Can effects from global warming be seen in Swedish snow statistics?

Transkript

1 Examesarbete vd sttutoe för geoveteskaper ISSN Nr 9 Ca effects from global warmg be see Swedsh sow statstcs? Mattas Larsso - -

2 Sammafattg Dea stude är ett resultat av e omfattade udersökg av söförhålladea Sverge seda börja av 9-talet. Jag har för detta ädamål aalyserat data av maxmala södjup och atalet dagar med sötäcke per kalederår frå ett 4-tal utvalda statoer. Dessa statoer har seda delats upp på olka regoer varefter medelvärde har räkats fram resp. fall. Datamateralet llustreras här form av olka stapeldagram uppdelat på fyra följade kategorer; hela tdssere, perode 96-23, kosekutva -årsmedelvärde samt e tdssere med de mest högfrekveta sväggara bortdämpade. För att kua bedöma evetuella treder de upprtade tdsserera så har jag avät mg av de båda statstska metodera ekel ljär regresso resp. Ma-Kedall's test. Tllhörade beräkgar redovsas på tabellform. För att svara på fråga om de globala uppvärmge ka sättas sambad med de seaste 3-4 åres övervägade söfattga vtrar södra Sverge så har jag studerat korrelatoe av södata getemot det orra halvklotets vtermedeltemperatur. Motsvarade beräkgar av korrelatoskoeffceter har också geomförts för de sveska vtermedeltemperature Utslaget på testera vsar att det te har skett så dramatska förädrgar söförhålladea på låg skt. Magtude på lutgskoeffcete för de apassade regressosljera tyder på att det maxmala södjupet och atalet dagar med sötäcke medeltal har legat på e gaska kostat vå uder de seaste hudra åre. När det gäller maxmala södjup så ka ma paradoxalt og se e tedes tll e svag uppgåg för Götalad och orra Norrlad. Det är också de eda falle som är statstskt säkerställda för tdssere som helhet. För de kortare perode så ka ma däremot se att atalet dagar med sötäcke har mskat relatvt kraftgt södra Sverge motsvarade e edgåg på crka 4 % Götalad och 2 % Svealad. Test med ekel ljär regresso ger sgfkata resultat båda falle meda Ma-Kedall edast fastställer trede för Götalad. E ärmare udersökg av det maxmala södjupet för de kortare tdssere ger dock te lka tydlgt utslag statstke me ma ka trots allt ursklja e sgfkat mskg för Svealad testet med ekel ljär regresso. Det rör sg här om e edgåg på crka 3% efter 96. Det går te att omedelbart relatera förädrgara det sveska söklmatet tll de globala uppvärmge. Beräkade värde på korrelatoskoeffcete ger te es sgfkat utslag för perode trots att de globala medeltemperature har ökat gaska markat seda 97. Motsvarade beräkgar för de sveska vtermedeltemperature vsar att de har väldgt stor betydelse för om ederbörde Götalad och Svealad faller som reg eller sö meda det för orra Norrlad te har ågo ämvärd påverka

