Constraining Characteristic Morphological Wavelengths for Venus Using Baltis Vallis

One of Venus' most enigmatic landforms is Baltis Vallis, the longest channel on the surface (∼7,000 km long). We identify a possible mid‐channel island that implies a south to north flow direction during formation. However, since the flow direction of Baltis Vallis is otherwise not well constrained, we analyze topographic conformity in both flow directions. In either case, topography appears to be altered across most analyzed wavelengths after the formation of Baltis Vallis. Fourier analysis shows two ranges of prominent wavelengths, 225 ± 15 km and ∼3,500 ± 1,200 km. The shorter wavelengths correspond to deformation belts that cross Venus' low plains. The longest is plausibly associated with the dynamic uplift wavelength of the crust by mantle plumes, but is less robustly detected. Higher resolution observations provided by the VERITAS and EnVision missions can help resolve the source location of Baltis Vallis and constrain if the longest wavelength postdated the canale's formation.


Plain Language Summary
Venus' surface is covered in a plethora of strange landforms, at least from the perspective of Earth. One of the longest is an about 7,000 km channel named Baltis Vallis, comparable to the Amazon and Nile rivers, but instead likely formed by volcanic processes. Baltis Vallis serves as a unique opportunity on Venus due to its length. The channel recorded surface altering processes in its topography, but we first check if the channel retained topographic information from when it initially formed. Our test shows that the topography has been altered by later processes and those processes should dominate the signal in analysis of the current topography. That analysis shows 2 length-scales are overrepresented in the topography. The shorter length-scale correspond to thin mountain range-like features that cross Venus' low plains. The longest wavelength is plausibly associated with uplift of the crust by mantle plumes and this value will be useful when creating models of Venus' interior.
the only published observations that point toward a southern source are from Bray et al. (2007). They assign possible branches at the northern end as distributaries, but we do not observe these branches in our mapping (perhaps because the mosaic used in Bray et al. appears to have been stitched incorrectly). We present new evidence supporting a southern source that consists of a possible mid-channel "island" with a lemniscate loop shape at 160.75°E, 42.12°N. For completeness, we will perform analysis and present results for both northern and southern sources.
The ability of BV to act as a recorder for the tectonic uplift history of Alta Regio and Rusalka Planitia after its formation is the focus of our study, especially if it can be used to constrain characteristic wavelengths of processes that do not have clear surface expressions. Similar studies used topographic profiles to obtain characteristic wavelengths tied to the elastic thickness of the crust (e.g., Rhea; Nimmo et al., 2010, and Charon;Conrad et al., 2021). Venus itself has also been studied in terms of its topographic characteristics (e.g., James et al., 2013;Sharpton & Head, 1986). However, except for an abstract (Jindal et al., 2018) and statements made without explicit numerical analysis (Baker et al., 1992), topographic power spectral analysis has not been used in the context of Venusian canali.
A major step in determining if we can apply the topographic power spectrum analysis to BV is to understand if significant information from BV's initial state as a drainage system remains. If so, our topographic analysis will be biased by that precursor information and could give us information about processes that occurred before the The standard proposed source of BV is at location A, and the end is at A' (Baker et al., 1992). Notice how BV avoids the topographic high to its southeast, but cuts through shorter wavelength topography. Panel (b) A close-in look at the canale at 160.75°E, 42.12°N. This section contains the possible lemniscate loop-shaped bar feature (further blown up in the subpanel). Panel (c) Topographic profile of BV with labels that correspond to the map locations. Vertical exaggeration is ∼2,500X.
10.1029/2022GL101268 3 of 9 formation of BV. We thus need a method to quantify how similar BV topography is to drainage systems on other worlds. This will be done using a technique developed for comparing drainage systems on Earth and Mars (Black et al., 2017). If this approach shows that BV lacks topographic information from its initial state, we can analyze BV using a topographic power spectrum technique to constrain characteristic wavelengths for profile-altering processes.

