[Norsk]

About the snow depth sensor

The snow depth sensor. Assembled sensor. The site of the sensor.

In Voksenlia in northern Oslo 349 metres above sea level the annual precipitation is more than 1000 mm, which means that there is a decent amount of snowfall during the winter; the snow cover is continuous usually from late November till late April. Snow depth monitoring may be of some general interest. Nearby at the same altitude is the Holmenkollen ski arena. Also close is the bus stop at Voksen Skog, which is another popular starting point for cross country skiers. Snow depth is currently already monitored in Oslo at Blindern (94 metres), Bjørnholt (360 metres) and Skullerud (175 metres). The greatest snow depth on record was 302 cm at Tryvasshøgda (514 metres above sea level) 2 km away from Voksenlia on the 8th April 1951. In winters like that the snow depth may be more than two metres even in Voksenlia, but in the typical winter the depth reaches around one metre. In the winter of 1951 there was still snow 200 cm deep 1 May at Tryvasshøgda, and the snow covered the ground from 29 October till 27 May. From 17 December to 10 May there was 100 cm or more. The winter of 2004-2005 had the least snow on record. At Bjørnholt (360 metres) all of February passed with depths less than 25 cm, which had never happened before since the observations begun in 1897. It was also snow free in mid January, despite that the November bore signs of a snow rich season; a depth of 45 cm was recorded 27 November 2004 (about as much snow as on the same day in 1950), and that, quite unlike 1950/1951, even became the greatest depth that season! The snow depth is usually measured manually by means of a rod. I've wanted to automate the monitoring and still get a precision at least as good as it would be if done manually. There are at least two ways to approach this: either by ultrasonic sensing (echo sensing) or by (infrared) light (using triangulation). A drawback using ultrasonic sensing is that the temperature also has to be monitored, since the speed of sound isn't constant. The main problem using light, however, is that the light might not work in bright sunlight. I bought both kinds of sensors and decided to try ultrasonics first, because the available sensors had a better range so that just one would suffice. If the sensor works well, the overall design would be simpler. I bought the Mini-AE from SensComp, which seemed to be precisely the stuff which I needed. According to the datasheet the sensor gives an analogue signal between 0 and 5V which is proportional to distance, with a range of 25 to 300 cm in a 15° angle. The signal is temperature compensated, which will simplify the design. In my case, however, the compensation could fairly easily have been done in software. The signal needs to be monitored digitally and for this task I chose to use the LP-THS from Springbok Electronics, which includes a DS2438 voltage monitor (0-10V) using a 10 bit A/D converter. SensComp has a nice box which fits their sensor, and for the LP-THS I found a suitable box at my local electronics store. I did the following to get the pieces work together: I used the same 12V power supply for both. According to the SensComp datasheet the sensor normally pulls 30mA, but will in short bursts of 500µs require 2A. In order to filter out these pulses I added a 470µF capacitor. I then connected the analogue output of the sensor to VAD on the DS2438 (through a 10K resistor). Normally the sensor will sample continuously at 10Hz, but it accepts an optional external trigger (TTL). So I used a signal in the LP-THS which triggers a led, as the external trigger. Now the sensor will become active only when the computer probes the LP-THS. I'll get the previous sample, though, but this is no problem if the samples are frequent. Snow depth doesn't change much from one minute to another, of course, but frequent sampling, as frequent as once every few second, greatly increases the precision. I mounted this and an accurate DS18B20 temperature sensor inside a pagoda from Davis Instruments. Strictly speaking, the temperature sensor wasn't necessary since the Mini-AE does its own temperature compensation. I included it so I would have a reference in case the Mini-AE didn't do the compensation well. The pagoda offers radiation protection and proper ventilation needed for accurate temperature measurements. I cut orifices in it for the sensor and power connectors. I let the data cable (1-wire CAT5) exit through one of the ventilation slits. I