3 Abstract Ths study s a result from a major vestgato about the sow codtos Swede sce the begg of the tweteth cetury. For ths purpose, data were aalysed wth respect to the maxmum sow depth ad the umber of days wth sow cover per year from some more tha forty selected statos. These statos were the dvded to dfferet regos ad meas were calculated for each seres. The data are preseted the shape of dfferet hstograms the four followg categores; the whole perod request (9-23), the latest 43 years (96-23), ad cosecutve mea values for every decade ad tme seres wth the hghest frequeted fluctuatos equalzed. To be able to detect ay treds the plotted tme seres two statstcal methods, smple lear regresso ad Ma-Kedall s test, were appled. The calculatos belogg to these tests are showed tables. To be able to aswer the questo f the global warmg ca be related to the latest 3-4 decades predomatly warm wters the souther part of Swede I have bee studyg correlatos sow data wth respect to the orther hemspheres mea temperature for the wter seaso. Correspodg estmates of the correlato coeffcets have also bee made wth respect to the Swedsh wter mea temperature. The respose of the tests shows that t has ot bee such dramatc chage the sow codtos the log ru. The magtude of the slope for the adjusted regresso les mples that the maxmum sow depth ad the umber of days wth sow cover average have bee o a farly costat level durg the latest hudred years. Whe t comes to the maxmum sow depth oe ca dstgush a tedecy for a small rse Götalad ad orther Norrlad. Ths s also the oly cases whch are statstcal sgfcat for the perod request (95-23). For the shorter perod however, the umber of days wth sow cover has decreased qute substatally the souther part of Swede correspodg to a decrease about 4% Götalad ad 2% Svealad. The test based o smple lear regresso gves sgfcat results both cases whle Ma-Kedall oly establshes the tred for Götalad. A closer vew of the maxmum sow depth for the shorter perod (96-23) does ot gve the same respose but there s at least evdece for a sgfcat decrease Svealad the test wth smple lear regresso. It correspods to a decrease of about 3% sce 96. Oe caot mmedately relate the chages the Swedsh sow clmate to the global warmg. Estmated values of the correlato coeffcet do ot eve gve sgfcat results for the perod despte of the fact that the global mea temperature has rased qute cosderably sce 97. The correspodg calculatos for the Swedsh wter mea temperature show that t plays a very mportat roll f the precptato Götalad ad Svealad s comg as ra or sow whle t does ot matter at all orther Norrlad

4 A wter vgette from Gyllberge, southwester Dalara. The llustrato o the frot page, take by Lars Adersso Borläge, shows the sow codtos Gyllberge about 2 km southwest of the tow 27 February 988. The place s kow as a forest area wth lots of sow the wter ad there s a well-prepared track system for cross-coutry skg. I the area there s ow also the automatc weather stato of SMHI ( Swedsh Meteorologcal ad Hydrologcal Isttute) Stora Spåsberget. Earler there was a maual stato measurg of precptato ad temperature that was establshed 964. Quotato of the dary otes from Lars Adersso from 27 February: "Check of sow depth Gyllberge: 9- cm o the hghest areas stuated 45-5 meter above the sea. All trees/bushes completely ecapsulated dry sow + some ce covergs. Because of strog wds there are sowdrfts here ad there o exposed places. As the su was shg costatly that day oe could go skg aroud ad look at all beautful sow formatos ad take photographs colour". A supplemet oted o the 29:th: "A pole was broke about oe klometre from the TV-mast o Stora Spåsberget at 2:3 a.m. at whch tme the rado soud dsappeared Dalara. Reports the local ewspapers that the Telecommucatos Admstrato had to tur out ad that they frst thought that the 3 metres hgh mast had collapsed, but t was ot that bad. Accordg to the ewspaper the sow depth there was -,5 meter." The wter of was souther Swede relatvely warm wth plety of precptato ad lots of sow lyg the hgher terra, where especally orther Svealad recorded large sow depths. Borläge receved etrely 79,5 mllmetres (mm) durg Jauary followed by 69, mm February ad 33,7 mm March. The correspodg fgures for the weather stato Idkerberget were 9,5-6,2-53,5 mm. (Idkerberget s stuated 5 km east of the TV-mast o Stora Spåsberget.). The day whe the pcture was take Gyllberge Borläge had oly 32 cm sow that s cosderably less tha at the locato o the photo

5 Table of cotets Sammafattg...2 Abstract...3 Table of cotets...5. Itroducto A short descrpto of the Swedsh sow clmate Collectg of data Theory Smple lear regresso Defto of the correlato coeffcet Ma-Kedall s test Calculato of fltered mea values Results Average umber of days wth sow cover The complete tme seres The perod Cosecutve mea values for every te year Tme seres wth weghted mea values Average maxmum sow depth The complete tme seres The perod Cosecutve mea values for every te year Tme seres wth weghted mea values Dscusso Number of days wth sow cover Maxmum sow depth Coclusos...44 Ackowledgemets...45 Refereces Appedx. Wter mea temperature durg the perod Appedx 2. Wter temperatures for three dfferet Swedsh places Appedx 3. Matlab-programme for mplemetato of Ma-Kedall s test

