How Mars loses its water

An attempt to summarize the content of Medvedev & Trinh (2026) (I’m just looking for an excuse to yap about my first time actually making a significant contribution to a paper :D).

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Artist illustration of early Mars

Current Mars (by OSIRIS camera on Rosetta)

Mars is dry, pretty obviously. But it wasn’t always. The surface is covered in ancient river valleys, lake beds, and mineral deposits that only form when there’s liquid water around. Mars lost most of that somewhere between then and now, and it’s still losing what’s left, very slowly, very high up in the atmosphere.

This post is about that process, and about the modelling work I spent a semester on in Göttingen. Mars loses roughly 400 grams of hydrogen to space every second during its most active season, and has been doing that for billions of years.

Why hydrogen?

Water is H₂O (duh). When water vapor drifts high enough into the Martian atmosphere, above roughly 40 to 60 km, the Sun’s ultraviolet radiation (specifically Lyman-alpha photons) breaks it apart:

$${\text{H}}_2\text{O}+h\nu \to \text{H}+\text{OH}$$

Atomic hydrogen is the lightest thing in the atmosphere, so at a given temperature it’s also the fastest, and some of the H atoms rattling around in the upper thermosphere are moving fast enough to leave. If an atom reaches the exobase (the altitude, around 200 to 250 km, where the atmosphere is so thin that collisions are rare) and it is going fast enough, it escapes Mars’s gravity for good. This is Jeans escape, or thermal escape, and it is the dominant mechanism by which Mars loses hydrogen today (Jakosky et al., 2018).

The oxygen left behind mostly gets locked into the surface through oxidation, which is part of why Mars is red.

So over long enough timescales hydrogen escape is water loss, which is why quantifying it is worth the trouble.

The problem of the gap

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Mars atmospheric layers by Emirates Mars Mission (EMM)

The model we use at the institute, the Mars Atmosphere Observations and Modeling General Circulation Model (MAOAM-MGCM, or just MGCM), solves the three-dimensional thermo- and hydrodynamic equations of the Martian atmosphere from the surface up to a pressure level of $3.6\times 10^{-6}$ Pa, corresponding to roughly 130 to 160 km altitude (Hartogh et al., 2005; Medvedev et al., 2011). But the exobase, where escape actually happens, sits somewhere around 200 to 250 km. There is a gap between the top of our model and the place we need to compute escape.

Shaposhnikov et al. (2022) showed that above roughly 130 km, molecular diffusion dominates the vertical transport of tracers, such that large-scale wind-driven advection can be neglected. So the region above the model top can be handled with a 1D diffusion equation instead of the full 3D model.

The diffusion equation for atomic hydrogen number density $n$ is:

$$\frac{\partial n}{\partial t}=-\frac{\partial \varphi }{\partial z}$$

where the vertical flux $\varphi$ accounts for three contributions (Chaffin et al., 2017):

$$\varphi =-D\frac{dn}{dz}-D\left(\frac{1}{H}+\frac{1+{\alpha }_T}{T}\frac{dT}{dz}\right)n$$

The first term is standard diffusion down a concentration gradient. The second accounts for gravitational settling via the scale height $H=k_{B}T/\mu g$, where $\mu$ is the mass of a hydrogen atom: gravity pulls hydrogen back down. The third involves the thermal diffusion factor ${\alpha }_T=-0.25$ (following Krasnopolsky, 2002), which captures the tendency of light species like hydrogen to migrate up a steep temperature gradient. At the top of the atmosphere, temperatures rise sharply toward the exosphere, so this term nudges hydrogen upward toward escape.