mounted the pagoda at the end of a bar which in turn was mounted on a pole. The sensor needs to be at a distance away from the pole, so it doesn't get into the sensor's range. If the sensor is mounted 250 cm above ground, it needs to be at least 33 cm away from the pole. My bar makes sure it's twice that distance away. Update 6 April 2007: It should be easy to couple any 1-wire board which has a DS2438 with the Mini-AE. A good choice is the solar sensor board from Hobby Boards. This board is very small and fits easily inside the Mini-AE case. The drawback is that there is no signal on this board which can be used to trigger the Mini-AE, so we're stuck with the Mini-AE's default frequency of 10 Hz. I've successfully built a distance sensor using the Mini-AE (20' and 10V version) and the solar sensor board in this way: Mini-AE pin 1 is connects to 12V, pin 2 to ground and pin 6 to VAD on the DS2438 on the solar sensor board. The solar sensor board was assembled without the photo diode. That's it! But you might still want to add that 470µF capacitor. Update 10 April 2007: The use of CTNL on the DS2409 as an external trigger for the Mini-AE assumes that the bus on the LP-THS is being switched on and off, but the software may not do this if the LP-THS is the only board on the main bus. It may therefore be necessery to add another sensor to the main bus to be able to trigger the Mini-AE as I've suggested on this page. Update 30 September 2007: It's possible to make the LP-THS fit into the Mini-AE enclosure by a bit of cutting. I've done so with a 20' and 10V version of the Mini-AE, which soon will be put into operation at a new site at Tranby in Lier. I plan to add another sensor of this kind for a station on the island of Tjøme, but the Mini-AE for that one isn't working properly and I might not be able to repair it or get a replacement in time for this season. Below is a picture of the new sensor. It could be powered through the RJ-45 connectors, but I prefer separate connectors. The SensComp sensor has several potentiometers for calibration. I adjusted them so it gives 0V at about 25 cm and 7V at about 275 cm (this gives a range of 250 cm, which is sufficient in Oslo). I also set it for maximum sensitivity, because it will measure the distance to snow, which may absorb sounds well. Some indoor tests in stable temperature conditions demonstrated that I could achieve an accuracy of ±5 mm for the whole range. Inaccuracies are likely to increase in unstable temperature conditions, though. I also noticed that some foamy substances would barely echo even at maximum sensitivity. Therefore, the sensor ought to be mounted a bit lower than its maximum range so that missed echos can be detected and discarded. Update 23 November 2007: The 20' version of the Mini-AE is more sensitive than the 10' version, so if the sensitivity is set to maximum, the sensor will occationally report the maximum snow depth. I had to set it to about 60-65%, which seems to eliminate the problem while it still is sufficiently sensitive for snow detection. After a few weeks of testing I found and calibration I found that the relationships between real and measured distances were: True distance Measured distance 250.0 cm 249.5 cm 200.0 cm 199.9 cm 150.0 cm 149.8 cm 100.0 cm 100.6 cm 50.0 cm 50.1 cm I regard this as sufficiently accurate and the differences are too small to bother to do further testing to find ways of doing precise compensations in software. In September 2005 it was about time to do some field tests of the sensor, when the snow was still one or two months away. The sensor was mounted 238.3 cm above a smooth surface. The terrain in Voksenlia is quite steep, about 30°, so the location of the sensor is more or less a shelf. It's located 349 metres above sea level in a somewhat forested area, and the place is pretty similar to much of ski track terrain near the city. However, because the slope is facing the afternoon sun, the snow disappears somewhat earlier (in mid April to late April) than in more shady parts of the forest. Even in changing temperature conditions, wind and rain the level sensing was surprisingly stable, just ±1.2 cm using a 5 minute log interval, each of which consisting of about 100 individual samples. These variations quickly drop with more extensive averaging. False echos or absorbed echos seemed to be a non-existing problem with no snow on the ground. Infrequent errors of this kind may easily be corrected, anyway, by using filters or a suitable weighting between means and medians.

