network involves iterating over so-called mini-batches, and the trainable parameters of the network are adapted at each iteration. More precisely, in each training step, a mini-batch B={(An,Gn)}n=14 is built by generating a total of four synthetic radar images and corresponding ground truth images. Each training sample is chosen as follows: With a probability of 0.75, it is uniformly sampled from the training dataset Dtrainm and therefore features both meteorological and non-meteorological echoes. Otherwise, we either sample it from Dtrainw or Dtrains, with a probability of 0.125 for each case. The mixed radar images are sampled most frequently since only they contain boundaries between meteorological and non-meteorological echoes, which are the most difficult regions to classify. The winter and cluttered summer samples ensure that the network also handles radar images featuring only one type of echo. For each training sample (An,Gn) of the mini-batch B, with n∈{1,2,3,4}, the network output fθ(An) is computed and compared to the ground truth image Gn using the binary cross-entropy loss, which is a measure of how well the network outputs match the ground truth images. More specifically, for any batch B={(An,Gn)}n=14 and vector of trainable network parameters θ∈Θ, the cross-entropy loss Lθ(B) of the batch is given by Lθ(B)=-14∑n=14∑(i,j)∈Ωℓ(fθ(An)i,j,(Gn)i,j), where ℓ(y,x)=xlog⁡(y)+(1-x)log⁡(1-y), with fθ(An)i,j and (Gn)i,j denoting the entries of fθ(An) and Gn, respectively. After computing the cross-entropy loss Lθ(B), its gradient is computed with respect to the vector of trainable network parameters θ. Based on that, this parameter vector θ is then adjusted using the Adam optimizer  with a learning rate of 10-3. The network was implemented and trained using PyTorch 2.8.0 . The batch size, the sampling probabilities, and the learning rate were fixed before training and are not subject to the model selection described in Sect. . An overview of the hyperparameters of the network is shown in Table .

The number nf of feature channels, see Sect. , determines the number of trainable parameters of the network. If it is too small, the network cannot learn the features that distinguish meteorological from non-meteorological echoes; if it is too large, the network can overfit, i.e., it may adapt to details of the synthetic training data that do not carry over to measured radar images. Similarly, the network is expected to fit the training data more closely with each training step, which can also lead to overfitting. Since suitable values are difficult to determine a priori, the number nf of feature channels and the length of training are selected based on the validation datasets described in Sect. . More precisely, a fixed validation set V={(Anval,Gnval)}n=1N⊂Dvalm∪Dvalw∪Dvals consisting of N=144 validation samples is generated once before the training process. The training samples are generated in each training step as described in Sect. . Then, for each nf∈{8,16,32,64}, one network is trained as described above for up to 100 epochs consisting of 42 training steps each. For each e∈{1,…,100}, its validation loss after e epochs is given by Lnf,eval=-1N∑n=1N∑(i,j)∈Ωℓ(fθnf,e(Anval)i,j,(Gnval)i,j), where θnf,e denotes the network's trainable parameters after e epochs. To prevent overfitting, the training is stopped early once the validation loss has not decreased over three consecutive intervals of five epochs, i.e., after the smallest epoch e∈{20,25,…,100} for which Lnf,e-15val≤Lnf,e-10val≤Lnf,e-5val≤Lnf,eval. If there is no such epoch, the training ends after 100 epochs. The last epoch is denoted by enfend.

The number of feature channels and training epochs of the network are selected based on the moving average of the validation loss over the set Enf,e={e-2,…,e+2}∩{1,…,enfend} of up to five epochs surrounding e∈{1,…,enfend}, given by L‾nf,eval=1|Enf,e|∑k∈Enf,eLnf,kval. This moving average is considered in order to reduce the influence of fluctuations between single epochs, which can be quite large due to the small validation set. For the first two and the last two epochs, the set Enf,e contains only three or four epochs, so that the last epochs are not excluded from the selection. Among all pairs (nf,e) with nf∈{8,16,32,64} and e∈{1,…,enfend}, the selected number of feature channels nf∗ and the selected epoch e∗ are then given by (nf∗,e∗)=argminL‾nf,eval,nf∈{8,16,32,64}e∈{1,…,enfend} and the trainable parameters of the selected network are denoted by θ∗=θnf∗,e∗.

To quantitatively evaluate the segmentation performance, we compare the network output against corresponding ground truth. For that purpose, pixels (i,j)∈Ω with a horizontal reflectivity value of Ai,jH=-40dBZ are excluded from the evaluation, as they conclusively do not correspond to meteorological echoes. Furthermore, the physical area of a radar gate gi,j increases linearly with its distance from the radar. Therefore, to obtain metrics with a meaningful physical interpretation regarding the spatial extent of the echoes, we introduce a weight matrix W=(Wi,j)∈Rnr×na. For each pixel (i,j)∈Ω, its weight Wi,j is given by Wi,j=ai,if Ai,jH>-40dBZ,0,otherwise. Here, ai=πna(2ri-w)w denotes the physical area of radar gate gi,j, where w=250 is the range resolution in meters, and ri=iw is the outer radius of the radar gate. Using the weights of the individual pixels, we define the weighted area A(Ω′) of any subset of pixels Ω′⊂Ω as the sum of the weights of the pixels in that set, given by A(Ω′,W)=∑(i,j)∈Ω′Wi,j.

Using a radar image A∈D=R3×nr×na as input, the network output fθ∗(A)∈[0,1]nr×na is transformed into a binary prediction P=(Pi,j)∈{0,1}nr×na by thresholding at 0.5. Specifically, the prediction Pi,j at pixel (i,j)∈Ω is given by Pi,j=0,if (fθ∗(A))i,j<0.5,1,if (fθ∗(A))i,j≥0.5, where prediction Pi,j=0 represents meteorological echoes, and Pi,j=1 represents non-meteorological echoes.