The Mid Channel Feature
Located at 160.75°E, 42.12°N in the midsection of BV is a possible mid-channel "island" (Figure 1b) that takes an elongated teardrop-like shape. If this feature was generated in the process that created BV, its shape can give us insight into the flow direction. The teardrop-like shape is commonly referred as a lemniscate loop (Komar, 1984) and it is generated by fluid drag eroding and lengthening "islands" such that the elongated tip points in the flow direction. Komar (1984) found that lemniscate loop shaped features on Earth and Mars follow a set relationship between the length-to-width ratio and area. The lemniscate loop shape is defined best by: Here A is the enclosed area, L is the length and W is the maximum width of the feature respectively. We can use Equation 1 to determine if this mid-channel "island" matches our expectation by inputting geographical information obtained from ArcGIS software. The enclosed area is 10.3 km 2 , length is 7.03 km, and maximum width is 1.91 km. These values set at 0.77, which is only ∼2% higher than the expected value of π/4, meaning that this feature is well described by a lemniscate loop generated by a south to north flow.
We will not solely focus in on the southern source scenario (i.e., south to north flow) for the rest of the study due to this being a singular ∼7 km long feature in a 7,000 km canale, and studies arguing for the northern source scenario (Baker et al., 1992). While outside the scope of this study, searching for other flow direction indicating structures in canale across Venus would be a fruitful study in the lead up to Veritas and EnVision.

Topographic Conformity
While the modern-day BV topographic profile does not conform to a typical fluvial system (Figure 1), we want to assess the extent of post-formation processes over a broad wavelength range. If we follow Baker et al. (1992)'s BV formation flow direction interpretation, the profile has been tilted along its complete length. However, the canale's path and elevation profile might contain some sort of initial information at shorter wavelengths. We want to determine if that initial formation information exists as an observable factor in the topography and if so the length scales over which it competes with post-formation processes. To determine this, we will consider two metrics from Black et al. (2017) for comparing the "drainage" pattern of fluvial systems to topography over a wide range of wavelengths. The two metrics, percent downhill (%d) and conformity factor (Λ), were used by Black et al. to analyze the drainage systems of Earth and Mars. The metric %d is equal to the proportion of points along the path of drainage that are at a higher elevation than the next point downstream. Λ is defined as Λ = median(cos(δ)), where δ is the angle between the system's drainage direction and the direction of the maximum negative topographic gradient. These metrics can be thought as how well the elevation and its gradients respectively conform to topography. This analysis is performed on a range of wavelengths by generating topography from spherical harmonic coefficients (SHC; details given in Text S1 in Supporting Information S1). Topography is incrementally built up with filtered SHC, with higher degree (shorter wavelength) SHC iteratively added to the topography. With each new maximum degree (l max ), we sample BV and calculate the %d and Λ from that and the surrounding topography. For Venus, our SHC are calculated from Ford and Pettengill (1992)'s Doppler-sharpened radar topography.
Black et al. found that for drainage systems on Earth and Mars, as topography is built up, the metrics trend toward 100% for %d and 1 for Λ. This is the expected result when the drainage systems are formed concurrently or after tectonic uplift. In addition to this high l max asymptotic behavior, there are also signatures of the relative timing of fluvial and tectonic processes in the behavior of the metrics at lower degrees/longer wavelength. This is present in how the Earth's metrics lag beneath Mars at lower l max , which is expected for drainage systems that are still evolving in response to ongoing tectonic uplift. If our results differ from Earth and Mars', this will tell us that BV has experienced a measurable degree of post-formation deformation.
We perform the metric analysis on BV and compare it to Black et al.'s Earth and Mars results. However, since BV is a singular flow feature compared to the numerous rivers and channels that Black et al. (2017) used for Earth and Mars, we need to be aware of possible biases in our results, particularly those that arise from using a singular, geographically constrained profile. To study this, we generated a set of 1,000 synthetic Venus-like topographic SHC from which we can generate topography of synthetic-BVs. Details describing this process are given in Text S2 in Supporting Information S1. While the processes that altered the real BV are not random, in the context of the drainage metrics tectonic processes that occur after the drainage system is formed and unable to adapt will produce results that are equivalent to randomized topography. Using this randomized synthetic topography allows us to understand the range of metric values that we would expect for a feature whose modern topographic information is dominated by post-formation, non-fluvial processes.