At the exobase itself, we impose an upper boundary condition: the upward flux must equal the Jeans escape flux (Chaffin et al., 2018):

$${\varphi }_{\text{esc}}=n(z_{\text{exo}})\cdot v_{\text{eff}}$$ $$v_{\text{eff}}=\frac{v_{\text{mp}}}{2\sqrt{\pi }}(1+\lambda )e^{-\lambda },\lambda =\frac{GMm}{k_B{T}_{\text{exo}}{R}_{\text{exo}}}$$

Here $v_{\text{mp}}=\sqrt{2k_B{T}_{\text{exo}}/m}$ is the most probable Maxwell-Boltzmann speed, and $\lambda$ is the Jeans parameter, the ratio of gravitational potential energy to thermal kinetic energy at the exobase. A smaller $\lambda$ (higher temperature, lower gravity) means faster escape.

This system, solved numerically using a Crank-Nicolson scheme on a vertical grid extending from the MGCM top to the exobase, gives us the hydrogen density profile and escape flux at every horizontal grid point and at every moment in time.

Bridging the gap: extrapolating to the exobase

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The black dots are the actual temperatures calculated by the 3D model, and the red line is the mathematical fit projecting all the way up to the exobase where escape happens.

To apply the diffusion scheme, we need to know the temperature profile between the MGCM top and the exobase, and we need to know where the exobase is. Neither is given directly by the model.

We handle this with an extrapolation. For each horizontal grid point, we fit the uppermost MGCM temperature levels to a four-parameter inverted Gaussian profile (Krasnopolsky, 2002):

$$T(z)=T_{\text{exo}}-(T_{\text{exo}}-T_0)\exp \left[-\frac{(z-z_0{)}^2}{{\sigma }_z^2}\right]$$

The fitting uses a Levenberg-Marquardt nonlinear least squares algorithm, with physically motivated bounds on the parameters (for example, $T_{\text{exo}}$ must exceed the maximum temperature in the input data, to ensure a physically meaningful upward gradient). The exobase altitude is then defined as the height where the extrapolated profile approaches $T_{\text{exo}}$ to within $10^{-5}$ K.

This procedure works well most of the time, with fits achieving $R^2\approx 1.0$ and RMSE below 0.1 K. There are occasional failures in grid columns with noisy or poorly structured temperature profiles, but these affect only a few points out of roughly 2048 at any given time, so their impact on global diagnostics is negligible.

Results: what the simulations show

The simulations cover Martian Years 34 and 35 (MY34 and MY35), chosen because they fall in a period of low solar activity, which lets us isolate the effects of season and dust without the confounding influence of the solar cycle. MY34 also had a Global Dust Storm (GDS) in it, so we get a direct comparison with the relatively quiet MY35.

Where hydrogen comes from

Atomic hydrogen production peaks between 40 and 60 km throughout both years, following the Sun: it is strongest in the summer hemisphere at high latitudes during solstices, and in low to mid-latitudes during equinoxes. These results are consistent with observational estimates from the Atmospheric Chemistry Suite instrument on the Trace Gas Orbiter (Alday et al., 2021) and with the photochemical modeling of Kleinböhl et al. (2024).

Production alone doesn’t determine escape though. The circulation also has to carry the hydrogen upward, and mostly it doesn’t. Most of what gets produced stays trapped in the lower atmosphere and accumulates at the poles, and only a small fraction reaches the thermosphere.

The seasonal water pump

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The colors show the concentration of atomic hydrogen, while the gray contour lines map the atmospheric circulation. During the southern summer solstices (bottom panels), a strong upward current at the south pole carries hydrogen into the upper atmosphere.

The main pathway for hydrogen to reach the exobase is the meridional circulation during the southern summer solstice. When Mars is closest to the Sun (perihelion falls near the southern summer solstice), strong upward circulation in the southern hemisphere lifts both water vapor and atomic hydrogen from the middle atmosphere up to roughly 90 to 100 km. Above that, molecular diffusion carries them the rest of the way to the exobase. This is the same “seasonal water pump” that Shaposhnikov et al. (2019) identified for water vapor, and hydrogen uses it too.

