# WindSightNet: The Inter-Annual Variability of Martian Winds Retrieved From InSight's Seismic Data With Machine Learning

Alexander Stott, Raphael Garcia, Naomi Murdoch, David Mimoun, Mélanie

Drilleau, Claire Newman, Aymeric Spiga, Don Banfield, Mark Lemmon, Sara Navarro, et al.

► To cite this version:

Alexander Stott, Raphael Garcia, Naomi Murdoch, David Mimoun, Mélanie Drilleau, et al. Wind-SightNet: The Inter-Annual Variability of Martian Winds Retrieved From InSight's Seismic Data With Machine Learning. Journal of Geophysical Research. Planets, 2025, 130 (2), 10.1029/2024JE008695. hal-05070531

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Distributed under a Creative Commons Attribution 4.0 International License
JGR Planets

RESEARCH ARTICLE

10.1029/2024JE008695

**Key Points:**

* We introduce a neural network to produce wind retrievals from the seismic data on InSight

* A year-to-year comparison confirms the consistency in the winds at InSight predominantly driven by large scale circulation

* Several transient year-to-year variations are linked to local atmospheric dust content and differences in baroclinic periods or phases

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

A. E. Stott,
alexander.stott@isae-supaero.fr

**Citation:**

Stott, A. E., Garcia, R. F., Murdoch, N., Mimoun, D., Drilleau, M., Newman, C., et al. (2025). WindSightNet: The inter-annual variability of martian winds retrieved from InSight's seismic data with machine learning. *Journal of Geophysical Research: Planets*, 130, e2024JE008695. https://doi.org/10.1029/2024JE008695

Received 4 SEP 2024

Accepted 4 FEB 2025

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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# WindSightNet: The Inter-Annual Variability of Martian Winds Retrieved From InSight's Seismic Data With Machine Learning

Alexander E. Stott¹ ID, Raphael F. Garcia¹ ID, Naomi Murdoch¹ ID, David Mimoun¹ ID, Mélanie Drilleau¹ ID, Claire Newman² ID, Aymeric Spiga³ ID, Don Banfield⁴, Mark Lemmon⁵ ID, Sara Navarro⁶, Luis Mora-Sotomayor⁶ ID, Constantinos Charalambous⁷ ID, William T. Pike⁷, Philippe Lognonné⁸ ID, and William B. Banerdt⁹ ID

¹Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Université de Toulouse, Toulouse, France, ²Aeolis Research, Chandler, AZ, USA, ³Laboratoire de Météorologie Dynamique/IPSL, Sorbonne Université, CNRS, Ecole Normale Supérieure, PSL Research University, Ecole Polytechnique, Paris, France, ⁴NASA Ames, Mountain View, CA, USA, ⁵Space Science Institute, Boulder, CO, USA, ⁶Centro de Astrobiologia (CAB), CSIC-INTA, Madrid, Spain, ⁷Department of Electrical and Electronic Engineering, Imperial College London, London, UK, ⁸Université de Paris, Institut de physique du globe de Paris, CNRS, Paris, France, ⁹Jet Propulsion Laboratory – California Institute of Technology, Pasadena, CA, USA

**Abstract** Wind measurements from landed missions on Mars are vital to characterize the near surface atmospheric behavior on Mars and improve atmospheric models. These winds are responsible for aeolian change and the mixing of dust in and out of the atmosphere, which has a significant effect on global circulation. The NASA InSight mission recorded wind data for around 750 sols. The seismometer, however, recorded data for around 1400 sols. The dominant source of energy in the seismic data is in fact due to winds. To this end, we propose a machine learning model, dubbed WindSightNet, to map the seismic data to wind speed and direction. The trained network achieves wind speed and direction measurements with errors of 0.932 m/s and 32.6°. We use WindSightNet to retrieve winds from the entire time the seismometer was recording to compare year-to-year wind variations at InSight. The continuous nature of the data set enables the extraction of periodic behavior. We observe a pattern of waves due to baroclinic activity with periods of ~2–3, ~4, ~5–7 and ~9–20 sols occurring $L_s = 180–360°$. We also observe periodicity during the day due to convective cells. This is used to estimate the boundary layer height, yielding values between 2.3 and 7.7 km. A data-science based metric is proposed to provide a quantification of the year-to-year differences in the wind speeds. This highlights variations linked to dust activity as well as other transient differences. On the whole, the seismic-derived winds confirm the dominance of the global circulation leading to repeatable weather patterns.

**Plain Language Summary** Wind measurements made on the surface of Mars are relatively rare, but are vital to understand how the atmosphere behaves. Near-surface winds cause dust lifting/mixing in the lower atmosphere. This is important on Mars because the atmosphere is very thin, hence dust blocks radiation from the Sun and impacts circulation. NASA's InSight mission recorded wind data for around 750 Mars days to study such effects. However, the seismometer recorded for almost 1400 sols. This seismometer recorded vibrations generated by the wind. We propose to estimate the winds based on the seismic measurements using advanced data processing to expand the wind data set. We use this data set to examine the year-to-year variation of the wind in terms of their daily and seasonal cycles. The fact the data set is so continuous also enables the extraction of atmospheric waves with periods of multiple sols and other phenomena such as convective cells. Finally, we propose a statistical method to quantify the year-to-year differences in wind speeds which highlights those due to atmospheric dust content variability as well as others for further study. These observed differences, however, are shown to be relatively minor compared to the major weather patterns which repeat from year to year.

## 1. Introduction

The NASA InSight mission was a geophysical observatory on the surface of Mars. The primary goal was to collect high-quality seismic data in order to determine the inner structure of Mars and characterize its seismicity (Banerdt et al., 2020; Lognonné et al., 2019). The observations in the mission data have proved sufficient in meeting the mission science goals and beyond (e.g., Drilleau et al., 2024; Khan et al., 2021; Knapmeyer-Endrun
et al., 2021; Lognonné et al., 2020; Samuel et al., 2023; Stähler et al., 2021). As well as seismic data, the mission collected wind, pressure and temperature data (Banfield et al., 2019). These environmental factors were expected to generate significant noise sources for the seismometer (Mimoun et al., 2017; Murdoch, Kenda, et al., 2017; Murdoch, Mimoun, et al., 2017). This atmospherically induced noise was indeed observed to limit seismic event detectability (Ceylan et al., 2022; Charalambous et al., 2021; Clinton et al., 2021; Pinot et al., 2024; Stott et al., 2023). On top of verifying the seismic results, the in situ meteorological data set has proved useful to study the atmosphere at the InSight landing site on Elysium Planitia (Banfield et al., 2019, 2020; Murdoch et al., 2023; Onodera et al., 2023; Spiga et al., 2018; Temel et al., 2022). The data confirmed the global circulation-induced wind patterns as well as revealing information on planetary scale (e.g., baroclinic) waves and smaller-scale gravity waves (Banfield et al., 2020). Furthermore, the continuous wind data set was useful to characterize turbulence (Chatain et al., 2021; Spiga et al., 2021) which is responsible for most short-term variations in the atmosphere. During the daytime, the turbulence is generated by convective activity and many associated pressure drops have been observed on the pressure sensor data (Lorenz et al., 2021; Murdoch et al., 2021).

At its conclusion, the InSight seismometer, SEIS, had successfully operated almost continuously from the final placement of the wind and thermal shield on sol 66 of the mission until its final transmission on sol 1440 (a sol is Martian day, whose duration is 24 hr 40 min). Sol 66 of the mission corresponds to solar longitude ($L_s$) 335° during Mars year 34, where Mars years are defined by a calendar of $L_s$ = 360° years in Clancy et al. (2000), Piqueux et al. (2015). The seismic data therefore covers the end of Mars year (MY) 34, MY 35 entirely and MY 36 up to $L_s$ =355°. On the other hand, the wind data set from the TWINS sensor, is mainly limited to the first Mars year of operations with data spanning around 750 sols. This is mostly complete in coverage from Sol 4 of the mission ($L_s$ = ~300° in MY 34) until around $L_s$ = ~330° in MY 36, with some data gaps due to operational issues. These data gaps became more prevalent after Sol ~580, $L_s$ = ~230° in MY 35. When possible, the sampling strategy for both seismic and wind data was for continuous round the clock observations of the entire sol.