The gray regions in Figure 2 represents the standard deviation of our 1,000 synthetic BV metric results. This envelope allows us to observe the trends in the metric ranges expected from long term tectonic processes. As  Baker et al. (1992). Bottom: Λ with the same set of sources. Earth and Mars data are from Black et al. (2017). Beyond some spikes, the results for BV fall within the standard deviation envelope determined from the synthetic topography.
we expect for enough sets of randomized topography, the average metrics are 50%/0 for %d and Λ respectively. For both metrics, the envelope starts with a wide range that narrows in as l max increases, although the Λ envelope is relatively wider over the entire wavelength range. The synthetic group's behavior at all but the longest wavelengths is distinct from Black et al. (2017)'s results for Earth and Mars. Based on the synthetic envelope, we should expect a channel-like feature with altered topography across its entire length to start with a wider possible range of long wavelength metric values and then narrow toward ∼50%/0 with the addition of shorter wavelength topography.
For the BV curves (orange and blue), we plot up the results for both possible source locations. Given that the vast majority of the analysis is on the same points in opposite directions, the two curves end up nearly mirrored across the 50%/0 values of the metrics. Both BV curves lie within the synthetic envelope across most of the SHC degree range we studied. This signals that in the context of fluvial morphology BV is equivalent to a feature with randomized topography, especially at high l max as the shorter wavelength topography is added and the overall topography becomes closer to that observed.
While both metrics in both sources are broadly separate from Black et al.'s values, a clear issue with using a single canale can be observed in the curves' erratic behavior. This occurs because a single feature's topography can change wildly with the addition of a single degree's worth of topographic power, especially with higher power lower spherical harmonic degrees. A striking example is at l max = 9, where Λ jumps about 0.5 away from the previous metric value. While this outlier only exists strongly in Λ, it is nearly equal to the end-to-end great circle distance (∼4,000 km compared to 4,220 km for l max = 9) and its origin might deserve further analysis beyond the scope of this study. In contrast, the excursion in both metrics from l max = 17 to 22 (∼2,200-1,700 km) is intriguing because it occurs over the same wavelengths as a dip in Black et al.'s Earth metric curves. One explanation for this match is that a similar process is driving the change in the metric values. The length scales of dynamic uplift due to convection (1,000-2,000 km wavelength on Earth, Al-Hajri et al., 2009) are a potential explanation for the observed behavior.
If we assume that the initial BV curve shape is Mars-like, this implies that the topography of BV has been altered and modified across all our analyzed wavelengths. We make this assumption due to the short time scales of feature formation (∼1-100 years; Kargel et al., 1994) relative to longer deformation timescales. If so, then the amounts by which the metrics have decreased as a function of wavelength may reveal which wavelengths the altering processes acted on most strongly. This explanation works well with the dip at l max = 17 to 22 in the northern source curves and would imply that dynamic uplift altered the topography creating uphill gradients along the canali path. It would not work in the southern source scenario, since this would imply that degrees 17-22 were preferentially not altered by subsequent processes, which seems unlikely. This argument therefore favors the northern source scenario. We will however note that the timing of the processes which generated this wavelength range cannot be constrained if the southern source scenario is correct (see below).

Topographic Power Spectrum
The topographic power spectrum is a powerful tool used to analyze topography. The spectrum allows us to quantify topographic roughness as a function of wavelength (Araki et al., 2009;Ermakov et al., 2018;Nimmo et al., 2010;Shepard et al., 2001). This tool has been used on a wide range of worlds, including Venus (e.g., Bills & Kobrick, 1985), to understand those worlds' topographic roughness. We obtain Baltis Vallis' discrete power spectrum using the discrete Fourier transform (details given in Text S3 in Supporting Information S1; Press, 1992). This calculation removes the full profile's tilt to reduce short wavelength ringing in the power spectrum. The wavelength of this tilting process is longer than the profile itself and would not get captured in our analysis. The results for the power found over the range of possible wavelengths can be found in Figure 3.
