The wind measurement sensors of Viking Lander 1 (VL1) were only fully operational for the first 45 sols of the mission. We have developed an algorithm for reconstructing the wind measurement data after the wind measurement sensor failures. The algorithm for wind reconstruction enables the processing of wind data during the complete VL1 mission. The heater element of the quadrant sensor, which provided auxiliary measurement for wind direction, failed during the 45th sol of the VL1 mission. Additionally, one of the wind sensors of VL1 broke down during sol 378. Regardless of the failures, it was still possible to reconstruct the wind measurement data, because the failed components of the sensors did not prevent the determination of the wind direction and speed, as some of the components of the wind measurement setup remained intact for the complete mission.
This article concentrates on presenting the wind reconstruction algorithm and methods for validating the operation of the algorithm. The algorithm enables the reconstruction of wind measurements for the complete VL1 mission. The amount of available sols is extended from 350 to 2245 sols.
The primary goal of the Viking mission was to
investigate the current or past existence of life on Mars. The Viking
Lander's payload
Viking Lander 1 (VL1) landed on Mars on 20 July 1976. The location of the landing spot was a
low plain area named Chryse Planitia, which has a slope rising from south to
west. The landing coordinates of VL1 were
VL1 operated for 2245 Martian sols, which is much longer than was expected
The Finnish Meteorological Institute (FMI) has developed a set of tools that
enable processing the Viking Lander meteorological data beyond previously
publicly available data in the National Aeronautics and Space Administration's
(NASA) Planetary Data System (PDS;
The state of the wind measurements from the surface of Mars is quite limited,
because the wind measurements of other missions to the surface of Mars have
either failed or produced a shorter data set than that of VL1. After the
Viking mission there was a 20-year gap before the research on the
surface of Mars was finally resumed. The Mars Pathfinder (MPF) conducted wind
measurements on the surface of Mars for 86 sols
This article focuses on the reconstruction of the VL1 wind measurements. Section
The significance of this work lies in the fact that other missions on the surface of Mars have not yet succeeded in measuring a data set equal to the size of that of VL1. Even though the VL1 landed on Mars 40 years ago, not all the data from the VL1 wind instruments have been analyzed and published due to various complications that are described below.
The Viking Lander wind measurement setup consisted of two hot-film wind sensors
and a quadrant sensor
The wind sensor design is presented in Fig.
There exists a fourfold ambiguity in the wind velocity measured by the two
wind sensors. The ambiguity is caused by the wind sensors only measuring the
wind velocity component normal to the sensor, and it is resolved using the
quadrant sensor
Wind sensor design. The hot films were mounted at the end of two separate holders,
which were set perpendicular to each other
Quadrant sensor design
The quadrant sensor was designed to provide a secondary measurement to solve
the ambiguity in the wind direction. The design of the sensor is presented in
Fig.
The data used in the wind reconstruction algorithm are from NASA's Science
Analysis of Meteorology (SANMET) program
The heater element of the VL1 quadrant sensor was thought to be damaged
during the 45th sol
After the failure of the quadrant sensor's heater element, the SANMET process for determining the wind direction was no longer fully reliable. It is assumed that both of the quadrant sensor thermocouples remained functional for the whole VL1 mission. Therefore the instrument can be used whenever the radiance of the Sun is strong enough to heat the quadrant sensor's heater element to a temperature where the bias-corrected thermocouples' signals exceeded 0.05 mV.
In addition to the failure of the quadrant sensor's heater element, one of
the two hot-film wind sensors of VL1 broke down during sols 377–378. The
decay of the VL1 wind sensor 2 is illustrated in Fig.
Failure of the heater element of VL1's quadrant sensor during sol 46.
The decay of the VL1's wind sensor 2 (WS2) during sols 377–378.
Due to the failures of the quadrant sensor and one of the hot-film wind
sensors, the reconstruction of wind directions and speeds have to be carried
out in two stages. The complete workflow of the wind reconstruction
algorithm is presented in the schema of Fig.
Schema of the complete processing chain of the wind reconstruction algorithm.
In the first stage the wind directions of the fully functional quadrant
sensor are used to calibrate the two hot-film sensors' Nusselt numbers. The
method of calibrating the Nusselt numbers with the correct wind direction
data from sols 1–45 is presented in Sect.
In the second stage the reconstructed wind directions, determined using the
Nusselt numbers of wind sensors, are used to calibrate the quadrant sensor
voltages. The quadrant sensor thermocouple pairs continued working nominally
after the heater element failure. The voltages observed by the thermocouples
are weaker and contain more noise, but they have the same dynamic as
during sols 1–45, when the heater element was intact. Section
After calibrating the voltages of the quadrant sensor, the wind directions can be solved for sol 377 and beyond. With the reconstructed wind direction and one stream of intact wind component data the wind speeds can be solved for sol 377 and onwards. The complete VL1 mission was reconstructed using the calibrated quadrant sensor signals, which were calibrated using the Nusselt number wind direction estimates from stage one.