The limitation in the TWINS data set coverage was due to power constraints caused by increasing dust accumulation on InSight's solar panels. To mitigate the loss in power, seven solar array cleaning experiments were conducted by dumping scoops of soil above the lander deck during periods of high wind (Golombek et al., 2023). This action dispersed sand onto the panels, which kicked dust off and suspended it in the atmosphere, thereby increasing power by approximately 15% during these periods (Golombek et al., 2023). This boost in power enabled the mission to continue its primary goal of continuous seismic observations until the final 200 Sols ($L_s$ > 230° in Mars year 36), when only partial sections of sols could be recorded.

Despite these efforts, the power issue was further compounded by the impending northern hemisphere winter, leading to the eventual end of the mission. The focus on seismic observations meant that pressure and wind data collection was severely limited. As a result, it is only possible to perform a limited inter-annual comparison with the recorded meteorological data. To address this gap, we propose a machine learning model, dubbed WindSightNet, to leverage the atmospherically induced noise seismic data and estimate winds over two Mars years.

This extends the work in Stott et al. (2023), which introduced a model to predict the seismic noise level induced from the atmospheric variations. The use of machine learning enables a robust capture of the various pathways and impacts on the ways in which wind can generate vibration on the seismometer (Charalambous et al., 2021; Stott et al., 2023) and so produce robust retrievals of wind speed and direction over the entire mission. Using machine learning in this way leverages the cross-sensitivities of instruments and separates the data in terms of physically meaningful signals which can be directly interpreted as if they were directly from a wind sensor. This approach helps counteract one of the main fall-backs of machine learning, where it often creates a “black box” and does not necessarily relate to any physical relationship. This application therefore represents a strategy that can be built upon to improve the data return and sensor systems in planetary missions.

This paper is organized as follows. We first introduce the physical mechanisms for wind-induced noise on the InSight seismometer which are utilized by the eventual machine learning model. We then describe WindSightNet's architecture and implementation of the neural network model, with a validation of its performance. We can then use WindSightNet to produce a catalog of wind speeds and directions over the entire InSight mission, which covers over 2 Mars years. We then highlight the relative qualities of the retrieved winds from WindSightNet and TWINS, which shows they are a close match in terms of distribution. Following this, we demonstrate the main seasonal weather patterns at InSight. As the WindSightNet provides a wind catalog over 2
Mars years with a sampling strategy designed to obtain continuous observations over the entire sol for every sol, we use it to provide an assessment of inter-annual variability between MY 35 and 36. The comparison of the PDFs of the wind speed and direction over these years match closely for most of the time, highlighting the seasonal weather patterns. This is in line with the expected repeatability of Martian weather. Utilizing the continuity of the wind speed signal, we extract the periodicity during the main convective hours (1000–1600 LTST) and use it to estimate the evolution of PBL height over the sol and the seasons. At periods over a sol, we extract the pattern of baroclinic waves during the winter seasons. Finally, we introduce a data science motivated metric to quantify the difference between wind speed distributions for the same 20 sol periods year-to-year. This further verifies that the main overall control of the winds is consistent year-to-year but also highlights some changes which can be linked to differences in optical depth as well as some which are not clearly linked. As a result, this work can help assess the complex impact of dust content in the variation of atmospheric conditions on Mars. WindSightNet adds to the growing library of in situ meteorological data sets on Mars. The combination of multi-year continuous data collection and static location offers a unique opportunity for future comparison to the long term data sets from Perseverance and Curiosity missions, which are designed to rove across the terrain (Gómez-Elvira et al., 2012, 2014; Martínez et al., 2017; Viúdez-Moreiras, Lemmon, et al., 2022; Viúdez-Moreiras, Torre, et al., 2022).

## 2. A Machine Learning Wind Catalog From Seismic Data

### 2.1. Atmospherically Induced Signals on the InSight Seismometer

Seismic installations are usually placed in vaults or buried to help isolate the sensor from atmospherically generated noise. Nevertheless, signals induced from wind (Dybing et al., 2019; Quigley & West, 2024), temperature (Doody et al., 2018) and pressure (Zürn et al., 2022; Zürn & Widmer, 1995) are commonplace in seismic data. This is also the case for InSight on Mars, where the seismometer is placed directly on the ground with additional protection provided by a wind and thermal shield. The physical pathways for this noise injection are well established in the pre-mission modeling of Mimoun et al. (2017) which was subsequently validated with the in situ data in Pinot et al. (2024).

The most significant energy contribution to the seismic data is from wind generated signals. The predominant source of this contribution arises from wind-induced lander vibrations, as expected from the pre-mission modeling and validated in Stott et al. (2021) and Pinot et al. (2024). These wind generated signals occur as both a broadband excitation as well as strong resonant modes in the seismic data. Such effects are observed across the full spectrum of the recorded data, up to 50 Hz. We focus particularly on the effects within the 0.1–5 Hz range as this is covered by the majority of the continuous data of the mission, where the sampling rate was at 10 or 20 Hz. The broadband excitation arises from wind forcing on the lander through aerodynamic drag, as modeled in Murdoch, Mimoun, et al. (2017) and shown in Pinot et al. (2024). These vibrations couple through the regolith to the sensor. To capture the impact of these effects, Charalambous et al. (2021) provided an analysis of the sensitivity of the seismic data to the wind over the sol and seasons as well as across different frequencies. This demonstrated that the seismic velocity signal power, that is, the root mean square (RMS) envelope, is correlated to the wind speed. The relationship is, therefore, in terms of a modulation of the seismic data by the wind. The observed correlation between wind speed and seismic velocity RMS was demonstrated to be able to generate local fits of the seismic data to wind speed. Stott et al. (2023) further utilized this approach to estimate the atmospherically generated noise with the bandwidths of interest for detecting seismic events (0.4–1 Hz and 2.2–2.6 Hz).

On top of the broadband excitation, the wind excites resonant modes of the lander which is modeled in Murdoch et al. (2018) and the vibrations couple through the regolith in the same way. These modes are highly sensitive to the wind (Charalambous et al., 2021) and their characteristics are described in Dahmen et al. (2021). Some resonances are also present from the seismic sensor assembly, as described in Hurst et al. (2021). Other sources such as pressure forcing are also present but only when not masked by the wind signature and are more prevalent at lower frequencies, ~0.05–0.2 Hz (Garcia et al., 2020). The temperature sensitivity mainly induces signals below 0.01 Hz (Lognonné et al., 2020; Pinot et al., 2024; Stott et al., 2021). The physical links between the meteorological and seismic data on InSight are well understood.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Diagram of the WindSightNet architecture.</figcaption></figure>

## 2.2. WindSightNet Architecture

The goal is to produce an end-to-end pipeline which takes the raw seismic data as an input and outputs an estimate of the wind speed and direction. The focus is to create a robust and reliable retrieval. As a result, we design an architecture to produce wind estimates at a sampling rate of 0.01 Hz. Such a sampling rate is useful to analyze the large-scale winds at the InSight lander, indicative of global circulation, weather patterns and diurnal circulation. For example, Newman et al. (2022) utilize 60 s wind averages for model comparison, which is of a similar order. The choice of 0.01 Hz ensures a consistently good correlation between the seismic signal power and wind data (Charalambous et al., 2021; Stott et al., 2023), with minimal impact from shorter term variations in the seismic data not due to winds such as glitches (Scholz et al., 2020).

We choose the WindSightNet architecture to produce an estimate of the wind speed and direction for a single point in time based on a single sample for an input feature relating to the same point in time, where this time point represents the 0.01 Hz sampling rate. This is illustrated in Figure 1. This one-in, one-out approach aims to mimic the abilities of an ideal sensor, whereby the output is based on the information the sensor observes at that point. The architecture should then represent a causal relationship without hysteresis. In doing so, the model does not learn patterns over time. Although learning such wind patterns themselves may be of interest, such an approach would limit the predictive abilities of the network necessary to create a trustworthy wind catalog. For example, previously unseen patterns could not be robustly produced by such an architecture. This follows the discussion in Kumar et al. (2023), who implemented a variety of machine learning models for TWINS wind sensor retrievals and identified there was little improvement from more complex architectures and including time lag. Using this one-in one-out approach is also appropriate based on the physical cause of wind-induced signals outlined above. Over the 0.01 Hz sampling rate the relationships can be considered instantaneous.

## 2.3. Data and Pre-Processing Pipeline

Prior to the machine learning implementation, data must be pre-processed to a suitable format. We base this pipeline on that in Stott et al. (2023), where SEIS and TWINS data were processed to remove instrument response, clean and align sampling rates.