The electronics.

Encased electronics.

Update 22 October 2005

The sensor has now had its first experience with snow. About 9 mm of rain fell early in the morning of 22 October and the temperature was around +6 °C, but later on in the morning it dropped towards +0.5 °C, and when it had dropped below +1.0 °C, the rain turned into snow. The ground had no frost, it was wet, and the air temperature was still above 0 °C, so the snow didn't accumulate well. An additional 7 mm of precipitation fell (as snow), which resulted in just 1-2 cm of wet snow on the ground. The sensor didn't seem to detect this snow clearly; the samples were within the -0.5 to +1.5 cm range. That is, it seemed to indicate a snow depth of 0.5 cm. Clearly, the ultrasound was penetrating the snow and reflecting off the much denser ground below.

It was snowing densely at times, and the sensor showed no signs of receiving echos off the snowflakes.

In the evening the snowfall was very light at the temperature dropped to -1,0 °C. There was an additional 2 mm of precipitation and the snow depth increased to 4 cm. Now the sensor began to show 2-3 cm consistently. It seems that the new, thin, light layer of snow and the layer below which now had more ice in it became sufficient to reflect the sound.

During the next day as the air temperature approached 0 °C and the warm ground made the snow wetter, the snow became once again "transparent" and the sensor reported around 0.5 cm even though the depth still was 4-5 cm. It continued to snow lighly throught the day, but this snow was insignificant.

The first test shows that the sensor is able to measure the distance to snow, but also that the texture of the snow plays a part. This will be investigated further when more snow arrives.

Update 25 October 2005 The sensor continued to measure a depth of 2 cm, whereas true depth was 3-4 cm. The next snowfall brought more snow than the first. It started as dry snow, the air temperature was -2 °C, and the sensor readings increased steadily, except that there was one spike from 4 cm to almost 12 cm and back again, which I cannot explain. Such spikes are easily removed by a filter, anyway. When 9 mm (water equivalent) of snow had fallen, the sensor reported 10-11 cm. I checked the depth manually and found it to be 11-12 cm depending on the exact spot. The precipitation was now turning into a mix of hail and drizzle bringing news of warmer air above, and the snow was getting wet. Shortly after the air temperature at the sensor site was above freezing. The erratic behaviour seen during the first snowfall was gone. But the sensor still reported 1-2 cm less snow than what it actually was. If this is a regular pattern, a correction by adding 1.5 cm will work well. The results from this snowfall were promising; the sensor seems to work well, but it frequently fails to report snow depths less than 4 cm, possibly because the echo from the ground below is too loud for the echo from the snow to be detected in a reliable manner. In that case, a foamy ground surface might help. Anyway, there are only a few days in a season when the snow depth is 4 cm or less, so it's not a great problem. Also, if I'm right about the cause, it should mainly be a problem with the first snow in the autumn, because when the last snow melts, it's much denser and will probably reflect better. The weather forecast issued 25 October reports that there are several warm days ahead, so chances are good that this will provide me data for melting snow. The figures below show a graph of 5 minute means and a graph in which these have been averaged into six hour means and corrected for underreporting.

Update 29 October 2005

Very warm air arrived as forecasted and the snow melted quickly; it was gone so quickly that I was unable to get a manual reading of the last snow. Anyway, there was snow on the ground for six days which gave sufficient data for some calibrations which hopefully also will be valid in the future when the winter returns. Below the corrected graph may be compared to the raw data.

The corrections are as follows. First, the samples are avareged to a sliding 6 hour mean which removes the uncertainty of single samples. Because of the fluffiness of snow the ultrasound penetrates slightly into the snow, and consequently the sensor misses the true snow depth by 1-2 cm when it's calibrated for the hard ground below. Also, occationally, if the snow cover is less than 4 cm and there is little ice in the snow, the echo from the ground below might be too loud for the echo from the snow to be detected. Therefore, 1.5 cm are added to the readings, but to avoid that a snow free ground gets interpreted as 1.5 cm deep snow, the 1.5 cm shift is only done if the sensor gives uncorrected readings above 1.5 cm for at least one hour during the next 12 hours (if they exist yet) and at least another hour during the previous 18 hours. Repeated readings above 1.5 cm are a sure indication that there is a snow cover. This shift significantly increases the chances that a thin layer of snow, which otherwise not always is detected, is reported. The addition varies between 0 and 1.5 cm depending on how many hours a snow cover was detected during the two periodes. This still results in some underreporting when there is only a thin snow layer, which can be seen between the two snowfalls 22 and 25 October in the graph when there wes in fact a depth of 3-4 cm, whereas the graph only shows around 2 cm.

If the ground surface were made up of something with the same reflective properties of snow while it also was hard enough so that any weigth of snow on top of it wouldn't deform it (if such materials exist), the sensor could be calibrated for materials like this and no other adjustments ought to be necessary.