The wind direction can be obtained from the Nusselt numbers. This is because
the Nusselt numbers are dependent on the wind components normal to the
hot-film sensors. The first stage of the wind reconstruction algorithm relies
on the assumption that the wind sensors get similar values for Nusselt
numbers during the period of interest to those during sols 1–45. The values of
Nusselt numbers for both wind sensors were examined from arbitrary sols from
the sol interval 46–377 of the VL1 mission. The results from this spot check
were encouraging as the Nusselt numbers of the wind sensors remained the same
order of magnitude during the examined sols. The method of using the Nusselt
numbers for estimating the wind direction was first studied by
The reconstruction algorithm begins by computing first the calibration
functions
After the values for
Because the Nusselt numbers depend on the wind velocity, the velocities were
divided into four different velocity classes. For each velocity class the
calibration function was obtained using the method described earlier. Table
The calibration functions
Calibration function
The velocity classes of the wind reconstruction algorithm.
The data for the calibration functions in Figs.
Calibration function
Calibration function
Calibration function
To reconstruct the wind directions of a complete sol, the algorithm
calculates for each measurement sample the value of function
The coefficients
VL1's look-up table of the developed wind reconstruction algorithm.
When the absolute value of the bias-corrected quadrant sensor voltages exceeded
the threshold value (0.05 mV), the correct quadrant for wind direction was
established from the quadrant sensor signals using a look-up table presented
in Table
The orientation of VL1's wind sensor assembly, adapted from
The ambiguity of the wind direction is settled by selecting from the set of candidate angles the specific angle that is in the correct wind quadrant, as determined by the quadrant sensor voltages. If there are many candidate angles in the same wind quadrant, the wind direction is arbitrarily selected to be the smallest angle from the set of candidate angles.
For cases of the quadrant sensor voltages not exceeding the threshold value, time
continuity is used for determining the wind direction. Time continuity works
as follows: the chosen candidate angle is the one nearest to the last-determined
angle, albeit only if the time difference between that one and the
current one is less than 1 h. This principle is sufficient when the
elapsed time between the measurement samples is not too long, as wind often
exhibits continuous behavior. However, if the time between the two samples
exceeds the threshold of 1 h, the use of time continuity is likely not
valid, and in these cases the dynamic wind table (DWT) is used to determine
the correct angle. The operation principle of the DWT is described in Sect.
Time continuity was used for approximately 60 % of the reconstructed angles of VL1 during sols 46–377. The DWT was developed to determine the wind direction when the use of time continuity was not possible. Notably, the DWT is capable of taking into account Mars' seasonal variations in wind direction.
The DWT was implemented using a hash table, with the Lander Local Time (LLT) in hours as the key. The value of the table is a queue containing the mean value of the reconstructed angles for the corresponding hour. When reconstructing a new sol, new values for hourly mean wind direction were calculated and then added to the DWT's queue. The DWT's queue for hourly mean wind direction will hold data at most from the last 10 reconstructed sols.
When the use of time continuity was required due to the quadrant sensor voltages being too low, the time difference in hours between the current sample and last-measured sample was solved. In the case of the time difference of samples being more than 1 h, the time value was used to obtain the mean wind direction of the hour from those of the last 10 sols where data from the hour in question were recorded. A maximum allowed rate of wind direction change was defined to prevent error values filling the DWT. If the allowed rate of change is exceeded, the wind direction is not added to the DWT, thus preventing outliers from distorting the correct average values.
The algorithm for wind reconstruction in the first stage (sols 46–377).
The bias corrections of the thermocouple pairs QS1 and QS2 do not stay constant during the VL1 mission. There exists a drift in both of the pairs' voltages. Therefore a diurnal bias correction for QS1 and QS2 is required to distinguish more reliably the correct quadrant sensor signals from noise. The samples used in determining the bias corrections were from nighttime records during light-wind conditions.
The criterion for nighttime was defined to be that the sample is measured
between 00:00 and 06:00 LLT, and the criterion for light-wind conditions was that
the wind velocity is less than
Bias correction of QS1.
Bias correction of QS2.
In the second stage of the wind reconstruction algorithm, the recalibration
of the quadrant sensor signals is required. For calibrating the voltages of
the quadrant sensor, a second calibration function, called
The fitting of Eq. (
The values of parameters
After obtaining all the values for Eq. (
Calibration function
Calibration function
The distribution of
The distribution of
The error analysis of the wind reconstruction algorithm is done by comparing the data produced by the the algorithm with the VL1 SANMET wind data. Because the VL1 wind measurement instruments remained fully functional for the first 45 sols of the VL1 mission, it is assumed that the data for that period are correct and can be used as a reference for the comparison. The behavior of the algorithm was tracked for every reconstructed sol, and data for the error analysis were gathered simultaneously with the reconstruction. The key indicator for the performance of the algorithm is the absolute difference between SANMET and reconstructed angles:
The angle difference of Eq. (
The diurnal mean angle difference.