Wind data are required as targets for the optimization of the machine learning model. The TWINS instrument comprises of two wind sensor booms situated at the edges of InSight's deck (Banfield et al., 2019). These booms
face outward over InSight's west and east solar panels, measuring the horizontal winds. A composite data channel is derived by selecting the output from the boom which is most appropriate to sense wind from the prevailing direction.

The wind sensors are calibrated based on a grid obtained in wind tunnel testing (Banfield et al., 2019). The best resolution of the calibration grid spacings is for middling winds, with higher wind speeds and lower wind speeds less accurately determined. Note that this calibration grid is in terms of the Reynolds number and not wind speed. As a result, the performance depends on the conversion of the Reynolds number to wind speed, due to variations in density and turbulence in the wind flow. There are no calibration points for Reynolds numbers below 50 and only a coarse grid between 50 and 150. This often appears as a wind speed sensitivity threshold in the seismic data for wind speeds around 2 m/s, where the exact value of this threshold varies according to the Reynolds number.

The seismic data are taken from the Very-BroadBand (VBB) sensor (Lognonné et al., 2019), which operated almost continuously from sol 66 of the mission following the deployment of the wind and thermal shield (WTS). An initial data cleaning step is required to limit the impact of known problematic noise sources on the seismometer. The first of these is glitches, which occur due to small acceleration steps likely from thermal expansion effects (Scholz et al., 2020). These are extremely frequent and are removed using the developed “ISAE” method in Scholz et al. (2020). A further cleaning step is taken to remove tick noise which is electronic cross-talk from the clock (Ceylan et al., 2021), also outlined in Scholz et al. (2020). Following this cleaning process, the next step is to remove the instrument response which is achieved through a deconvolution of the collected data and the calibrated instrument response (Lognonné et al., 2019). Finally, the 3 axes of the VBB U, V, W sensors are rotated to vertical, Z, north, N, and east, E, coordinate system. This is because the individual components of the VBB are not orthogonal and are in a flattened Galperin configuration. This pre-processing, including the instrument response deconvolution, is computed using the ObsPy toolbox (Krischer et al., 2015; Megies et al., 2011).

The seismic data are next transformed into the input features for the machine learning model. These features are chosen to best represent the variation in the seismic data that relates to the wind. As discussed above, this takes the form of the RMS envelopes of the seismic velocity data based on Charalambous et al. (2021). To that end, we select the input features as several RMS envelopes of the seismic data corresponding to different bandwidths and for each of the vertical and horizontal axes. The selected frequency bandwidths of the RMS envelopes are given as.

* 3.7–4.3 Hz—resonant mode

* 1.2–1.9 Hz—resonant mode

* 2.8–3.6 Hz—resonant mode

* 0.5–1 Hz—flat spectral variation with wind speed

These bandwidths are primarily selected to cover the frequencies of resonances from the InSight lander (Dahmen et al., 2021; Murdoch et al., 2018) as they represent the frequency bands which are most sensitive to wind speed (Charalambous et al., 2021). Using several different modes provides more information as each mode behaves slightly differently in response to the environment, as demonstrated in Dahmen et al. (2021). These modes have damping ratios between 0.5% and 1.5% (Dahmen et al., 2021) and therefore a Q-factor sufficient for their excitation to be considered instantaneous for the output sampling rate of the wind at 0.01 Hz. An additional RMS envelope bandwidth, 0.5–1 Hz, which does not contain a resonant mode, is chosen to provide additional information and capture the broadband energy injection from wind signals as discussed above and modeled in Murdoch, Mimoun, et al. (2017). In the 0.5–1 Hz range, the velocity spectra exhibit a flat spectral response to wind and was successfully used to analyze atmospheric injection into marsquakes in Stott et al. (2023). In total, this leads to 12 RMS envelopes to use as input features for the machine learning model.

Following the feature transformations, a further cleaning step is performed to limit outliers, decimate, remove artifacts generated by the processing (based on the pipeline in Stott et al. (2023)) and normalize it. The decimation step for the seismic RMS envelopes and the wind data includes an anti-aliasing filter prior to downsampling. The data pre-processing pipeline steps for the seismic data are then summarized as.

1. Load data corresponding to a single sol, perform de-glitching, de-tick and removal of instrument response.

2. Rotate from flattened galperin U, V, W axes to orthogonal Z, N, E axes.

3. Filter each trace according to the feature envelope bandwidths.

4. Calculate the RMS envelopes of each filtered trace for sliding windows of size 40 s.

5. Median filter the RMS envelopes over 5 s windows.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Flow chart of pre-processing steps for the VBB data.</figcaption></figure>

6. Decimate the seismic envelopes and wind data to a rate of 0.01 Hz.

7. Mask processing artifacts and large outliers.

8. Normalize the data set to have a minimum value of -1 and maximum value of 1.

This is demonstrated as a flow chart in Figure 2. This pipeline is developed to take into account data from the multiple sampling rates of the TWINS and SEIS data over the mission. The VBB collected data at 10 Hz or 20 Hz sampling rates, while the wind data has been collected at 0.1 Hz, 0.5 and 1 Hz sampling rates. Furthermore, the training stage requires the wind data to be aligned with the available seismic data in time. This subset of data is created through masking values of the input features where wind samples are not available. As discussed above, the relationship between the two can be assumed instantaneous at these time scales. The alignment between wind and seismic features maintains the phase between the wind and seismic data.

## 2.4. Neural Network Implementation

As discussed above, we aim to develop a machine learning model to provide a regression between the wind data and seismic data-derived features. We choose to implement a multilayer perceptron neural network (Goodfellow et al., 2016) for the task, based on its successful usage in Stott et al. (2023). The architecture is demonstrated in
Figure 1. The model will output a value of wind speed and direction for a given input of the 12 RMS envelope features calculated above. Each input is a single value of that RMS envelope for the same time instance as the predicted output.

Between the input and output layers, the neural network architecture consists of several sequentially connected hidden layers with a given number of neurons. Each neuron in each layer is fully connected to those on the preceding layer, meaning the output values from all neurons of a previous layer are taken as inputs for each neuron in the current layer. Each neuron applies an activation function to its inputs to transform the data, where the combination of these transforms eventually results in the final fit.

The first layer ingests the current sample of each of the 12 RMS envelope features and passes through a linear activation function as

$$f(\mathbf{x}) = \mathbf{b}^{\top}\mathbf{x} + c. \qquad (1)$$

where **x** corresponds to a vector containing the 12 inputs and **b** is a vector of the selected weights and **c** is a bias. For the hidden layers, between the input and output layers, we select a ReLu (rectified linear) activation function given as

$$f(\mathbf{x}) = \max(0, \mathbf{b}^{\top}\mathbf{x} + c). \qquad (2)$$

where **x** is a vector of the outputs from the previous layer's neurons, **b** a vector of weights and **c** a bias which are optimized for each individual neuron. The final layer is a linear layer with the weights and biases selected to output values for the wind speed and direction.

The values of each activation function's weights and biases are set through an optimization process with example training data, that is, example inputs from the seismic data and the corresponding recorded wind. The target wind data, y, are used to compute the mean square error (MSE) of the neural network prediction, ŷ, based on N given input samples as

$$MSE = 1/N \sum_{n=0}^{N-1} (y_n - \hat{y}_n)^2. \qquad (3)$$

This represents the cost function to be optimized through a type of stochastic gradient descent algorithm. This algorithm updates the weights and biases in steps based on the iteratively evaluated gradient, thus minimizing the cost function. The training process consists of a number of epochs which represents a pass of the complete data set used for optimization. Within each epoch the gradient descent iteration is evaluated for a batch of data, where the size of the batch, N, can be selected to improve computational efficiency as well as acting as a regularization.

The full training process requires three different groups of data: a training set for the optimization, a validation set to check for overfitting and a test set for final performance evaluation. These data sets are selected from an initial data set containing all the values where there is both seismic and wind data available following the pre-processing above, which is 475,110 samples. These data are split into 1 hour chunks. 20% of these hour long chunks are randomly selected and set aside as the test data, equating to 95,022 samples. Of the remaining 80% of the chunks, 20% (76,018 samples) are randomly selected for the validation data set and the remaining data (304,070 samples) constitute the training data set. The separation of data in terms of hour long chunks avoids too many correlated samples being present in each data set and so prevents data leakage and overfitting. The random separation of the 1 hour chunks is done according to indexing drawn from a uniform distribution and so each data set is shuffled and contains a proportion of blocks uniformly spread over the available data.