Since the data roughly conforms to a power law distribution, we can perform a linear fit on the data's logarithm. We only use data points that lie above the spacecraft resolution thresholds in the fit. The wavelength limit is set by the spatial footprint size of Magellan's radar. This varied across the surface due to the spacecraft's elliptical orbit but reaches a maximum width of ∼30 km (Rappaport et al., 1999;Wieczorek, 2015). The wavelength limit is twice that value (60 km) due to two points defining a waveform. Although BV is in a region of higher resolution topography and we sampled topography at that higher resolution, we chose to be conservative in the wavelength limit determination. The power limit is determined from the vertical accuracy of the radar measurements. This value is ∼10 m, considerably smaller than the horizontal footprint. The power is determined from the topographic coefficients squared, which means the power limit is 100 m 2 . Any points below that value are likely dragged down by incoherent noise in their topographic data and are unlikely to represent true topography.
We choose to use a 90th percentile threshold to highlight the most-prominent high-power points of the spectrum. The four high-power points include two shorter wavelength points at 213 ± 3 and 235 ± 4 km, a moderate wavelength point, at ∼640 ± 29 km, and a long wavelength point at ∼3,500 ± 1,200 km. Due to the discrete Fourier transform process requiring evenly spaced topography, the actual wavelengths will be displaced onto discrete wavelengths determined by the grid spacing and length of the profile. We give each wavelength an uncertainty based upon half the average difference between that wavelength and its neighbors. This is important for the longest wavelength high-power point, where the actual wavelength could be anywhere between 2,300 and 4,700 km. If the noise thresholds were reduced (especially the power limit), the slope of the fit would increase, and the long wavelength point at ∼3,500 ± 1,200 km would not clear the 90th percentile threshold.
The only two wavelengths that clear a higher 95th percentile threshold are the two shorter wavelengths (213 ± 3 km and 235 ± 4 km), and their clustering makes it more likely that they are related to a specific surface feature generating processes. To check for any features that correlate with these wavelengths, we filter out all wavelengths but these and compare the resulting topography to geological maps of the BV region. We find that the filtered topography matches deformation belts, thin and sinuous mountain ranges (Young & Hansen, 2005), common along BV's path. Based on the resolution of imagery available, deformation belts that interact with BV deform the canale rather than BV carving through them. The existence of two points is a result of both the variability in the size of deformation belts and how BV is intersected by belts. As such the wavelength is likely better described as a range from 210 to 240 km, possibly wider if we consider the clustering of points near the 90th percentile. These prominent wavelengths support the hypothesis that deformation belt formation is geologically recent or perhaps ongoing (Young & Hansen, 2005).
In the middle of the high-power wavelengths is a point at ∼640 ± 29 km. However, this wavelength does not correspond to any obvious surface feature along the length of BV. One possibility is that this is the characteristic deformation wavelength of the elastic lithosphere (i.e., the flexural parameter). If we apply the equations that allow Figure 3. Discrete topographic power spectrum of Baltis Vallis (orange points lie above the topographic noise limit) with the best single power-law slope fit plotted in blue. We also plot the 90th percentile (dashed blue line) of the distribution to show prominent points. Points below the noise threshold are included as unfilled dots. us to determine the thickness of the elastic lithosphere from the flexural parameter (Turcotte & Schubert, 2014, Equation 3.127;parameter values from McGovern et al., 2013), we obtain a value of ∼275 km. This is well above the global range that varies from less than 10 km up to 50 km (e.g., Anderson & Smrekar, 2006;McGovern et al., 2013;McKenzie & Nimmo, 1997). The high thickness value we obtain implies that this wavelength is not the flexural parameter and could either be the result of random chance, or perhaps the consequence of a set of unidentified processes.