6 . Itroducto. The ma goal wth of work was to study varatos ad extremes the Swedsh sow codtos sce oe started to measure the sow depth the begg of the 2:th cetury. For ths purpose I have aalysed data of maxmum sow depth ad umber of days wth sow cover from some more tha 4 statos, whch all together correspods to about 8,8 measured values. The formato ths study s ot based o tradtoal wter seaso but o caledar year (Ja Dec). The curret opo the socety today s that the wters are ot as sowy as earler tmes myth or realty? Ths questo s also oe of the startg-pots my study of the Swedsh sow clmate. The creasg terest alpe sports makes t eve more mportat to thoroughly vestgate wth ths clmatc aspect. Processg of data was accomplshed wth help of the graphc art programme MATLAB. I have there sketched up tme seres the shape of hstograms to be able to detect sgfcat chages durg from year to year. Whe t comes to the aalyss of possble treds the materel I have appled smple lear regresso respectvely Ma-Kedall s test. The later method does ot gve ay quattatve formato about the respose o the test but oly a ht about the tred tself (dowward/upward). To be able to vestgate a possble coecto to the Gree house effect I have addto calculated correlatos of sow data wth respect to wter mea temperature for the orther hemsphere (defed for the perod Ja Aprl + Nov/Dec). I have also made correspodg calculatos for the Swedsh wter mea temperature. Fally I have studed the correlato of maxmum sow depth wth respect to the total umber of days wth sow cover. My dea s here to vestgate f hgh sow depth s favoured by log wters wth stable sow cover

7 2. A short descrpto of the Swedsh sow clmate. To gve a outsder some basc kowledge what s ormal for the Swedsh sow clmate I have here preseted maps llustratg the average umber of days wth sow cover (fgure 2.) ad average maxmum sow depth (fgure 2.2) sce the begg of the tweteth cetury ad owards. The maps are based o my formato for the perod These two llustratos show moreover a very good agreemet wth the ormal maps publshed Bertl Erksso s sow report from 989 (see the lst of referece for more detals!). If you have the opportuty to borrow ths report from the lbrary please compare wth maps 8A ad o page Statstcs showg regoal mea values of maxmum sow depth ad umber of days wth sow cover are llustrated wth hstogram ad cumulatve dstrbutos fgure 2.3 ad 2.4. The chapter s the fshed wth a table showg some extreme values of maxmum sow depth for every stato. The thckess of the sow cover s to great extet determed by factors as the lattude for the stato, alttude above sea level ad the dstace to the coast ad bgger lakes. The sow depth s geerally oly exceedg the magc oe-meter level the moutas of Lapplad ad the wester moutas of Jämtlad wth a dstct peak for Rksgräse- Katterjåkk the most orth wester part of Lapplad. From a maxmum the moutas the sow depth s decreasg gradually closer to the coast of Norrlad where t s somewhere betwee 5- cetmetres from Gävle ad further orthwards to Haparada. The sow codtos Götalad ad Svealad, except for Dalara ad orther Värmlad, s showg a farly eve dstrbuto wth values about 2-3 cetmetres. The absolutely hghest sow depth ever measured Swede was o 327 cm 28 February 926 at the stato Kopparåse about 5 km east of Rksgräse. If the observatos had ot bee terrupted at that day the record would probably have bee eve more mposg. Cosderg ths approved record oe must otce that the stato was stuated close to a powerful mouta slope where sow was blowg dow ad accumulated! If oe however looks to the hghest kow sow depth outsde the moutas Degersjö Ågermalad was worst wth 9 cm February 967. Amog other peaks we ca for example meto Luvos (straght west of Jokkmokk) 87 cm Aprl 936; Hattsjöbäcke (Ågermalad) 8 cm 2 March 995 ad Blåbärskulle (Värmlad) 8 cm March 95. The total umber of days wth sow cover per year shows large varatos betwee the orther ad souther parts of the coutry. The wter s domat the teror regos ad moutas of Norrlad ad the orthwester part of Dalara where the groud average s sow covered more tha 5 percet of the year! It s most marked the orthwester part of Lapplad where at least two thrds of the year s sow covered. Alog the west- ad south coast the total umber of days wth sow cover s o the cotrary ofte less tha two moths. For orther Norrlad (fgure 2.3 a) the maxmum sow depth durg the perod most ofte led betwee 7- cm whle the correspodg value for Götalad (fgure 2.3 g) les o -4 cm. The statstcs for Svealad ad the souther part of Norrlad show more scattered data. The meda dvdes the observato materel to two equal parts. By lookg at the cumulatve dstrbutos the rght colum we get the followg regoal average; orther Norrlad: 85 cm, souther Norrlad: 67 cm, Svealad: 45 cm, Götalad: 23 cm ad the coutry as a whole 53 cm. I fgure 2.4 whch s showg regoal averages of the umber of days wth sow cover durg the perod 9-23 the patter s gettg more splt as further south oe goes. Every bar the hstogram correspods to te uts o the x-axs. The spread of data s cosequetly much larger Götalad compared to for example orther Norrlad; from -4 days Götalad (fgure 2.4 g) to 6-23 days orther Norrlad (fgure 2.4 a). If we aga take the meda as a average of the sow statstcs we get the followg values; N Norrlad: days, S Norrlad: 65 days, Svealad: days, Götalad: 7 days ad the coutry as whole 35 days