Here, we use the ADAM optimizer (Kingma & Ba, 2014), which requires a selected learning rate that defines the step in the direction of the gradient on each iteration. This sets the speed of convergence but also influences the final accuracy. To implement our neural networks, we used the Keras Python package (Chollet, 2015).

The next task was to select the best neural network topology. This was achieved through a process known as tuning where several neural networks were trained for a given number of hidden layers, number of neurons on
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Training and validation data set error over training epochs for the final selected topology of the WindSightNet neural network. The loss value is normalized.</figcaption></figure>

each layer and batch size. Each network was trained for 400 epochs and the final error was evaluated on the training and validation data sets to determine the optimal network without overfitting. Following this procedure, we selected a network trained with 14 layers and 30 neurons, trained with a batch size of 4096. This choice represents the best performance in terms of error where increased complexity did not have a significant effect. The relatively large batch size provides regularization. Figure 3 shows the validation and training data set error over the training epochs for this network. The match between the validation and training error indicated there was no overfitting. Furthermore, the errors reached a plateau after and so the model was sufficiently trained. To illustrate the tuning process, the training and validation errors of several networks used for this tuning are shown in the Figure S1 in Supporting Information S1 for a batch size of 4096. Smaller and larger batch sizes were tested and were seen to increase the error.

The final error on the training data for the wind speed was 0.926 m/s and 30.0° for the wind direction. In comparison, the errors for the test data set were 0.932 m/s for the wind speed and 32.6° for the wind direction. The training and test errors are very close and as such demonstrate a robust fit. The

TWINS sensor has stated relative accuracy of ± 15% for winds in the range 1–60 m/s (Banfield et al., 2019) and resolution 0.4 m/s for speeds below 10 m/s and 2 m/s for speeds up to 60 m/s. As such, the error of the neural network prediction is of a similar order to the sensor performance, which indicates it approaches the limitations of the training data. Several networks had a similar performance and so provide further confidence we have reached the limits of the current approach.

## 3. Analysis of the Wind Speed and Direction Retrievals

The final trained neural network was used to estimate wind values from across the entire mission, including when the TWINS sensor was not operating. From here, we refer to these wind predictions from the selected neural network as the WindSightNet retrievals. Based on the consistency between the training and test errors, the prediction over data used for training and test can now be considered equivalent and so the WindSightNet retrievals represent a wind catalog at InSight over the entire mission. In the following section we analyze the relative qualities of the WindSightNet and TWINS catalogs and examine the wind behavior over the InSight mission using both data sets. The WindSightNet wind catalog produced over the entire mission is available Stott (2024a) and example usage code Stott (2024b).

### 3.1. Comparison of WindSightNet and TWINS Wind Catalogs

Figure 4 shows the wind speed and direction retrievals from the TWINS sensor and those from WindSightNet. This shows an overall good match between the time series for both wind speed and direction, with the same diurnal and seasonal patterns visible in both data sets. Furthermore, Figure 4 highlights the extended coverage provided by WindSightNet, particularly for the second Martian year of the mission after Sol 668. As expected, this demonstrates that the same general seasonal pattern is observed for the second Martian year.

The prediction performance in terms of the wind speed distributions is further demonstrated in Figure 5, which shows the 0th, 25th, 50th, 75th and 100th percentile of the wind speed distributions for each sol over the length of the mission for both WindSightNet and TWINS. The 0th and 100th percentile refer to the minimum and maximum wind speeds observed on a given sol. In the first year the WindSightNet and TWINS percentiles are in agreement. This verifies that the wind speed prediction is suitable, especially for statistical analysis as the distribution's moments will match those of TWINS.

There is some discrepancy between the 0th percentile, the minimum wind speed, evaluated on WindSightNet and TWINS. As discussed above, the calibration grid used for TWINS wind retrieval is more sparsely defined at lower wind speeds and so their is a coarse level of accuracy. Recall also the grid spacing is defined in terms of Reynolds number and so the accuracy is not directly interpretable in terms of wind speed. This means that the target data used to train the network does not contain the necessary information to differentiate between different values of low wind speeds. For example, similar given inputs may correspond to multiple observed wind speeds within the
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Comparison of wind speed and direction data across the InSight mission retrieved from TWINS and WindSightNet. The vertical axis denotes the local true solar time (LTST) and the horizontal axis denotes the day (sol) of the mission/solar longitude $L_s$. The color denotes the speed/direction and saturated colors indicate missing data.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** 0th, 25th, 50th, 75th and 100th percentile of the wind speed distribution on each sol over the InSight mission for WindSightNet (full lines) and TWINS (dark dashed lines).</figcaption></figure>

data. Moreover, at a certain point the seismometer noise level will come into play at these low wind speeds, where the system is not sensitive to such low winds. As a result, in these conditions the WindSightNet output in these conditions indicates more constant low winds. This is in fact reflective of the knowledge of the wind speed at this point. However, this means that WindSightNet will not predict values near 0 m/s. Nevertheless, the WindSightNet retrievals provide an appropriate data set to study the winds on Mars and produce an inter-annual comparison.

To further explore the match between the WindSightNet and TWINS retrievals over a sol, Figure 6 shows the wind speeds and directions for 6 representative sols of the martian year in each 60° $L_s$ seasonal time period. Note that the same sol of the martian year is also shown from the second year of the mission in the case of WindSightNet, and all WindSightNet predictions over the seasonal period are shown in gray. The match further confirms that the mean wind speed and direction is well predicted. During the daytime the wind fluctuates more considerably which is also captured by WindSightNet. In some cases the TWINS retrieval produces slightly higher and lower speeds than that of WindSightNet, which is due to the fact that there are fewer samples at the extremes (as the distribution has heavy/long tails) and so not enough information of these extremes is captured in training. On the other hand, the wind direction retrieval from WindSightNet shows some stronger variability than the TWINS retrieval. This may be because the TWINS algorithm has to select a boom which is most sensitive to the current prevailing wind direction, potentially missing rapid direction shifts that can be observed by the seismometer.

Most seismic events are observed during what is termed the quiet period (Ceylan et al., 2022; Clinton et al., 2021), a section of time following the collapse of the boundary layer from ~1700-0300 LTST and the wind speed is between ~0–2 m/s. The WindSightNet prediction shows a slowly varying low wind speed. On the other hand, the TWINS outputs more discrete steps, which demonstrate the coarser calibration grid at these Reynolds numbers. These aspects are seen in $L_s$ = 0 – 120° after 1700 LTST in Figure 6. To this end, the WindSightNet output is generally more smooth than TWINS but can miss evidence of low wind speed fluctuations. This quiet period disappears from $L_s$ = ~200 – 350°, where WindSightNet and TWINS outputs match more closely.

The gray shaded lines in Figure 6 are each of the WindSightNet retrievals over the respective $L_s$ period, representing the overall wind distribution. This shows the consistency of the diurnal variation within a season and the slow progression between the characteristic behaviors. The lighter red line is the WindSightNet wind retrieval for the sol one Mars year after the sol used to compare to TWINS. These each show very similar behavior year-to-year.
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Wind speed and direction over a sol for over $L_s$. The WindSightNet prediction (red) is compared to the TWINS estimate (blue) and the WindSightNet prediction for the sol exactly one Mars year later (light red). The gray shaded lines are the WinSightNet retrievals over the stated $L_s$ period.</figcaption></figure>