So escape peaks during the southern summer solstice, with globally averaged rates reaching $2.5\times 10^{26}$ H atoms per second, about 400 g/s. Outside that season it’s typically an order of magnitude lower.

The dust storm

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Hydrogen escape rates over the course of a Martian year ($L_s$ is the solar longitude, essentially the Martian calendar). The red line shows global escape rates. Notice the massive spike around $L_s=270^{\circ }$ (the southern summer solstice). The smaller bump in MY34 around $L_s=200^{\circ }$ is the effect of the Global Dust Storm.

The MY34 GDS, which began around $L_s=185°$, produced a roughly tenfold increase in hydrogen production by lofting water vapor to altitudes where it could be photolyzed. It also intensified the circulation, shortening the pathway from production to escape, and shifted the circulation pattern toward the solstitial type that would occur naturally later in the season (A. Medvedev et al., 2013).

Its contribution to the annually integrated escape is limited though. The secondary peak associated with the GDS reaches about $10^{26}$ s${}^{-1}$, which is 2.5 times smaller than the seasonal perihelion peak, and the late-year regional dust storms in both MY34 and MY35 produced enhancements comparable to or smaller than the aphelion solstice values. It comes down to duration. The GDS was intense but short, and the perihelion enhancement is broader and lasts much longer.

So the annually integrated hydrogen escape from Mars is driven mostly by seasonal variability rather than by episodic dust storms.

How much water is Mars actually losing?

Integrating over a full Martian year gives about 24,000 to 26,000 tonnes of water equivalent lost per year (expressed as H₂O, since 2 H atoms escaping = 1 water molecule lost). These values are consistent with, though at the lower end of, the range of 160 to 1800 g/s estimated from MAVEN observations by Jakosky et al. (2018).

Caveats

Some assumptions worth being upfront about.

Our model does not include photochemistry. Hydrogen in the lower and middle atmosphere participates in chemical reactions that can reform water, effectively removing it from the pool available for escape. Kleinböhl et al. (2024) argued that photolysis dominates over recombination above roughly 60 km, and Montmessin et al. (2022) similarly showed that production increasingly dominates loss above roughly 50 km. Both results suggest the hydrogen available for escape in our model is likely overestimated, though these one-dimensional estimates cannot fully capture the three-dimensional variability in temperature, winds, and water vapor that our GCM does resolve.

There is also a second source of overestimation: in the lower ionosphere (110 to 200 km), hydrogen atoms encounter a different chemical environment where ion-neutral reactions act as both local sources and sinks. Our diffusion scheme does not include these processes below its lower boundary. As noted by Kleinböhl et al. (2024), these high-altitude ion-neutral reactions are also the primary drivers of non-thermal hydrogen escape. Non-thermal escape (energetic atoms produced by chemistry rather than thermal motion) can constitute a significant fraction of total H loss (Cangi et al., 2023; Gregory, Chaffin, et al., 2023; Gregory, Elliott, et al., 2023). Because our framework focuses on bulk transport and its contribution to thermal escape, we do not track these pathways, and neglecting the ionospheric sinks contributes to the overestimation of the thermal hydrogen population available for transport to the exobase.

Our numbers also sit low. Observationally derived global escape rates span roughly 1 to $11\times 10^{26}$ s${}^{-1}$ (Jakosky et al., 2018), and our perihelion maximum of $2.5\times 10^{26}$ s${}^{-1}$ sits at the lower end of this range, which is expected given the low solar activity during MY34 and MY35: solar activity affects escape by altering photodissociation rates, thermospheric temperatures, and the effusion velocity (Mayyasi et al., 2023). Higher escape rates reported in the literature were often measured during more active periods.

What I actually did

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The colored lines show the hydrogen density profile evolving over time until it converges to the steady-state mathematical solution (dashed black line) in less than a third of a Martian day.

