Dust storm events have seasonal patterns, which recur year after year, thus it is reasonable for us to estimate the dust storm activities in EDL season (Tamppari et al., 2008; Vasavada et al., 2012). Hence, it is extremely vital to understand the dust storm probability of Tianwen-1 mission in EDL season expecting to improve the landing safety and accuracy for the landing mission success.
3.1 Dust storm activity of a Martian year round
The daily mean probability of dust storm activity is an extremely significant factor to Mars landing probe, due to its function of improving landing accuracy, which may be affected by severe conditions such as strong winds and dust storms (Vasavada et al., 2012). The daily mean probability P(A) of dust storm activity can be given by (Cantor et al., 2019):
$$P(A)=\left{ {\sum\limits_{{i=1}}^{4} {\frac{{N(i,d) \times A(i,d)}}{{n(d)}}} } \right}$$
1 In Eq. (
1), i is the index of the four Martian years in MGS MOC observations, N(i, d) is the number of dust storms identified on a sol (d) of the given Mars year (i), A(i, d) is the total dust storm area identified on a sol (d) of the i Mars year divided by the whole study area, which is the percentage of dust storm area on the sol (d) of the i Mars year. Four Martian years in total, n(d) is the sum of dust storms identified on the same sol of four Martian years. This paper has corrected the partial area coverage of each storm and the probabilities of the all MOC observations. The higher the value of P(A) is, the larger the daily coverage of dust storm in monitoring area is. However, the probability of dust storms recurring in the same sol was not taken into account or reflected in Eq. (
1). Taking two arbitrary sols, sol 1 and sol 2, as an example, there are dust storms in sol 1 in all four Martian years, but the area of these dust storms is small. P(A) of sol 1 is the average percentage of dust storms in four years. While in sol 2, dust storms occur only in one Martian year, but the area of dust storms is large. It is unreasonable that probability of dust storm activity in sol 1 is larger than that of sol 2. In this paper, the probability P(d) of dust storms recurring on the same sol (d) in four Martian years can be given by:$$P(d)=\left{ {\sum\limits_{{i=1}}^{4} {\frac{{Is(i,d)}}{4}} } \right}$$
2 where Is(i, d) indicates whether there is a dust storm on sol (d) of Martian year (i). If dust storms occur on sol (d) of Martian year (i), the Is(i, d) is 1; while there is no dust storm, the Is(i, d) is 0. According to Eqs. (
1) and (
2), the daily mean probability P(d, A) of dust storm (considering both time probability and area probability) is as follows:$$Adp_ds{\text{=}}P(d,A)=P(d) \times P(A)$$
According to Eq. (
3
), the daily mean dust storm activity probability in the Chryse area and within its 1600 km radius ring is shown in Fig.
3
in line with 1172 dust storms observed during MY 24–28.
(1) As shown in Fig.
3
, Adp_ds in the Chryse area showing blue color and within its 1600 km radius ring showing red color peaked at 42.9% with Ls = 223° and 20.9% with Ls = 225°, respectively. The minimum of Adp_ds in Chryse and within its 1600 km radius ring was 0. For example, during Ls = 39°-72°, no dust storm was identified in the four Martian years’ MOC MDGMs in the Chryse area. Adp_ds in the Chryse area and within its 1600 km radius ring was one order of magnitude higher than that (the maximum was 5%) calculated by Cantor et al. (
2019
) at candidate landing sites for NASA Mars 2020 Rover mission. The four Martian years’ MOC MDGMs at Ls = 223° in the Chryse area were shown in Fig.
4. At Ls = 223° of MY 24 and MY 27, dust storms almost covered the whole Chryse area (Fig.
4
a and d). While at Ls = 223° of MY 25, the dust storms were excluded because of the PEDE; and at Ls = 223° of MY 26, there was no dust storm in the Chryse area (Fig.
4b and c). As a result, it was reasonable to make a conclusion that the Chryse area had a large Adp_ds (42.9%) at Ls = 223° for MY 24–28. In addition, Adp_ds in the Chryse area was higher than that within its 1600 km radius ring at the same sol, which may be caused by the fact that the area of the latter (8.04 × 10
6 km
2) is larger than that of the former (6.20 × 10
6 km
2).
(2) Adp_ds in the Chryse area and within its 1600 km radius ring showed obvious in-homogeneity and seasonality within a Martian year. In the Chryse area, dust storm activity was the most frequent from the northern hemisphere autumnal equinox (Ls = 177°) to the end of autumn (Ls = 239°), with an average Adp_ds of 9.5%. Another period with high Adp_ds in the Chryse area was from the northern hemisphere winter solstice (Ls = 288°) to the next spring (Ls = 4°) on Mars, with an average Adp_ds of 4.1%. The active period of these two dust storm activities within Chryse’s 1600 km radius ring was longer than those in the Chryse area. Their duration ranged from Ls = 152° to 247° and from Ls = 269° to Ls = 92° with their mean Adp_ds of 2.9% and 1.0%, separately. This was not due to the study area's growth, but the northward movement of the 1600 km radius ring near the seasonal cover edge in the northern hemisphere, where dust storms occurred frequently (Cantor et al.,
2001
; Cantor,
2007; Cantor and Malin, 2007). Moreover, a small number of dust storms occurred during Ls = 93°-123° within Chryse’s 1600 km radius ring.