8 Fgure 2.. Map over Swede that shows the average maxmum sow depth durg the perod Data gve cetmetres

9 Fgure 2.2. Map over Swede that shows the average umber of days wth sow cover per year durg the perod

10 a) umber of obs Mea maxmum sow depth N Norrlad b) rel. frequecy Cumulatve dstrbuto N Norrlad c) 4 umber of obs. 3 2 Mea maxmum sow depth S Norrlad d) rel. frequecy Cumulatve dstrbuto S Norrlad e) umber of obs Mea maxmum sow depth Svealad f) rel. frequecy Cumulatve dstrbuto Svealad g) umber of obs Mea maxmum sow depth Götalad h) rel. frequecy Cumulatve dstrbuto Götalad ) umber of obs Mea maxmum sow depth Swede j) rel. frequecy Cumulatve dstrbuto Swede Fgure 2.3. Hstogram that shows the dstrbuto of the average maxmum sow depth durg the perod The correspodg cumulatve hstogram s dsplayed o the rght sde. - -

11 a) umber of obs c) 4 umber of obs. Number of days wth sow cover N Norrlad Number of days wth sow cover S Norrlad b) rel. frequecy d) rel. frequecy Cumulatve dstrbuto N Norrlad Cumulatve dstrbuto S Norrlad e) umber of obs Number of days wth sow cover Svealad f) rel. frequecy Cumulatve dstrbuto Svealad g) umber of obs Number of days wth sow cover Götalad h) rel. frequecy Cumulatve dstrbuto Götalad ) umber of obs Number of days wth sow cover Swede umber of days j) rel. frequecy Cumulatve dstrbuto Swede umber of days Fgure 2.4. Hstogram that shows the dstrbuto of the average umber of days wth sow cover durg the perod The correspodg cumulatve hstogram s preseted o the rght sde. - -

12 Table 2.. Maxmum sow depth per year - the lowest ad hghest measured value durg the perod for each stato wth belogg year brackets. Maxmum sow depth [cm] Maxmum sow depth [cm] Stato Abs. hghest Abs. lowest Stato Abs. hghest Abs. lowest Borås 7 (945) (99) Lud 49 (929) (989,99) Delsbo/Bjuråker 6 (966) 5 (93) Malug 9 (95) 2 (993) Falu 9 (966) 3 (974) Pteå 37 (938) (933) Gäddede 98 (943) 24 (93) Rksgräse/Katterjåkk 265 (993) 72 (95) Gällvare/Malmberget 43 (936) 32 (933) Skara 7 (966) 6 (926) Gävle 3 (998) (95,94) Stockholm 76 (99) 3 (99) Göteborg/Säve 53 (967) (949) Stesele 8 (977) 33 (93) Halmstad 44 (97) (989,99) Storle/Vsjövale 232 (976) 37 (93) Haparada 24 (969) 2 (93) Sveg 24 (966) 24 (933) Hemava/Täraby 22 (943) 54 (93) Säle/Trastrad 55 (966) 35 (95) Härösad 58 (98) 9 (95) Sära 23 (966) 43 (996) Jokkmokk 49 (936) 43 (95) Umeå 27 (988) 22 (933) Jököpg 7 (979) 4 (949) Uppsala 66 (985) (974) Karesuado 4 (993) 3 (949) Vsby 73 (987) 3 (974,99) Karlsham 6 (942) (989) Väersborg (97) 3 (96,9) Karlstad (966) 7 (989) Västervk (985) 8 (949) Krua 42 (935) 47 (97) Västerås 65 (985) 4 (99) Krstastad 52 (929) (989,99) Växjö 63 (95) 7 (932) Kvkkjokk 59 (96) 43 (932) Örebro 85 (966) 4 (99) Lköpg/Malmslätt 73 (966) 3 (949) Östersud/Frösö 8 (92-3) 6 (933) Table 2.2. Statstcal data for the maxmum sow depth based o the formato fgure 2.. Mea value [cm] Stadarddevato Hghest mea-max. (Year) Lowest mea-m. (Year) N Norrlad (96) 5 (933) S Norrlad (966) 3 (93) Svealad (966) 24 (95,99) Götalad (979) 7 (949,99) Table 2.3. Statstcal data for the umber of days wth sow cover based o the formato fgure 2.2. Mea value [# days] Stadarddevato Hghest average (year) Lowest average (year) N Norrlad (968) 68 (953) S Norrlad (94) 29 (93,953) Svealad (985) 77 (2) Götalad (985) 4 (989) - 2 -