The practical work was building a 1D diffusion module that takes outputs from the MGCM at each horizontal grid point, runs the diffusion equation up to the extrapolated exobase, and outputs hydrogen density profiles and escape fluxes across the globe and through time.

The solver has two modes: a time-dependent Crank-Nicolson scheme and a direct steady-state solver (setting $\partial n/\partial t=0$ and solving the resulting linear system with the Thomas algorithm). An early result was that the time-dependent solver converges to the steady state within about 0.3 Martian sols, so for the global diagnostics we could use the cheaper steady-state one.

The temperature extrapolation described above took up a lot of the time. Getting the Levenberg-Marquardt fitter to behave across thousands of atmospheric columns with varying thermal structure needed a two-tier fallback: when the direct fit to a given column came out poor (low $R^2$), a spatially smoothed profile (Gaussian-weighted average with neighboring columns) was used instead, with the smoothing width increased until the fit was acceptable.

The code is available (Trinh, 2026).

References

Alday, J., Trokhimovskiy, A., Irwin, P. G. J., Wilson, C. F., Montmessin, F., Lefévre, F., Fedorova, A. A., Belyaev, D. A., Olsen, K. S., Korablev, O., Vals, M., Rossi, L., Baggio, L., Bertaux, J.-L., Patrakeev, A., & Shakun, A. (2021). Isotopic fractionation of water and its photolytic products in the atmosphere of Mars. Nature Astronomy, 5(9), 943–950. https://doi.org/10.1038/s41550-021-01389-x ↩

Cangi, E. M., Chaffin, M., Yelle, R., Gregory, B., & Deighan, J. (2023). Fully Coupled Photochemistry of the Deuterated Ionosphere of Mars and Its Effects on Escape of H and D. Journal of Geophysical Research: Planets, 128(7), e2022JE007713. https://doi.org/10.1029/2022JE007713 ↩

Chaffin, M. S., Chaufray, J. Y., Deighan, J., Schneider, N. M., Mayyasi, M., Clarke, J. T., Thiemann, E., Jain, S. K., Crismani, M. M. J., Stiepen, A., Eparvier, F. G., McClintock, W. E., Stewart, A. I. F., Holsclaw, G. M., Montmessin, F., & Jakosky, B. M. (2018). Mars H Escape Rates Derived From MAVEN/IUVS Lyman Alpha Brightness Measurements and Their Dependence on Model Assumptions. Journal of Geophysical Research: Planets, 123(8), 2192–2210. https://doi.org/10.1029/2018JE005574 ↩

Chaffin, M. S., Deighan, J., Schneider, N. M., & Stewart, A. I. F. (2017). Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water. Nature Geoscience, 10(3), 174–178. https://doi.org/10.1038/ngeo2887 ↩

Gregory, B. S., Chaffin, M. S., Elliott, R. D., Deighan, J., Gröller, H., & Cangi, E. M. (2023). Nonthermal Hydrogen Loss at Mars: Contributions of Photochemical Mechanisms to Escape and Identification of Key Processes. Journal of Geophysical Research: Planets, 128(8), e2023JE007802. https://doi.org/10.1029/2023JE007802 ↩

Gregory, B. S., Elliott, R. D., Deighan, J., Gröller, H., & Chaffin, M. S. (2023). HCO+ Dissociative Recombination: A Significant Driver of Nonthermal Hydrogen Loss at Mars. Journal of Geophysical Research: Planets, 128(1), e2022JE007576. https://doi.org/10.1029/2022JE007576 ↩

Hartogh, P., Medvedev, A. S., Kuroda, T., Saito, R., Villanueva, G., Feofilov, A. G., Kutepov, A. A., & Berger, U. (2005). Description and climatology of a new general circulation model of the Martian atmosphere. Journal of Geophysical Research: Planets, 110(E11), E11008. https://doi.org/10.1029/2005JE002498 ↩