The diurnal standard deviation of the angle difference.
The reconstruction of wind direction is very accurate during the first 45
sols of the VL1 mission. The reconstructed wind speed shows reasonable behavior
as the wind speed begins to increase after sunrise around the seventh hour
of LLT. The standard deviations in the reconstructed wind speed are much
larger than in the SANMET wind speeds. In general, the hourly mean of the
reconstructed wind speed is greater than the SANMET-determined mean value.
However, the SANMET-determined mean value for wind speed is within the error
limit of the reconstructed wind speed in all hours except the 20th and 21st.
In Fig.
The hourly mean wind direction and speed from SANMET and reconstruction during sols 1–45
(
Wind direction and speed during a 6 min time period from the forenoon of sol 3 (
Wind direction and speed during 1 h at the midday of sol 41 (
The method by which a particular measurement sample was determined was also
recorded during the reconstruction process. In total, 45 VL1 sols were
reconstructed for the analysis. During these sols, 53 070 samples were
measured. During the reconstruction process 52 570 samples (
Mean absolute difference of the angles during sols 1–45.
Standard deviation of the angle difference during sols 1–45.
Another validation method for the reconstruction algorithm is based on the
physical fact that there should exist slope winds in the reconstructed wind
data. The VL1 landed on a slope rising to the south and west. In this case the
slope winds in the VL1 area will form when the nocturnally cooled dense air is
accelerated down the slope by gravity. Therefore, in nocturnal hours, the
direction of wind should be in the interval
The statistical distribution of wind directions was examined during sols
1–45; the distributions are presented in Fig.
The algorithm was used to reconstruct all available VL1 sols, and the results
from the reconstruction are presented in this section. The statistical
distribution of wind directions is shown in a histogram in Fig.
Two clear peaks are visible in Fig.
Statistical distributions of wind directions during VL1 sols 1–45.
Comparison between SANMET and reconstructed wind direction during the complete VL1 mission.
To illustrate the reconstructed wind measurements, sols 15 and 1413 of
the VL1 mission are presented in Figs.
The hourly mean of wind directions and speeds for both sols are shown in
Figs.
Comparison of SANMET and reconstructed hourly wind directions and speeds for sol 15.
The article focused on developing an algorithm to reconstruct the wind measurements during the complete VL1 mission. VL1 performed wind direction and speed measurements on the surface of Mars for 2245 sols; thus the data set produced by the wind reconstruction is significant in its size.
The wind measurement system of VL1 consisted of two orthogonal hot-film wind sensors and a quadrant sensor for solving the ambiguity in wind direction. The quadrant sensor failed during sol 45, and one of the wind sensors broke down during sol 378; thus only one of these three instruments remained fully intact for the VL1 mission. However, with the algorithm described in this report, it was possible to reconstruct the wind measurements with a reasonable accuracy.
The wind reconstruction was completed in two stages. In the first stage the quadrant sensor signals from sols 1–45 were used to calibrate Nusselt numbers of the hot-film wind sensors. The wind sensors were then used to estimate wind directions during sols 46–377. With the estimated wind directions the quadrant sensor was recalibrated and was then used to reconstruct all the wind directions from the VL1 mission. The reconstruction of wind speed was also possible with one wind velocity component and the wind direction. The results from the reconstruction of the wind speeds are not always very reliable, because the reconstruction of wind speed required knowledge of both the wind direction and the wind velocity component from the nominally working wind sensor. The wind directions contain variable amounts of error between different sols. Therefore, the reconstruction quality of the wind speed is weaker for sols with more error in the wind direction.
The reconstructed hourly wind directions and speeds for sol 1413.
The developed algorithm for wind reconstruction shows the presence of slope
winds in the VL1 area. The accuracy of the algorithm compared to the data
measured by fully functional VL1 wind measurement instruments is reasonable.
On average the mean of the absolute difference between wind direction was
determined to be
The new wind reconstruction algorithm developed in this article extends the amount of available sols of VL1 from 350 to 2245 sols. The reconstruction of wind measurement data enables the study of both short-term phenomena, such as daily variations in wind conditions or dust devils, and long-term phenomena, such as the seasonal variations in Martian tides.
The data are not publicly available as they are currently in an immature state but will be made completely available later on, likely through the PDS. At present the data are available upon request; please bear in mind that the data may be subject to changes.
The authors declare that they have no conflict of interest.
The authors are thankful for the Finnish Academy grant no. 131723. Edited by: Valery Korepanov Reviewed by: Jim Murphy and one anonymous referee