To compare the relative qualities of the WindSightNet data for different atmospheric conditions we calculated the RMSE between WindSightNet and TWINS wind speeds during 0100–0600, 1000–1500, and 1900–2300 LTST independently. The RMSE was 0.7, 1.4, and 0.7 m/s respectively. In terms of percentage of the mean wind speed, these errors correspond to 12%, 20%, and 16% during these times. The relative differences are of a similar order to TWINS stated accuracy of ±15%. The larger absolute difference during the middle of the day is also consistent with the WindSightNet retrievals being more smooth than TWINS, as mentioned above. Overall, this indicates that WindSightNet does not produce as large extremes or variations compared to TWINS.
<table><caption>**Table 1**
Main Wind Regimes at InSight</caption><thead><tr><th>L<sub>s</sub> (°)</th><th>Period</th><th>Characteristics</th></tr></thead><tbody><tr><td>L<sub>s</sub> = 35–180°</td><td>R<sub>1</sub> - global Hadley circulation Spiga et al. (2018)</td><td><ul><li>Prevailing winds are north-westerly</li><li>Strong convective turbulence during the day</li><li>Quiet periods evolving to north-easterly downslope winds and a low-level jet at night</li></ul></td></tr><tr><td>L<sub>s</sub> = 245–305°</td><td>R<sub>2</sub> - global Hadley circulation Spiga et al. (2018)</td><td><ul><li>Prevailing winds are south-easterly</li><li>Higher atmospheric dust content</li><li>Winds modulated sol-to-sol by baroclinic instabilities</li></ul></td></tr><tr><td>L<sub>s</sub> = 207–320°</td><td>Season 5 Chatain et al. (2021)</td><td><ul><li>Turbulence throughout the entire sol</li><li>Nocturnal winds from shear driven turbulence from an enhanced low-level jet</li></ul></td></tr><tr><td>L<sub>s</sub> = 180–245° and 305–35°</td><td>Transition period Spiga et al. (2018)</td><td><ul><li>Regular switching between R<sub>1</sub> and R<sub>2</sub></li></ul></td></tr></tbody></table>

## 3.2. Diurnal and Seasonal Wind Patterns at InSight

Figure 4 also highlights the general pattern of winds over the Martian day and season. Spiga et al. (2018) described with global climate modeling two main regimes of the Hadley circulation observed by InSight over the Martian year. The first regime, denoted as $R_1$, takes place from $L_s = 35–180°$, over the northern hemisphere spring and summer. At this time the winds are due to the northward return branch of the Hadley circulation which are then modified by the Coriolis force and the regional topography of the dichotomy and Elysium Mons, resulting in prevailing winds from the south-east. This seasonal behavior was observed during the daytime in the early stages of the mission (Banfield et al., 2020). Classically, these daytime winds on Mars are characterized by strong convective turbulence (Spiga et al., 2021). This is driven by large thermal gradients arising from the rapid heating of the ground from solar irradiance and relatively inefficient heating of the air. Spiga et al. (2021) demonstrated that the ground temperature is indeed a suitable explanatory variable for InSight's observed daytime convective activity. As a result, over the day large planetary boundary layers (PBLs) can evolve with large convective cells. With a sampling rate of 0.01 Hz, the winds retrieved by WindSightNet do not clearly show the turbulent fluctuations themselves. However, they do characterize the larger scale wind patterns which can be associated with turbulent conditions to help their overall characterization, such as turbulent cells. During the $R_1$ season, these turbulent cells are advected by the prevailing Hadley circulation. On the other hand, at night the gradient similarly disappears quickly and the PBL collapses and the atmosphere becomes stably stratified with very low wind. This quiet period is the best time of the mission for observing marsquakes (Clinton et al., 2021; Pinot et al., 2024; Stott et al., 2023). Regional topography can also give rise to slope winds. Despite the relatively low slope at InSight, downslope winds from a rise in elevation toward the dichotomy (east north easterly) can be observed (Banfield et al., 2020). At night a low-level nocturnal jet can develop. This generates stronger winds which lead to shear driven turbulence.

Later in the year a second Hadley circulation regime, denoted $R_2$, occurs for $L_s = 245–305°$. At this time the winds switch to come from the north and are again modified by topography and the coriolis force to generate south-easterly winds (Spiga et al., 2018). At this time of year, the atmosphere generally has a higher dust content and so has different thermal properties. This $R_2$ regime overlaps with a period identified in Chatain et al. (2021) for $L_s = 207–320°$ where there is persistent turbulence present throughout the entire sol, including the night. The nocturnal low-level jet is enhanced leading to shear driven turbulence, as shown by Richardson numbers calculated to be in the critical range. During this period, the winds are also modulated by baroclinic waves from midlatitude instabilities over periods of several sols, in contrast to the minimal sol-to-sol variation during $R_1$. Between these dominant large-scale regimes $R_1$ and $R_2$, there is a period of transition. As this time, the observed large-scale circulation may switch between $R_1$ and $R_2$ with varying strengths. Table 1 provides a summary of the main weather regimes at InSight and their characteristics.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Matrix of wind rose plots of wind direction over 60° *L*<sub>s</sub> bins (columns) and 4 hr LTST bins (rows) where the rose is a polar representation of a histogram PDF estimate normalized in density. The angle indicated corresponds to the direction the winds are coming from. Red is the WindSightNet prediction during Mars year 35, purple is the WindSightNet prediction during Mars year 36 and gray is the TWINS data recorded during Mars year 35.</figcaption></figure>

# 4. Interannual Comparison From WindSightNet Retrievals

## 4.1. Distributions of the Wind Direction

Figure 7 shows a wind rose (a histogram in polar coordinates) of the wind directions for *L*<sub>s</sub> in bins of 60° across the columns and LTST for bins of 4 hr over the rows, starting at 2200-0200 LTST. The distributions are separated in terms of Mars years 35 and 36. The red line is the WindSightNet wind direction for Mars year 35 and the purple is the WindSightNet retrieval for Mars year 36. The gray line is the TWINS retrieval for MY 35 for comparison. This first demonstrates that the distribution of the TWINS wind direction for mars year 35 is similar to that of WindSightNet, adding further confidence in the retrieved wind directions.

The pattern of Figure 7 outlines the evolution of the diurnal wind distribution over the seasons. This follows the outlined patterns of the main Hadley circulations $R_1$ and $R_2$ during $L_s = 35–180°$ and $L_s = 245–305°$, where the winds are north westerly and south easterly during the day respectively. At night, the winds rotate due to slope winds and the low-level nocturnal jet. This is enhanced during the period $L_s = 207–320°$ as identified by Chatain et al. (2021), and the wind direction remains that of the global circulation (south easterly) until 0600–1000 LTST.
The transition periods exhibit the most varied period of wind directions where the distribution does not show a prevailing direction. This is particularly evident for 1000–1400 LTST during $L_s = 180–240°$ and, to a lesser extent, 300–360°. This may be due to local turbulent wind fluctuations generating random directions which are stronger than any winds advecting them. During these periods the relative contribution of any prevailing north-easterly winds is greater for MY 36 than 35, indicated by the relatively lower density of other directions in the normalized PDF. At this point in MY 36 the atmospheric dust content is higher than in MY 35, which may affect the relative impact of turbulence and prevailing winds.

Overall, the wind directions highlight the repeatability of the winds year-to-year, driven by the large scale circulation effects. The main observed periods of year-to-year divergence are during 0200–0600 LTST for $L_s = 60–120°$ and then throughout the night for $L_s = 120–180°$. Starting at 0200–0600 LTST for $L_s = 60–120°$, the north-easterly winds during MY 36 are rotated further east than for MY35. This direction persists over the nighttime for $L_s = 120–180°$ in MY 36, whereas the direction shifts to be easterly for MY 35.

## 4.2. Distributions of the Wind Speed

Figure 8 shows the PDF estimates (as a Kernel Density Estimate (KDE)) for the wind speed over different periods of $L_s$ and LTST, with the quartiles and mean indicated by dashed and dotted lines respectively. These are plotted separately for MY 35 and 36 back-to-back for a direct inter-annual comparison. These again demonstrate a high level of repeatability year-to-year, highlighting the main characteristics of the circulation regimes as outlined in Table 1. Figure S2 in Supporting Information S1 shows the same analysis using the TWINS winds for MY 35 instead of WindSightNet.

For $L_s = 0–180°$, the daytime winds are marked by significant convective turbulence, which are characterized by a wide distribution and are positively skewed toward higher wind speeds around 10 m/s. Recall, this does not necessarily capture turbulent fluctuations as the sampling rate is 0.01 Hz, but the larger scale structures associated with convective activity such as convective cells. The 1400–1800 LTST bins cover the collapse of the PBL and so are bimodal. Murdoch et al. (2023) observed that the shut-off of the PBL is faster than its onset and, moreover, the spectral slope of the wind is different after the collapse of the PBL than it is prior to the PBL onset. This asymmetry indicates that alternative processes are at play for the heating/cooling of the surface/atmosphere at the onset and conclusion of the PBL. The bimodal nature of the distribution for 1400–1800 LTST over sunset in $L_s = 0–180°$ supports the fast shut-off, particularly as the time is mostly covered by daytime. On the other hand, there is less of an effect for distributions covering sunrise. Later in the night and into early morning, the winds increase due to the development of a low-level nocturnal jet. This is characterized by a narrower distribution than that of the convective turbulence with a lower mean. During the first half of the year the nighttime winds are generally weak, although speeds of up to 10 m/s can be reached briefly.