To quantify segmentation performance, we compute the area-weighted intersection over union (IOU), also referred to as the critical success index . For class c∈{0,1}, the class-specific IOU is defined as the ratio of the area of the intersection of pixels classified as class c in the prediction and pixels labeled as class c in the ground truth, to the area of their union, given by IOUc(G,P,W)=A(Ω|P=c∩Ω|G=c,W)A(Ω|P=c∪Ω|G=c,W). Here, the set of pixels assigned to class c by the prediction P and the set of pixels labeled as class c in the ground truth G are given by Ω|P=c={(i,j)∈Ω:Pi,j=c}andΩ|G=c={(i,j)∈Ω:Gi,j=c}, respectively. We then obtain a single performance metric for the entire radar image by computing the combined IOU as the area-weighted sum of the class-specific IOUs, given by IOU(G,P,W)=∑c∈{0,1}A(Ω|G=c)A(Ω)IOUc(G,P,W). While the area-weighted IOU is an effective aggregate metric for overall segmentation quality, it does not distinguish between incorrectly classifying pixels as meteorological and incorrectly classifying pixels as non-meteorological echoes. Therefore, it is helpful to quantify the portion of correct predictions within specific regions, e.g., regions labeled as class c=0 in the ground truth. To this end, we define the area-weighted accuracy on a subset Ω′⊆Ω. This metric calculates the portion of the weighted area within Ω′ that is correctly classified and is given by ACC(G,P,W;Ω′)=A(Ω′∩Ω|P=G)A(Ω′), where Ω|P=G={(i,j)∈Ω:Pi,j=Gi,j} denotes the set of all correctly classified pixels. Setting Ω′=Ω yields the area-weighted accuracy for the entire radar image.

This general formulation allows us to derive the class-specific precision and recall, which provide insight into specific error types. The precision PREc corresponds to the accuracy evaluated on Ω|P=c, i.e., the set of pixels classified as class c. It quantifies the correctness of the prediction, where a low precision implies a high rate of false positives for class c, i.e., a large portion of pixels classified as class c are incorrectly classified. Conversely, the recall RECc corresponds to the accuracy evaluated on Ω|G=c, i.e., the set of pixels labeled as class c in the ground truth. It measures the completeness of the detection, where a low recall implies a high rate of false negatives, i.e., a large number of pixels with ground truth label c are incorrectly classified. These metrics are given by PREc(G,P,W)=ACC(G,P,W;Ω|P=c)andRECc(G,P,W)=ACC(G,P,W;Ω|G=c). While false positives for meteorological echoes (lower REC1 and PRE0) introduce undesirable noise, missing weather events (lower REC0 and PRE1) constitute a severe loss of information. From a meteorological perspective, a high recall REC0 for meteorological echoes is essential to ensure that weather events are correctly identified. This is particularly important for meteorological echoes with high reflectivity values, as they correspond to severe weather events. Therefore, we also investigate the network performance with respect to the horizontal reflectivity values AH. For this, we evaluate the segmentation performance on subsets of pixels with horizontal reflectivity values Ai,jH in the semi-open interval [z,z+5) for z∈R, given by Ω|AH∈[z,z+5)={(i,j)∈Ω:Ai,jH∈[z,z+5)}. Similarly, we analyze the segmentation performance with respect to the distance from the radar, i.e., on subsets of pixels Ω|i∈[r,r+19]={(i,j)∈Ω:r≤i≤r+19}, for range indices r∈{1,…,nr-19}. This is motivated by the fact that non-meteorological echoes in winter radar images, which are rare but can appear close to the radar station, as shown in Fig. d, result in incorrect ground truth labels in the synthetically generated training data.

Using these subsets of pixels, we compute the area-weighted accuracy depending on reflectivity and distance from the radar, given by ACCH(G,P,W;z)=ACC(G,P,W;Ω|AH∈[z,z+5)),ACCD(G,P,W;r)=ACC(G,P,W;Ω|i∈[r,r+19]), respectively, and the recall for class c∈{0,1} depending on reflectivity and distance from the radar, given by RECc,H(G,P,W;z)=ACC(G,P,W;Ω|G=c∩Ω|AH∈[z,z+5)),RECc,D(G,P,W;r)=ACC(G,P,W;Ω|G=c∩Ω|i∈[r,r+19]), respectively.

Note that the introduced metrics can be computed for individual radar images and corresponding ground truth images, as well as for datasets D={(An,Gn)}n=1N⊂D×{0,1}nr×na consisting of N∈N such image pairs. In this case, the metric is first computed for each radar image in the dataset individually and then aggregated as an area-weighted sum. For example, the area-weighted accuracy ACC on subsets Ω′=(Ωn′)n=1N∈ΩN for the dataset D is given by ACC(D;Ω′)=1∑n=1NA(Ωn′,Wn)∑n=1NA(Ωn′,Wn)ACC(Gn,Pn,Wn;Ωn′), where Pn∈{0,1}nr×na is the prediction and Wn∈Rnr×na is the weight matrix for the n-th radar image. As before, setting Ωn′=Ω for all n∈{1,…,N} yields the area-weighted accuracy for the dataset D, while the evaluation on Ωn′=Ω|Pn=c and Ωn′=Ω|Gn=c for all n∈{1,…,N} and c∈{0,1} yields the class-specific precision and recall for the dataset D, respectively. Analogously, the intersection over union IOU for the dataset D is given by IOU(D)=1∑n=1NA(Ω,Wn)∑n=1NA(Ω,Wn)IOU(Gn,Pn,Wn).