(3) The green curve shows the average optical depth provided by the Spirit Rover during the mission, with increments of 2.5° Ls, eliminating the responses of the PEDE in MY 29 (Lemmon et al.,
2015
). The average optical depth peaked at 1.0 (Ls = 160°), 1.2 (Ls = 240°) and 1.45 (Ls = 330°), respectively. The elevated optical depth obtained by the rover was related to storm activity observations in the Chryse area and its 1600 km radius ring, except for the first peak (Ls = 160°) (Fig.
3). Chryse and the Spirit Rover were located in different parts of Mars (far away from each other), but the dust storm curves and optical depth obtained from them were similar in laws and shapes. Dust storms at the end of summer in the northern hemisphere (Ls = 160°) mainly occurred at the edge of the Antarctic cap that recedes seasonally, while the edge of the Arctic cap recedes toward the north pole of 75° N. Spirit Rover located in the southern hemisphere of Mars (14.6° S) and was closer to the south polar cap edge than the Chryse area, which would be easily affected by the storms from the south polar cap edge around Ls = 160°. However, the Chryse area was far away from both south and north polar caps at Ls = 160° and there was nearly no dust storm.
(4) Dust storm activity in both Chryse and within its 1600 km radius ring was mainly centered during the period from Ls = 180° to Ls = 240°. We deemed that these storms were resulted from the Acidalia-Chryse channel of dust storm. Acidalia-Chryse channel was the most common development mode of dust storm sequences and each sequence propagated along the same path repeatedly, lasting for 5-plus sols. It seemed to have a bearing on frequent frontal eruptions (or "pumping" of storms by frontal systems) in high latitudes of the northern hemisphere. In each sol, one or more dust storms appeared in the Acidalia-Chryse channel during Ls = 214°- 228° in MY 27 (Wang et al., 2015).
3.2 Latitudinal distribution of dust storms within Chryse’s 1600 km radius ring In order to study the relationship between location (latitude) and time of dust storm occurrence within Chryse’s 1600 km radius ring, we have made a 2D scatter map which took the central latitude and sol of dust storm activity as the Y and X axis (Fig.
5).
The latitude of Chryse’s 1600 km radius ring ranges from 60° N to 20° S, where the center of dust storm identified in this paper is located. Major storm activity in the Chryse monitoring area was ongoing early in the Martian year (Ls = 0°), originating along the arctic cap edge, the north of the Chryse, which recedes seasonally. From Ls = 0°-90°, as the dust storm centers gradually moved northward, the dust storm in south of the Chryse would gradually disappear with the seasonal arctic cap edge having receded poleward of 83° N. As Ls increased, the quantities of dust storms decreased by degrees until Ls = 90° where dust storm can no longer be observed in the monitoring area. From the beginning of the northern summer solstice (Ls = 90°) to Ls = 130°, the northern hemisphere dust storm activity disappeared in the Chryse area, only once near the equator. We held that there was no dust storm activity in the Chryse’s 1600 km area at the end of the northern spring, which may be caused by: (1) a longitudinal offset in Acidalia storm zone (Hollingsworth et al., 1997), where the northern hemisphere spring dust storm activity is initiated; (2) the continued northward regression of the arctic polar cap edge, followed by most Martian storms (Cantor et al.,
2001; Cantor and Malin, 2007; Guzewich et al.,
2017); (3) the minimum period of storm activity in most parts of the Mars (including Chryse) is regarded as the solstice minimum (Ls = 90°). As storm activity recurred around mid-summer (Ls = 135°), some of the storms have transferred to the southern hemisphere, starting from the northern Argyre and Bosporus Straits during Ls = 135 °- 160° (Fig.
6a). These storms moved north toward the south of the Chryse area, but with their small size and little impact range (Fig.
6b and c).
The storm activity is becoming active in the Arctic and Chryse regions with the North autumnal equinox (Ls = 180°) arriving and the seasonal arctic cap edge expanding. During Ls = 180°-250°, the scale and range of dust storm activity gradually increased, as it moved southward. Most of dust storm activities came from the Chryse area or its north, observed in MOC MDGMs of four Martian years. There were not only native dust storms (white arrows in Fig.
7) originating in the Chryse area, but also multiple frontal/flushing dust storms (black arrows in Fig.
7) moving along the Acidalia cross-equatorial storm-track (green arrows in Fig.