The quiet periods following the PBL collapse no longer occur frequently for $L_s = 180–360°$, which covers the transition periods and second Hadley circulation regime. This is due to the generally dustier atmosphere. The distributions now have a more negative skew throughout the sol for the transition periods. For $L_s = 240–300°$, containing the Season 5 period of Chatain et al. (2021), the wind distributions are at least bimodal throughout the sol with generally higher winds than the preceding or subsequent $L_s$. During the daytime the winds are not generally as high as during the first half of the year with strong convective turbulence. The nighttime winds are significantly higher than in other seasons, linked to the increased shear driven turbulence.

Although the wind distributions patterns are generally similar, there are some notable differences between MY 35 and 36. During the first Hadley regime ($L_s = 0–120°$) the winds are consistently slightly stronger in MY 35 than in MY 36 during 1000–1400 LTST, highlighted by the higher mean and quartiles of the distribution. This corresponds to the period of the day with the strongest vertical temperature gradient and similar behavior is shown over the full sol in Figure 5. This is in agreement with Charalambous et al. (2023), which indicated lofting thresholds were more frequently reached during MY 35. There is also a slight period of difference for 1800–2200 LTST during $L_s = 240–300°$. The wind distributions share the same pattern and range of speeds, but with a higher density of high winds during MY 35. The differences during $L_s = 300–360°$ are likely not statistically significant over 60° of $L_s$ as the coverage of WindSightNet in this range is relatively sparse for MY 36 due to more gaps in the seismic data, shown in Figure 4. It is notable that the differences highlighted by the wind speed distributions are not during the same times as those shown by the wind directions, indicating different effects.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Matrix of violin plots for the WindSightNet's wind speed distributions for different LTST and Ls bins. Each violin represents the kernel density estimate (KDE) of the probability density function (PDF) of the wind speed on the Y-axis with the left side corresponding to Mars year 35 and the right side corresponding to Mars year 36. The dotted lines indicate the distributions quartiles and the dashed line the mean.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Evolution of the normalized PSD of three different two hour windows (left to right: 1000–1200, 1200–1400, 1400–1600 LTST) of wind speed over the mission.</figcaption></figure>

4.3. Estimation of the PBL Height

The continuous nature of the InSight data records enables techniques such as spectral analysis, as exploited in Murdoch et al. (2023), which analyzed the behavior of the spectral slope over the Martian day and seasons. This analysis characterized the behavior around the inertial regime of turbulence spectra, along with the transition to the source region.

Figure 9 demonstrates the normalized power spectral density (PSD) for each sol over the mission during the hours of 10–12, 12–14, and 14–16 LTST progressively, which are hours generally during the convective part of the sol. A periodic behavior is observed, evolving over the hours and seasons. This periodicity is due to the advection of the convective cells, and so adds further information on the source region of turbulence, extending the characterizations in Murdoch et al. (2023). On the whole, the observed peak becomes progressively lower frequency over the sol. This frequency relates to the size of the convective cells driven by the large vertical surface to air temperature gradients. Following Spiga et al. (2021), we can estimate the PBL height. The width of the convective cell is first calculated as the advection wind speed (the average wind speed over the 2 hr window) divided by the peak frequency from the PSDs in Figure 9. The calculated convective cell width can be transformed to the PBL height by dividing by a factor of 1.2 based on Willis and Deardorff (1979). This value is corrected according to Spiga et al. (2021) which empirically demonstrated that the true PBL height is a factor of ~2 lower than the estimate calculated in this way.

Table 2 summarizes the calculated PBL height estimates for each period of *L*<sub>s</sub> and LTST for WindSightNet data and TWINS for MY 35. The TWINS values are extracted from the same analysis as shown in Figure 9 and displayed in Figure S3 in Supporting Information S1. On the whole, the estimates of PBL height for MY 35 from WindSightNet and TWINS fall within the calculated standard errors of each other aside from 10 to 12 LTST for
<table><caption>**Table 2**
Estimated PBL Height</caption><thead><tr><th rowspan="3">L<sub>s</sub> (°)</th><th colspan="9">PBL height (km)</th></tr><tr><th colspan="3">1000–1200 LTST</th><th colspan="3">1200–1400 LTST</th><th colspan="3">1400–1600 LTST</th></tr><tr><th>TWINS</th><th>MY 35</th><th>MY 36</th><th>TWINS</th><th>MY 35</th><th>MY 36</th><th>TWINS</th><th>MY 35</th><th>MY 36</th></tr></thead><tbody><tr><td>0–60</td><td>2.7 ± 0.5</td><td>2.3 ± 0.2</td><td>2.4 ± 0.3</td><td>4.6 ± 0.4</td><td>4.6 ± 0.4</td><td>4.5 ± 0.4</td><td>6.8 ± 0.5</td><td>5.8 ± 0.4</td><td>5.6 ± 0.5</td></tr><tr><td>60–120</td><td>2.6 ± 0.2</td><td>2.6 ± 0.4</td><td>2.4 ± 0.3</td><td>3.8 ± 0.3</td><td>4.2 ± 0.4</td><td>3.3 ± 0.4</td><td>5.7 ± 0.6</td><td>5.4 ± 0.5</td><td>4.9 ± 0.4</td></tr><tr><td>120–180</td><td>2.8 ± 0.2</td><td>3.0 ± 0.4</td><td>2.7 ± 0.5</td><td>5.1 ± 0.5</td><td>5.5 ± 0.5</td><td>5.2 ± 0.6</td><td>7.8 ± 0.6</td><td>6.7 ± 0.5</td><td>7.0 ± 0.8</td></tr><tr><td>180–240</td><td>4.1 ± 0.5</td><td>3.1 ± 0.3</td><td>3.7 ± 0.5</td><td>5.8 ± 0.6</td><td>5.6 ± 0.5</td><td>4.5 ± 0.5</td><td>4.8 ± 0.6</td><td>4.8 ± 0.5</td><td>3.7 ± 0.5</td></tr><tr><td>240–300</td><td>3.2 ± 0.5</td><td>3.7 ± 0.5</td><td>-</td><td>3.0 ± 0.5</td><td>3.0 ± 0.3</td><td>3.0 ± 0.6</td><td>5.5 ± 0.9</td><td>3.9 ± 0.6</td><td>3.9 ± 1.3</td></tr><tr><td>300–360</td><td>2.6 ± 0.8</td><td>2.6 ± 0.3</td><td>-</td><td>4.1 ± 0.8</td><td>4.2 ± 0.4</td><td>-</td><td>4.5 ± 0.9</td><td>4.3 ± 0.5</td><td>-</td></tr></tbody></table>

$L_s = 180–240°$, $14–16$ LTST for $L_s = 0–60°$ and $14–16$ LTST for $L_s = 240–300°$. The disparity in each case is of the order of 0.1 km. These differences may be due to the increased gaps in the TWINS data, shown in Figure S3 in Supporting Information S1. The available data are particularly sparse for TWINS compared to WindSightNet after $L_s = 240°$ for MY 35.

The estimated values in Table 2 demonstrate that the PBL height generally increases over the daytime hours. The relative diurnal change and overall heights, however, vary over the year. During the spring and early summer the PBL height grows from around 4 km at 1000–1200 LTST to reach 6–8 km by 1400–1600 LTST. This behavior is shown to be consistent over $L_s \sim 30–150°$ in Figure 9. Following this, for $L_s \sim 150–180°$, the PBL height increases for all LTST, where Table 2 indicates an average of up to 11 km for LTST 14–16, with the largest individual estimates around 14 km. As the season progresses into the northern hemisphere autumn/winter (after $L_s = 180°$), the PBL periodicity varies more sol-to-sol in Figure 9. These periods translate to height estimates ranging from 2 to 12 km, throughout the sol. The average values for $L_s = 180–240°$ in Table 2 show the average PBL heights now peak during LTST 1200–1400, instead decreasing in later hours. The larger PBL height estimates for a particular sol may in fact be due to a lack of dominant periodicity, where frequencies at the lower limits may in fact indicate no structured convective activity. This can occur due to increasing amounts of well-mixed dust in the atmosphere in these seasons. Furthermore, erroneous PBL height estimates may occur due to convective cells not being consistently advected by a prevailing wind, as indicated by the highly variable wind direction in Figure 7 during $L_s = 180–240°$ for LTST 1000–1400. For $L_s = 240–300°$ higher dominant frequencies (lower PBL heights) are observed, still with significant sol-to-sol variation. During this period the average PBL height in Table 2 is relatively stable throughout the daytime at around 4–5 km, not reaching the same heights as earlier in the year. For $L_s = 300–360°$, the average PBL height reduces back toward ~4 km for LTST 1000–1200 and increases again to ~6 km at 1200–1400 LTST, remaining constant for the afternoon.