Update 28 November 2005

A long warm period followed. In fact, so warm that leaves were beginning to reappear on some trees. The winter returned 21 November, which brought wet snow on the ground. It measured only one or two centimeters, which the sensor detected correctly. Then there was a day of heavy rain, and the snow and ice melted. This was followed by a brief snowfall which left two or three centimeters of snow. This snow, however, was very light and the sensor failed to detect it. More snow fell gently and the depth increased to 8 cm, which was equivalent to only 2 mm of water. The sensor failed to detect it properly; it failed to get any echo at all, or it occationally detected a depth of 50 - 65 cm, which clearly indicated that it was picking up false echos, perhaps from nearby vegetation or the sensor mount.

I tried to pat the snow gently to make it more compact. This was sufficient. The sensor reported 6 cm (corrected as described in the previous update), which was quite correct. I decided to change the software so that rare echos in periods of many lost echos will be ignored. That is, only reproduceable results should be logged.

Update 6 December 2005

Most days during the following week have had some light snow. I checked the depth manually a couple of places beneath the sensor and found it to be 24.0 and 24.5 cm. The sensor reported 25.0 cm. This difference is acceptable.

The week brought more of the cases when the sensor had failed to detect an echo or it had detected false echos. It happens when the surface is made up of recently fallen dry and very light snow. I changed the software so that it now uses a mix of median values and averages, which so far has removed all clearly incorrect readings. The graph below shows the variations in the snow depth through 7 days. The incorrect readings have been removed by the software. The temperature was quite stable throughout the period, between -5.3 and 0.0 °C. Precipitation 15.6 mm.

Update 30 December 2005

In the early morning of 29 December there was very little wind, the temperature was about -10 °C, and some snow was falling gently. This gave 7-8 cm of snow, which should most accurately be described as "air"; it was hardly worth to shovel because it kind of blew away every time I put my shovel into it. Hardly surprising, the sensor completely failed to detect this snow. In fact, it reported 1-2 cm less snow than the day before, probably because the new snow caused increased absorption and less accurate readings of the hard snow beneath. This event demonstrates well that ultrasound isn't suited to measure snow of this kind. However, such conditions are rarely lasting, and in many ways it may be misleading to speak of an increased snow depth when the new snow has this quality and near zero water content.

It seems increasingly clear to me that if one wishes to measure new snow accurately by the minute or hour, it is better to use IR than to use ultrasound, but ultrasound is very good at measuring the total snow depth throughout a long winter if it's ok to get measurements of fresh snow not before it's settled a bit (usually within some hours, very occationally days). I think I will stick to ultrasound for the next season, but consider IR to measure new snow as a supplement to what I can measure today.

Later in the day the wind began to blow and it started to snow again. It was still relatively cold, -7 °C, but wind and drifting snow changed the quality of the snow; snowflakes are torn apart and turn into tiny ice crystals, which reflect sound well. The sensor reported the correct depth again.

Update 17 February 2006

Another heavy snowfall dumped an additional 50 cm of snow over a period of two days, and the sensor was reading a depth of 119 cm. Most of it fell during the early hours of 16 February when a downward wind seemed to carry a lot of snow from the upper side of the hill. It can be seen now that the site of the sensor could be better. It's fairly close to a slope leading up to the metro railway above just 10 metres away, and the surface below the sensor wasn't horizontal anymore; the surface levelled out just below the sensor and some small lumps of snow have fallen down the slope above, and they've settled just next to the spot measured. I didn't make any manual measurements of the depth, but to get close to the sensor I had to wade in snow which in most places reached my waist, so a depth of 119 cm doesn't seem to be a much off; it seems to be a representative figure for the spots with the most snow. The variations in the area were still significant; some places the snow only reached my thighs.

Update 3 March 2006

The third great snowfall this winter left 50 - 60 cm of snow on cleared ground during a period of three days. It was, however, the first time the snow caused blizzard like conditions. The wind direction varied somewhat, but the wind was mainly northeastern. Despite the wind, the sensor seems to have been in a fairly well sheltered area. The snow had settled evenly and there were no drifts. The temperature was between -5 and -11 °C. The sensor readings went from 81 to 129 cm. The snow surface was nearly horizontal, but there were two or three small lumps of snow beneath the sensor, which had rolled down from the banks of snow next to the nearby metro tracks. These lumps were unlikely to influence the readings this time, but again it's clear that the sensor should be located a bit further away from the metro tracks, so that snow from the banks wont roll down to the spot measured, which may happen when the snow depth is greater than the height of the fence (about 90 cm). It will probably suffice to move it 1 metre further away, unless there is more than 2 metres of snow (in which case the sensor will be buried anyway). The pictures below were taken 2 March.