Jakosky, B. M., Brain, D., Chaffin, M., Curry, S., Deighan, J., Grebowsky, J., Halekas, J., Leblanc, F., Lillis, R., Luhmann, J. G., Andersson, L., Andre, N., Andrews, D., Baird, D., Baker, D., Bell, J., Benna, M., Bhattacharyya, D., Bougher, S., … Zurek, R. (2018). Loss of the Martian Atmosphere to Space: Present-day Loss Rates Determined from MAVEN Observations and Integrated Loss through Time. Icarus, 315, 146–157. https://doi.org/10.1016/j.icarus.2018.05.030 ↩ ↩² ↩³

Kleinböhl, A., Willacy, K., Slipski, M. J., Poncin, L., Halekas, J. S., & Mayyasi, M. (2024). Hydrogen escape on Mars dominated by water vapour photolysis above the hygropause. Nature Astronomy, 8(7), 827–837. https://doi.org/10.1038/s41550-024-02268-x ↩ ↩² ↩³

Krasnopolsky, V. A. (2002). Mars’ upper atmosphere and ionosphere at low, medium, and high solar activities: Implications for evolution of water. Journal of Geophysical Research: Planets, 107(E12), 11–1. https://doi.org/10.1029/2001JE001809 ↩ ↩²

Mayyasi, M., Clarke, J., Chaufray, J.-Y., Kass, D., Bougher, S., Bhattacharyya, D., Deighan, J., Jain, S., Schneider, N., Villanueva, G. L., Montmessin, F., Benna, M., Mahaffy, P., & Jakosky, B. (2023). Solar cycle and seasonal variability of H in the upper atmosphere of Mars. Icarus, 393, 115293. https://doi.org/10.1016/j.icarus.2022.115293 ↩

Medvedev, A. S., & Trinh, N. H. D. (2026). Thermal Escape of Atomic Hydrogen on Mars: A Comprehensive View With a General Circulation Model. Journal of Geophysical Research: Planets, 131(6), e2026JE009747. https://doi.org/10.1029/2026JE009747 ↩

Medvedev, A. S., Yiğit, E., Hartogh, P., & Becker, E. (2011). Influence of Gravity Waves on the Martian Atmosphere: General Circulation Modeling. Journal of Geophysical Research: Planets, 116(E10). https://doi.org/10.1029/2011JE003848 ↩

Medvedev, A., Yiğit, E., Kuroda, T., & Hartogh, P. (2013, January). Response of the Martian Upper Atmosphere to Lower Atmospheric Dust Storms: GCM Study. ↩

Montmessin, F., Belyaev, D. A., Lefèvre, F., Alday, J., Vals, M., Fedorova, A. A., Korablev, O. I., Trokhimovskiy, A. V., Chaffin, M. S., & Schneider, N. M. (2022). Reappraising the Production and Transfer of Hydrogen Atoms From the Middle to the Upper Atmosphere of Mars at Times of Elevated Water Vapor. Journal of Geophysical Research: Planets, 127(5), e2022JE007217. https://doi.org/10.1029/2022JE007217 ↩

Shaposhnikov, D. S., Medvedev, A. S., Rodin, A. V., & Hartogh, P. (2019). Seasonal Water “Pump” in the Atmosphere of Mars: Vertical Transport to the Thermosphere. Geophysical Research Letters, 46(8), 4161–4169. https://doi.org/10.1029/2019GL082839 ↩

Shaposhnikov, D. S., Medvedev, A. S., Rodin, A. V., Yiğit, E., & Hartogh, P. (2022). Martian Dust Storms and Gravity Waves: Disentangling Water Transport to the Upper Atmosphere. Journal of Geophysical Research: Planets, 127(1), e2021JE007102. https://doi.org/10.1029/2021JE007102 ↩

Trinh, N. H. D. (2026). Thermal Escape of Atomic Hydrogen on Mars: A Comprehensive View With a General Circulation Model [Software]. https://doi.org/10.5281/zenodo.19913595 ↩