The data during Mars year 36 after $L_s = 200°$ generally contain more gaps which prohibit successful spectral estimation. As such, inter-annual comparison with the average values is not appropriate over $L_s$ bins of 60°. Nevertheless, the overall pattern is seen to repeat with similar periods in the same seasons.

### 4.4. Baroclinic Waves

Mid-latitude baroclinic waves are observable in the winds and pressure at InSight, despite its equatorial location, and have been reported in Banfield et al. (2020), Chatain et al. (2021). Such waves are also reported at Gale crater by Curiosity (Haberle et al., 2018). Banfield et al. (2020) demonstrated periodicities in the pressure/wind speed perturbations of 1.5, 5–6 and 4 sols over the first 200 sols of the missions. Later in the mission, at sol 600, Chatain et al. (2021) reported periods of 2–3 and 8–10 sols in the average wind speed. These averaged winds were shown to correlate to the local turbulence (short period pressure fluctuations) during the entire sol and so impact the meteorology at multiple scales. Baroclinic activity is often linked to dust storm behavior and the transition to longer periods has been linked to negative feedback for the development of dust storms (Battalio et al., 2016; Collins et al., 1996; Murphy et al., 1995).

In order to track the baroclinic activity throughout the mission, Figure 10 shows the continuous wavelet transform (CWT) computed on the WindSightNet retrieved wind speeds. The strongest period signal for most of the mission
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Continuous wavelet transform (CWT), with a Morlet mother wavelet, of wind speed from WindSightNet and TWINS over the data set shown in periods of sols. Black boxes are to mask artifacts due to data gaps.</figcaption></figure>

is the diurnal cycle. From sol ~550 until 750, however, the strength of this is reduced and almost disappears on occasions. These sols correspond to the northern hemisphere winter seasons during the *R*₂ season and enhanced for season 5 from Chatain et al. (2021). This behavior is repeated again from sol ~1200, roughly one Mars year later. During this season several broad spectral peaks with periods of several to tens of sols are observed, which correspond to the baroclinic waves. The broad peaks are due to the pseudo-periodic nature of the waves. Each particular wave frequency is shown to increase and decrease in amplitude over the season, indicating transitions between dominant modes. This activity is also usually stronger than the diurnal period. The lack of consistent dominant diurnal period highlights the different control mechanism for the winds, driven by larger scale activity. This is supported by the fact that the winds have less diurnal variation than during the summer, as shown in Figure 4.

The main observed spectral peaks corresponding to this pseudoperiodic behavior are for periods of ~2–3, ~4, ~5–7 and ~9–20 sols. The shorter ~2–3 sol periods are most prevalent at the beginning and end of the season, with the longer period activity at its peak in the middle of the season. The ~5–7 sol period is often the most dominant (largest amplitude) and fades in and out over the season. The ~4 sol period also appears transient and turns on and off faster than the longer periods and is usually less intense. The longest period activity, above 9 sol periods, appears more consistent throughout the season, varying in amplitude and shifts lower in frequency in the middle of the season. It is notable that the modes are often superimposed and are not just one mode shifted in frequency. In Banfield
et al. (2020), Chatain et al. (2021), the wind speed modulation is generally less clear than in the pressure, which may be due to the superimposing of effects and lack of dominant period on occasions. Moreover, winds are more impacted by local/regional effects while pressure is more controlled by planetary scale waves. The data gaps in the second Mars year make a detailed comparison of baroclinic activity difficult over multiple years, particularly for the longer periods. However, similar periodicities can be seen, most clearly for the ~5–7 sol periods. The main difference at a first order, is in the ~2–3 sol activity which appears more intense in the second year.

Figure 10 also shows the CWT computed for the TWINS data. The long period activity is less clear due to more gaps in the data set for the same periods as WindSightNet. This CWT analysis is particularly sensitive to data gaps and so even though many of these gaps are fairly short, the identification of multisol pseudoperiodic features is more difficult. This highlights the impact of continuous data sampling strategies for atmospheric observations in planetary missions. Nevertheless, the TWINS data exhibit a similar structure as the WindSightNet retrievals and the same modes can be observed when they are not obscured by the artifacts from gaps.

Outside of the baroclinic activity seen around the $R_2$ season, there are several more narrowband features with periods above 10 sols. One explanation of these modes is from processing artifacts. However, several modes match frequencies observed in the magnetometer data from InSight (Mittelholz et al., 2023). Most notably the strongest observed narrowband modes above 10 sols in Figure 10 correspond to 13 and 26 sol periods, which are the period and first harmonic of solar rotation. A mechanism for these cycles to appear in this data set is not immediately clear and so is left for further study. These periods are also observed in the TWINS data.

4.5. Quantification Metric of Inter-Annual Variability

As shown in Figure 8, over large periods of $L_s$ the wind speed distributions show only a few differences year-to-year. Characterizing wind speed in terms of distributions is suitable to capture the behavior of the dynamical system and stochastic behavior. A Weibull distribution has been frequently proposed as a suitable parameterization of wind speeds for analysis on Mars (Lorenz, 1996; Viúdez-Moreiras, Torre, et al., 2022). Figure 8 shows that the distribution character changes depending on the types of wind, that is, daytime convective or slope winds, and record a superposition of effects when both are present within the time window. To that end, we implement the Wasserstein metric (see Villani and Villani (2009)) to provide a quantitative measure between two wind speed distributions. This approach is non-parametric, which means it does not require prior assumptions of the distribution type.

The Wasserstein metric was calculated for wind speed data from windows of 20 sols with a sliding window every 2 sols. The window size was selected to highlight any transient changes as opposed to Figures 7 and 8, which demonstrates behavior over larger seasons. The metric was calculated for distributions from three time periods: for winds over the entire sol, for daytime only winds between 0600 and 1800 LTST and nighttime only winds between 1800 and 0600 LTST. These values are shown in the third panel of Figure 11 along with the individual histograms of the winds in each year (used to calculate the distance) in the top two panels and the optical depth (tau, a measure of atmospheric dust content from Lemmon (2024)) for each year in the bottom panel. This optical depth value is calculated from the InSight cameras and corresponds to a local value.

To maximize the available data for year-to-year comparisons we use the winds at the start of the WindSightNet catalog from sol 100 which corresponds to $L_s = 353°$ in Mars year 34. As such, Year 1 in Figure 11 begins at $L_s = 353°$ in MY 34 and wraps round to $L_s = 0°$ in MY 35. Year 2 then starts from $L_s = 353°$ in MY 35 and wraps round to $L_s = 0°$ in MY 36. The comparison is then between MY 35 and 36 up to $L_s = 353°$ and then between MY 34 and 35 afterward. The metric values are removed for situations where there is a large data gap and 1 year contains significantly less data than the other.

There are two periods with a sustained difference in local optical depth, $L_s = \sim45–65°$ and $L_s = \sim160–200°$. The first is during the $R_1$ season with an elevated tau value for year 1 (corresponding to MY 35) whereas the second is at the end of the $R_1$ season and into the transition period with an elevated tau value for year 2, corresponding to MY 36. Both of these instances are linked to large transient values of the distance metric, highlighting changes. Notably, these differences occur slightly before the difference in local optical depth where the transient peaks occur for $L_s = 35–50°$ and $150–180°$. This suggests the dynamical changes associated with the development of distant storms are sensed prior to the outflow of the storms. The distance value is also greater for the daytime only winds but is also seen to impact the nocturnal winds. There is also a difference in tau value for $L_s = 310°–353°$,
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Top two panels: Histogram (PDF estimate) evolution of the wind speeds for 20 sol periods in the first year (Sol 100–768) and second year (Sol 768–1436) of continuous operations of the mission. Third panel: Wasserstein distance as function of $L_s$ between the histograms (PDF estimates) from year 1 and year 2 over 20 sol moving windows for wind speeds over the entire sol, night only (1800–0600 LTST) and day only (0600–1800 LTST). Bottom panel: Local optical depth (tau) as a function of $L_s$ for each of the 2 year periods.</figcaption></figure>
however, there are few values where the metric can be evaluated at this time and also fewer calculated tau values to fully characterize the difference. For the $L_s > 353°$, the metric is similar showing little year-to-year difference for MY 34 to 35. This is in agreement with similar optical depths year-to-year.