If we have a look at the data for the whole winter so far, we can see that the incorrect readings when the snow is very light are similar regardless of snow depth. They usually indicate a depth 60 cm too much. The graph showing the 24 hour average (after the incorrected readings have been removed) is smooth and clean, and clearly shows how the snow has compacted in periods without snow. Long periods of a stable snow depth indicate furthermore that the snow has been hard and icy. We can also see that the October snow melted quickly, and that the snow returned in late November and stayed, and that there was relatively little snow until mid January, whereas there was a great deal of snow after mid February.

It's definitely more snow in the area now than in the average winter, as illustrated by the picture below. I'm running short of places to pile the snow. The view through a window in the ground floor was lost during the previous snowfall, and the view through the window in the floor above is now also beginning to disappear.

Update 10 March 2006

Update 9 April 2006

Update 20 April 2006

Update 22 April 2006

Update 26 April 2006

Update 1 May 2006

Update 10 May 2006

The daily mean temperature increased by 15 °C during the first week of May, which greatly accellerated the melting. The snow below the sensor disappeared late 4 May. The last pile of snow on my lawn disappeared during 10 May. Since heavy snowfalls later than 10 May are very rare (the last time it happened was 14 May 1999), it should be safe now to sum up this season like this: Snow cover in the periods 22 October - 28 October and 21 November - 4 May (171 days), first snowfall 22 October, last 1 May (sleet), greatest snow depth 129 cm (3 March). The average snow depths for all season months were 1 cm (October), 1 cm (November), 18 cm (December), 34 cm (January), 77 cm (February), 109 cm (March), 72 cm (April), 2 cm (May).

3 May	4 May	5 May

The graph for the whole season shows that the winter began with modest amounts of snow, whereas the late winter and the spring had plenty. The melting did not start until mid April. When the snow was gone, the sensor was again reporting 0 cm. That is, the calibration done in September was still valid, and we can assume that it was right throughout the winter.

The graphs below compare the measurements with data from nearby stations run by met.no. These are based on daily measurements taken 0600UTC. For comparable accuracy the data for Voksenlia are 6 hour means around 0600UTC. We can see that Voksenlia (349 meters above sea level) and Bjørnholt (360 meters) follow eachother fairly closely. The great peak in January at Bjørnholt is due to a snowfall which locally resulted in extremely light snow (more than one meter of fresh snow in two days some places) for a few days until it compacted. Skullerud is located at 175 meters and Blindern at 94 meters.

Update 28 August 2006

The sensor has been active all summer, but the ground beneath it got quickly overgrown, so the readings have been replaced by the correct depth of 0 cm. I've now cleared the area again and moved the sensor about 80 cm further away the fence and the slope behind it. It's now located about 2 metres away from the 30-40° slope. The previous winter showed that the snow covered slope moves sidewise at about the same rate as the snow depth changes (it touched the spot measured when the depth was at its peak at 129 cm), so today's location should be good for depths up to 2 metres. The sensor is now 252 cm above ground and can measure depths up to 218 cm. Such depths are only seen about once a century. The sensor is mounted on a longer arm, making it more sensitive to vibration due to wind. However, since the readings get averaged, it's unlikely that it will affect the accuracy.

Update 2 April 2007

The ground beneat the sensor reappeared 2 April after a winter with very little snow. The greatest depth was only 48 cm. The sensor has worked without any problems through another season, and it correctly measured 0 cm when the snow had gone. The picture to the right was taken 31 March.

Update 2 June 2008

The sensor has recorded its third season without any problems. There was snow on the ground 22 November, from 24 November to 15 April and 17 May.

Update 16 August 2008

29th July at 22:49 a lightning struck and destroyed among other things the snow depth sensor. I tried to repair it, but every single circuit that I tested was dead, and I gave up. I originally built two sensors, so I've now installed the spare. The picture to the right was taken by Hans Aspenberg and shows the very lightning that struck.