13 3. Collectg of data. Ths study s based o formato from 48 statos aroud the coutry dstrbuted o regos as follows: Götalad (7), Svealad (), souther Norrlad (9) ad orther Norrlad (2). A map that shows the posto of the statos s preseted fgure 3.2. I have my work almost exclusvely bee collected my data from dfferet reports ad jourals from the Swedsh atoal weather servce (SMHI). Whe t cocers processg of maxmum sow depth I have take advatage of table H the late meteorologst Helge Pershage s report from 98: Maxmum sow depth Swede The table gves a detaled complato of the largest measured sow depth for 4 Swedsh places from Karesuado the orth to Lud the south durg the perod The sow depth s gve cetmetres (cm). The collectg of data cocerg the frequecy of days wth sow cover has ot bee qute so smple. O the oe had the defto of a day wth sow cover has ot bee the same for the whole perod ad o the other t has sometmes ot bee possble to get strct formato because of bad qualty of the observato materal. The sow statstcs have prmarly bee obtaed from data old meteorologcal reports (the chapter Meteorologcal observatos Swede ). But from 96 ad owards I have got the formato drectly from the database of SMHI. Observatos of the sow cover Swede bega at the ed of the 9:th cetury but there are some cases well preserved jourals back to the 87-s. The thckess of the sow cover was commoly measured at frst 95. Statstcal data for Swedsh sow codtos s avalable from old meteorologcal yearbooks from 898. The measure of sow depth should accordg to the structos be performed o smooth groud where the sow s lyg farly evely dstrbuted. The sow depth s sutably measured wth a small stck, graded cetmetres. The measuremets should be performed o at least fve places wth some meters apart to get a represetatve mea for the place cocer. Whe t comes to apprasal of the spreadg of sow cover oe s usg of a four-graded scale: The groud s completely or almost completely sow covered (S). The groud s more tha half but ot completely sow covered (SB). The groud s more tha half but ot completely bare (BS). The groud s completely or almost completely bare (B). Whe the desgato SB s used a sow depth should be gve, but at BS sow depth should be reported as. The followg defto of a day wth sow cover was always used the yearbooks of SMHI utl 967: As a day wth sow cover s cluded every day whe the groud at seve a.m. (SNT) has bee completely or to some part sow covered. Ufortuately oe s cludg all days wth BS, whch gves a partly msleadg pcture of the sow statstcs as ordary people could fd the groud bare. Aother problem s also that may observers fd t dffcult to dstgush betwee B/BS ad thus gve wrog formato the protocol. Fred of order would certaly have preferred that I swept to cout all the days o the format (S,SB) but I was evertheless forced to buy data o the format t was set up the lterature wth respect to the all tme t would have take to go through all the jourals the archve. Fgure 3. below llustrates the percetage of days wth BS relato to the total umber of days wth sow (S,SB,BS). Oe ca see that these so called cheat -days of sow cover s qute eglgble the orth whle they souther Swede costtute somewhere betwee ad 2 % of the total umber of days wth sow cover. For statos ad perods wthout sow data the aual reports so I have bee forced to use old observato protocols the data archve at SMHI. A work that has bee very tme cosumg ad hard to grasp. Due to complete data seres ad/or the fact that the stato request has closed dow o later years I had to use data from reasoably stuated statos. Gustavsfors/Ko has for example bee completed wth data from Flpstad (97-6) ad Gåsborshytta (9-96)