7) (Wang et al.,
2005; Wang,
2007). Only three dust storms were located in the southern hemisphere of Mars. As the seasonal arctic cap edge had grown towards the equator of 55°N at the end of northern autumnal season (Ls = 250°-280°), the frequency and scope of dust storm activity reached to the minimum. About half a month after the winter solstice in the northern hemisphere (Ls = 270°), dust storm activities would recur in the monitoring area, mainly distributing at the edge of the arctic cap and the north of Chryse. There were also some small-scale dust storms in the southern hemisphere, probably starting from Argyre and Bosprous. These Chryse and arctic polar cap edge storms will last from Ls = 270° to the next Martian year, respectively.
The latitudinal distribution of dust storm center in the monitoring area with the criterion of Ls = 1° (Fig.
5) showed seasonal and spatial heterogeneity. Firstly, the dust storm activity frequency was closely related to the seasonal waxing and waning of the arctic polar ice cap. Dust storms within Chryse's 1600 km radius ring mostly arose during the rise or the decay of the polar cap rather than its quiescent stage when the cap’s change rate approached to the minimum. In the northern hemisphere, the dust storm activity at the edge of cap almost was at a standstill before or on the North Summer Solstice, and this stagnation lasted for a long time (Ls = 20°-90°). Secondly, the dust storm activity within the monitoring area mainly came from the Arctic Polar cap, Acidalia and Chryse, and a small numbers arose from the southern hemisphere (Argyre and Bosprous) northward. Nevertheless, the dust storms from the southern hemisphere are much smaller and much less frequent than the ones from the northern hemisphere. 3.3 Dust storm probability during the EDL season
Tianwen-1 mission is consisted of five phases (Ye et al., 2017): Earth-Mars transfer stage, Mars orbit insertion stage, Mars orbit parking stage, Deorbit and landing stage and Scientific exploration stage. Tianwen-1 and NASA Mars missions in 2020 have the homologous launch window. Assuming that Tianwen-1 will be launched in July 2020, the same time as NASA's Mars 2020, the EDL season of China's Mars mission is about April June 2021 (MY 36, Ls = 25.1°-65.4°), which is different from that of NASA's Mars 2020 (Ls = 345°-25°). Consequently, this paper tends to set the EDL season as Ls = 345°-65° in combination with the Mars missions of China and NASA. According to Eq. (
3
), the Adp_ds during EDL season in Chryse and within its 1600 km radius ring were calculated and shown in Fig.
8
.
(1) As shown in Fig.
8
, Adp_ds from MOC MDGMs of MY 24-MY 28 in Chryse (blue color) area peaked at 30.6% (Ls = 348°) during EDL season. The dust storm activity in Chryse area is discontinuous by and large, but it is continuous in the range of Ls = 345°-3°, with an average Adp_ds of 4.8%. Afterwards, dust storm activity recurred from Ls = 13°-18°, but it was very weak with an average Adp_ds of 1.3%. As to dust storm activity within Chryse’s 1600 km radius ring, the Adp_ds peak decreased to 3.9% at Ls = 3.8° continuing almost throughout the EDL season (Ls = 345°-49°) with an average Adp_ds of 0.9%.
(2) We deemed that the dust storm probability in the Chryse area during EDL season had a bearing on northward movement of storm activity on the edge of the Arctic polar as the seasonal arctic polar cap edge receded northward from 58°N to 65°N. During the warm season in the northern hemisphere (Ls = 345°-5°), the arctic polar cap began to melt and a great quantity of carbon dioxide was released into the Mars Atmosphere. As the arctic polar cap edge receded northward, the cap-edge storms occurred and prevailed by degrees. These cap-edge storms move southward through the Chryse area along the Acidalia storm-track (Wang et al., 2015). In late northern spring (Ls = 45°-80°), as it receded, the northern polar cap was far away from Chryse and the change rate of arctic polar cap size was near the minimum, thus the dust storm activity probability was lowest within Chryse’s 1600 km radius ring .
(3) The success and accuracy during EDL season is decided by Chryse’s atmospheric conditions, especially the dust storm activity probability. It would be best to finish the landing procedure during the period with lower Adp_ds in EDL season so as to reduce the risk. In EDL season, dust storm lasted during Ls = 345°-3° and 13°-18° in the Chryse area, which was not the time for landing mission. While during Ls = 18°-65°, dust storm activity was found in only five sols, the Adp_ds ranged from ≤ 1.6% with an average of 0.15%. The probabilities above mentioned were consistent with the estimate of MSL candidate landing site, which wss less than 3%, that was 0.1% for the actual Gale site (Vasavada et al.,
2012
), ranging from 1.6% in the Colombian mountains to 3.2% in the Syrtis site for NASA 2020 Mars mission (Cantor et al.,
2019). We could come to a conclusion that dust storms will not give rise to major hazards to Ls = 18°- 65° in the EDL season of Tianwen-1 mission.