There is a change in behavior of the evaluated metric window-to-window for before and after $L_s \sim 200°$. In the first part of the year, the evaluated metric varies slowly between windows. Aside from the highlighted peak for $L_s = 35-50°$, the metric appears to vary over tens of $L_s$, with peaks at $L_s \sim 90°$ and $125°$. Moreover, this oscillatory like behavior appears to decay toward $L_s \sim 150°$. This behavior is not clearly linked to any consistent optical depth changes as there are only a handful of elevated values in year 1. This behavior is only present in the metric evaluated over the entire sol and daytime only values, and not at night which is if anything anti-correlated. This is in contrast to the optical depth related changes, suggesting a different mechanism.

In the second part of the year, after $L_s \sim 200°$, the window-to-window variation is more stochastic. At this time the optical depth is mostly the same with a handful of larger values in year 1 at $L_s = 250°$. The metric evaluated shows several differences of a similar value to those linked to dust variation and also a particularly large peak in around $L_s = 260°$, at the height of season 5. This period also corresponds to the season where the baroclinic waves start to become visible in the wind data. The metric will shown differences in the distributions should the dominant oscillation have a different period or be out of phase year-to-year. The difference will depend on the window size and period. The observed metric values are also the same for day and night, highlighting the pre-dominance of baroclinic activity over the diurnal cycle. Aside from this, the metric also indicates a period of little difference in the distributions around $L_s = 240°$. This aligns with the annual peak in optical depth, indicating similar wind distributions at this time.

We can now compare this transient behavior to the more seasonal behavior demonstrated in Figures 7 and 8 for direction and speed respectively. For the wind direction, the main seasonal variation was observed at night for $L_s = 60-180°$. This period begins after the end of the first tau-related difference and ends at the conclusion of the second tau-related difference seen by the metric. Recall, the direction differences are more pronounced later in this $L_s$ period and occur over a longer period of the night, so this may be due to the atmospheric dust content. However, the beginning of the observed wind direction behavior aligns with the period where the metric indicates little change in the nighttime wind speeds and only differences during the day. This daytime behavior, is also observed in Figure 8, which highlighted stronger winds in MY 35 at 1000-1400 LTST during $L_s = 0-120°$, which also covers the dust-related difference prior to $L_s = 60°$. On the other hand, the wind speed distributions in Figure 8 for $L_s < 180°$ show little difference, demonstrating that the changes seen over the 20 sol windows are smoothed when averaged over the season, supporting the interpretation that they are from periodicity or phase differences year-to-year.

## 5. Conclusion

We have presented a neural network, dubbed WindSightNet, which is used to retrieve wind speeds and directions from the seismic data recorded by the InSight mission to Mars. In doing so, a catalog of Martian winds can be retrieved from the entire continuous monitoring period of the seismometer, extending the available wind data. The performance of WindSightNet is shown to be sufficient for the analysis of winds in the same way as those from the dedicated sensor. As a result, the produced wind catalog represents a new long term continuous wind data set for use by the Martian atmospheric community.

We performed a statistical analysis of the WindSightNet catalog, which enables a direct comparison of winds in MY 35 and 36. This comparison demonstrates that the main driving features of the atmospheric circulation are the consistent year-to-year. It was shown that the winds are mostly described by the $R_1$ and $R_2$ regimes from pre-mission modeling (Spiga et al., 2018), driven by global circulation. In the first half of the year, $R_1$, the diurnal cycle is clear and independent of each sol. Daytime winds reach high speeds driven by strong convective activity while at night conditions are quiet. During the dustier part of the Martian year, $R_2$, the wind speed is modulated predominantly by longer period baroclinic instabilities. The main seasonal differences indicated were generally increased wind speeds for MY 35 during 1000-1400 LTST for $L_s = 0-120°$ and nighttime winds rotated to be more north-easterly in MY 36 for $L_s = 60-180°$.

The continuous nature of the WindSightNet catalog enabled the extraction of periodic signals from these baroclinic periods as well as convective activity. The baroclinic periods were seen to transition between dominant
modes between 2 and 15 sols. These modes are seen to often superimpose on each other rather than completely shut-off. The periodicity from convective cells enabled the estimation of the PBL height, directly useful for model comparison. There does not appear to be a clear difference in PBL height or baroclinic activity between MY 35 and 36.

A metric based on data science concepts was proposed to provide a quantification of differences between the wind speed distributions. This was evaluated over 20 sol windows to provide an analysis of transient year-to-year changes to compare to the seasonal changes. This metric indicated periods of difference which can be linked to the local optical depth, transient periods of difference in daytime winds during the $R_1$ season and stochastic differences in the $R_2$ season likely due to a different dominant baroclinic period or phase year-to-year. The differences observed by the metric prior to $L_s = 120^\circ$ are consistent with the seasonal wind speed analysis, with higher daytime winds for MY 35. However, the transient changes do not align with the differences in nighttime wind direction as no difference is seen for their speeds even though the effect is at the same time of year. During the second half of the year, the seasonal comparison does not show significant changes and so periodicity and phase effects are smoothed out and the overall behavior is similar.

WindSightNet and TWINS provide complementary data sets for future studies of the Martian atmosphere. WindSightNet is first useful for studies during periods where TWINS data are not available. The WindSightNet catalog is also more continuous and so is useful for periodicity analysis. On the other hand, the sampling rate of WindSightNet is lower than the TWINS data. Furthermore, WindSightNet retrievals are smoother than TWINS data and do not produce the highest variations or values of wind speed. The smoothness may be useful to remove discontinuities at low wind speeds where the TWINS calibration grid is coarse, for example, Where possible, the combined use of both data sets would leverage the increased information provided by the two different physical sensing modalities. In general, the WindSightNet retrievals are a good match to TWINS, particularly in terms of distribution, and faithfully reproduces the overall wind behavior.

Future work will provide a comparison to models and data sets from Curiosity (Gómez-Elvira et al., 2014; Viúdez-Moreiras et al., 2019a, 2019b) and Perseverance (Viúdez-Moreiras, Lemmon, et al., 2022; Viúdez-Moreiras, Torre, et al., 2022). Moreover, the approach presented here offers new opportunities in planetary instrumentation. Although physical isolation of instruments from noise sources is desirable, it is often not possible for in situ experiments on other planets. This approach instead uses machine learning to make the most of cross-sensitivities between instruments. A similar approach was also used for the SuperCam microphone on Perseverance (Stott et al., 2023). Using machine learning in this way yields a virtual isolation of sensors and also improves robustness. This is important in planetary environments, as demonstrated by the damage to the wind sensors on Curiosity and Perseverance (Gómez-Elvira et al., 2012; Viúdez-Moreiras et al., 2019b; Viúdez-Moreiras, Lemmon, et al., 2022). Furthermore, similar relationships are observed in seismic stations on Earth (Quigley & West, 2024) and so the approach can be used to take advantage of the increasing range of data sets available for geophysical analysis.

## Data Availability Statement

InSight's SEIS data are available at IRIS-DMC and PDS in SEED format (InSight Mars SEIS Data Service, 2019). TWINS Wind data are available on the PDS (Manfredi, Jose Antonio, 2019). The full data catalog produced by WindSightNet is available Stott (2024a) and code to recreate figures available Stott (2024b). InSight tau data available Lemmon (2024).

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## Acknowledgments

AES would like to thank the CNES postdoctoral fellowship for funding. CC would like to thank the UK Space Agency Fellowship in Mars Exploration Science under ST/Y005600/1. We acknowledge NASA, CNES, their partner agencies and institutions (UKSA, SSO, DLR, JPL, IPGP-CNRS, ETHZ, IC, MPS-MPG) and the flight operations team at JPL, SISMOC, MSDS, IRIS-DMC and PDS for providing SEED SEIS data. This work was supported in part by funding from the French Space Agency CNES and ANR MAGIS project (ANR-19-CE31-0008-08). We also acknowledge the help of the CALMIP computing cluster. We would like to thank two anonymous reviewers and associate editor German Martinez for their helpful comments in improving this manuscript.
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