Update 25 January 2009

The sensor at Tranby is now in its second season. It works well. It's base on the newer 10V and 20' version of the Mini-AE and the accuracy seems slightly better compared to the 5V and 10' version used at Voksenlia. A lightning strike destroyed this sensor last summer and it was replaced with an identical spare. The picture shows the sensor at Tranby 25 January 2009. The snow depth was 89 cm.

Update 20 April 2009

Update 28 February 2009

Update 5 August 2011

On 29th July at 12:41, exactly three years after the previous big lightning strik, another lightning struck and as in 2008 it destroyed the snow depth sensor. Even though the sensor was mounted at the end of 1.5 meter arm on a 3 meter metal pole which in turn is deeply rooted in the ground, this wasn't suffient to lead the currents away from the sensor. Note the bent metal plate. Pretty strong forces have been at work! There isn't much left to repair in this sensor, so I've replaced it with a spare, and I'll have to build another spare from scratch.

Update 22 March 2012

More recent SensComp sensors apparently behave slightly differently. After having replaced the damaged instrument with a new one, I had a lot of trouble getting it to work properly. When the sensor was set for high sensitivity it gave mostly random readings above snow free ground or crusty snow. When set for low sensitivity it worked over snow free ground, but failed to get readings over fresh snow. I tried several sensors and all behaved the same way. After a while I found that if I tilted the sensor a bit, it would work. The problem seemed to be that an echo will bounce up and down between the ground and the instrument if the sensor points straight down. The larger the case used for the sensor, the greater the problem. So tilting it solved the problem, but later I covered the underside of the casing by plastic foam (leaving an opening for the sensor). That will absorb the sound and stop the echo. Foam with an uneven surface should work even better, since the sound that isn't absorved then would spread more. Using this foam the sensor can point vertically again.

Comparisons with data from DNMI/met.no

These are comparisons of data from Voksenlia (VL, 349 meters) with met.no's data at Bjørnholt in Nordmarka (BH, 360 meters), Blindern (BL, 94 meters) and Skullerud (SK, 175 meters) for the season 2005/2006, snow depths in centimeters, measured daily 0600UTC. Clearly incorrect data have been removed. "-" means snow cover observed, but the amount wasn't sufficient for detection. Spaces means no observation.