The longest wavelength high-power point is at ∼3,500 ± 1,200 km. While this wavelength does not correspond with any individual feature in the filtered BV topography, and it is only a single point, there is a similarity to the thickness of Venus's mantle (e.g., Rolf et al., 2022;Weller & Kiefer, 2020). This case highlights in the power-spectral approach: long-wavelengths are difficult to convincingly identify from a single profile. Aino, the next longest canale (∼2,900 km; Komatsu & Baker, 1994), is comparable to BV's length, but we leave analysis of this feature to future work.
If the long wavelength we identify is a signature of dynamic uplift due to a convecting mantle, it is also consistent with the long-wavelength high correlations between gravity and topography on Venus, which also suggest an important role for convection (e.g., McKenzie, 1994). The ∼3,500 ± 1,200 km high-power wavelength does correlate well with the dips observed the northern source scenario, since the lowest end of this range (2,300 km) nearly overlaps with the metric dip observed from 2,200 to 1,700 km. Since this wavelength range dips below the synthetic BV envelope (Figure 2), topography of this wavelength was likely produced in the interval from BV's formation to the present (∼150-500 Myrs; Herrick & Rumpf, 2011). If dynamic uplift and convection are driving the high-power topography of this wavelength, linking it to BV's age timing will be useful for constraining and refining Venus interior models when improved data are obtained from VERITAS and EnVision.

Conclusion
Baltis Vallis is the longest canale, a group of enigmatic channel features across the surface of Venus. Even though the channel of BV was clearly carved out over its 7,000 km length, the feature lacks clear evidence as to the eroding fluid's flow direction. We identified a single possible mid-channel "island" that has the appropriate shape and dimensions to imply the flow direction went from south to north. This conclusion opposes previous hypotheses that place the source of BV to the north (Baker et al., 1992). Given the uncertainty of a singular feature, we performed later analysis in both possible flow directions.
While BV has been deformed and uplifted to the point that little information remains of its original topographic profile, this alteration of the features allows us to set a timescale on Venusian crustal deformation processes. We first showed that, depending on BV's flow direction, the initial topographic information of BV was modified over all (northern source) or most (southern source) analyzed wavelengths. The metric analysis shows that BV represents a system that was formed and then experienced tectonic evolution without an ability to evolve concurrently. The high-power topographic power spectrum data points represent the characteristic wavelengths of tectonic or convective processes that have shifted, tilted, and buckled BV's topographic profile after the canale's formation. The two shorter wavelength high-power points are at 213 ± 3 km and 235 ± 4 km, and a possible longer wavelength exists at ∼3,500 ± 1,200 km. These give some evidence toward the timing and strength of deformation belts and dynamic uplift. The wavelengths illuminated by this study can be used by modelers to help constrain and validate their results.
This study has potential to be expanded through data from the future VERITAS and EnVision missions. Much of our analysis is based upon radar imagery and topography derived from the Magellan spacecraft. A higher resolution, complete set of images along the profile of BV could help constrain the source location to a specific volcanic vent or find more features along the canale that imply a flow direction. Crucially, this would resolve the issue of whether dynamic uplift post-dated BV formation (northern source) or could have pre-dated it (southern source). Beyond the northern (184.6°E, 47.6°N) and southern (166.9°E, 11.5°N) ends of BV, images of specific areas with higher resolution/different incidence perspectives would provide insight. These areas include segments that are proposed to experience avulsion (e.g., 160.9°E, 40.7°N, Stewart & Head, 1999) and the possible lemniscate loop shaped structure we detailed at 160.75°E, 42.12°N (Komar, 1984). Baltis Vallis is particularly interesting because of its large lateral extent, which we have argued provides clues to the surface and internal evolution of Venus. Future studies of the feature should attempt to investigate the time evolution of mantle dynamic uplift by comparing model results with the observed topographic characteristics.