Date VL BH BL SK October 1 1 0 0 1. October 0 0 2. October 0 0 3. October 0 0 4. October 0 0 5. October 0 0 6. October 0 0 7. October 0 0 8. October 0 0 9. October 0 0 10. October 0 0 11. October 0 0 12. October 0 0 13. October 0 0 14. October 0 0 15. October 0 0 16. October 0 0 17. October 0 0 18. October 0 0 19. October 0 0 20. October 0 21. October 0 0 22. October 0 0 23. October 3 3 24. October 2 2 25. October 3 2 0 26. October 10 0 2 27. October 8 11 3 1 28. October 3 7 0 0 29. October 0 0 30. October 0 0 31. October 0 0 Dato VL BH BL SK November 1 2 0 0 1 November 0 0 2 November 0 0 3 November 0 0 4 November 0 0 5 November 0 0 6 November 0 0 7 November 0 0 8 November 0 0 9 November 0 0 10 November 0 0 11 November 0 0 12 November 0 0 13 November 0 0 14 November 0 0 15 November 0 0 16 November 0 0 17 November 0 0 18 November 0 0 19 November 0 0 20 November 0 0 0 0 21 November 1 1 2 1 22 November 1 1 23 November 1 1 24 November 1 1 25 November - 15 26 November - 5 27 November - 6 28 November 4 8 4 1 29 November 7 6 7 3 30 November 7 9 1 Dato VL BH BL SK December 18 26 7 10 1 December 7 11 10 5 2 December 10 13 10 5 3 December 8 12 10 5 4 December 9 12 9 5 5 December 17 16 11 6 6 December 19 19 5 11 7 December 26 29 0 12 8 December 30 40 4 18 9 December 29 39 1 18 10 December 27 38 1 12 11 December 22 38 6 8 12 December 17 30 5 7 13 December 17 25 3 7 14 December 16 25 3 6 15 December 16 24 3 6 16 December 16 24 3 17 December 16 24 3 18 December 16 24 7 19 December 16 25 6 10 20 December 30 10 10 21 December 17 29 10 10 22 December 17 29 8 10 23 December 17 29 8 10 24 December 16 28 8 10 25 December 16 28 8 10 26 December 18 27 7 10 27 December 17 28 7 10 28 December 18 28 7 10 29 December 17 35 7 12 30 December 29 43 12 28 31 December 27 44 15 Dato VL BH BL SK January 34 47 15 23 1 January 30 43 17 2 January 29 41 13 26 3 January 28 41 13 26 4 January 27 40 13 26 5 January 25 39 13 6 January 27 38 13 26 7 January 26 39 12 8 January 26 38 12 9 January 26 38 12 19 10 January 26 38 12 18 11 January 25 33 8 13 12 January 20 30 0 10 13 January 20 29 0 10 14 January 20 28 15 January 20 27 0 16 January 19 26 0 9 17 January 21 27 0 9 18 January 22 33 9 11 19 January 29 9 15 20 January 48 93 26 30 21 January 63 121 35 22 January 60 109 33 23 January 55 97 29 38 24 January 52 89 26 34 25 January 50 64 23 32 26 January 47 23 32 27 January 45 22 32 28 January 44 21 29 January 43 21 30 January 42 20 29 31 January 40 61 20 27 Dato VL BH BL SK februar 77 84 42 48 1 February 40 60 20 25 2 February 39 59 20 25 3 February 37 58 20 25 4 February 38 57 19 5 February 42 57 25 6 February 56 75 40 45 7 February 58 75 39 43 8 February 60 80 42 46 9 February 73 90 48 55 10 February 72 88 46 53 11 February 72 86 45 12 February 69 85 45 13 February 65 45 14 February 64 45 47 15 February 67 80 43 47 16 February 104 106 54 60 17 February 112 106 60 68 18 February 114 106 65 19 February 113 105 57 64 20 February 108 104 57 64 21 February 108 102 57 22 February 106 100 50 60 23 February 99 96 48 55 24 February 90 87 37 45 25 February 86 84 37 26 February 84 83 35 27 February 82 82 35 42 28 February 81 84 36 50 Dato VL BH BL SK mars 109 100 47 60 1 March 118 110 61 79 2 March 122 121 60 89 3 March 128 124 57 84 4 March 125 123 55 5 March 122 118 54 6 March 118 114 52 75 7 March 113 112 52 74 8 March 114 109 52 69 9 March 115 112 54 75 10 March 116 111 54 11 March 114 109 53 12 March 108 106 53 13 March 110 104 50 68 14 March 108 103 50 66 15 March 109 104 50 66 16 March 107 104 49 65 17 March 104 100 47 64 18 March 106 96 19 March 106 95 46 20 March 104 94 44 21 March 103 92 44 60 22 March 102 91 44 60 23 March 102 91 44 60 24 March 101 91 44 60 25 March 100 91 26 March 99 90 43 27 March 97 92 42 61 28 March 108 97 46 59 29 March 104 95 42 30 March 99 90 40 48 31 March 92 88 32 48 Dato VL BH BL SK april 72 70 9 21 1 April 90 87 32 2 April 91 86 29 3 April 93 84 26 50 4 April 89 82 23 48 5 April 87 23 48 6 April 87 80 21 7 April 88 81 21 46 8 April 87 18 9 April 93 95 18 10 April 89 90 11 11 April 87 84 11 42 12 April 87 87 10 42 13 April 87 8 14 April 85 85 6 15 April 82 82 0 16 April 79 79 0 17 April 77 76 0 18 April 74 73 0 25 19 April 71 0 0 20 April 68 68 0 0 21 April 66 65 0 0 22 April 64 63 0 23 April 58 56 0 24 April 55 51 0 0 25 April 49 47 0 0 26 April 46 43 0 0 27 April 41 37 0 0 28 April 38 33 0 0 29 April 35 30 0 30 April 29 25 0 Dato VL BH BL SK mai 2 2 0 0 1 May 25 21 0 2 May 20 19 0 3 May 17 18 0 4 May 8 13 0 5 May 0 0 0 6 May 0 0 0 7 May 0 0 0 8 May 0 0 0

steinar@latinitas.org (Steinar Midtskogen).