14 Further o Umeå has bee completed wth sow data from Bjurholm for the year ad Gällvare wth Malmberget for the year ad a average betwee Krua ad Jokkmokk for the years 97, 977, 984 ad The umber of days wth sow cover has correspodgly bee completed for Rksgräse (9-4), Krua (9-), Bjuråker (935), Säle (9-3), Kalmar (945) ad Karlsham (952 ad 959). I also wat to make a reservato for ucerta values at Hemava/Täraby for the moth of October durg the years ad for Rksgräse the moth of Jue Jököpg, Västervk ad Delsbo are further examples of statos that have bee dffcult to follow up recet years because of closures ad automatsato of statos. Statos the eghbourhoods have the bee used to fll out gaps the data seres. The mea temperature for Swedsh wter, dowloaded from database at SMHI, s based o te statos evely dstrbuted ad homogezed. Whe t comes to the temperature o the global scale I have used formato from Clmatc Research Ut at the Uversty of East Agla, Great Brta. For more formato about calculatos, the accurateess data etc. so I refer to the followg Iteret-page: Average umber of days wth (BS) relato to the total sow frequecy (S,SB,BS) durg the perod relatve frequecy N Norrlad S Norrlad Svealad Götalad umber of stato Fgure 3.. Hstogram that shows the fracto of days wth (BS) relato to the total sow frequecy. To get kowledge about whch stato that belogs to each umber o the x-axs, see table 3. below. Table 3.. A lst of statos used fgure 3.. Nr. Stato Nr. Stato Nr. Stato Karesuado 3 Sveg Skara 2 Krua 4 Delsbo/Bjuråker 26 Väersborg 3 Kvkkjokk 5 Gävle 27 Borås 4 Jokkmokk 6 Sära 28 Jököpg 5 Haparada 7 Malug 29 Västervk 6 Pteå 8 Falu 3 Göteborg/Säve 7 Hemava/Täraby 9 Karlstad 3 Halmstad 8 Stesele 2 Örebro 32 Växjö 9 Gäddede 2 Västerås 33 Karlsham Storle/Vsjövale 22 Uppsala 34 Krstastad Östersud/Frösö 23 Stockholm 35 Lud 2 Härösad 24 Lköpg/Malmslätt 36 Vsby - 4 -

15 Table 3.2. A detaled lst of the statos used the sow statstcs. Stato Provce Lat. N Log. E m.a.s. (m) Stato Provce Lat. N Log. E m.a.s. (m) Borås Västergötlad Ljugby Smålad Bjurholm Ågermalad Lud Skåe Bjuråker (9-966) Delsbo (967-23) Hälsglad Malmberget Lapplad Hälsglad Malmslätt Östergötlad Falu Dalara Malug Dalara Frösö Jämtlad Pajala Norrbotte Gustavsfors /Ko Värmlad Pteå Norrbotte Gäddede Jämtlad Rksgräse (94-97) Lapplad Gällvare Lapplad Skara Västergötlad Gällvare arport Lapplad Stesele Lapplad Gällvare /Flakaberg Lapplad Storle /Vsjövale Jämtlad Gävle Gästrklad Stockholm Upplad Göteborg Västergötlad Sveg Härjedale Halmstad Hallad Säle Dalara Haparada Norrbotte Sära Dalara Hemava (965-23) Lapplad Säve Bohuslä Hoburg Gotlad Söderham Hälsglad Hylta Smålad Trastrad Dalara Härösad Ågermalad Täraby (9-964) Lapplad Jokkmokk Lapplad Ulrceham Västergötlad Jusele Ågermalad Umeå Västerbotte Jököpg (closed 978) Smålad Umeå flygplats Västerbotte Jököpg arport Smålad Uppsala Upplad Kalmar Smålad Vsby Gotlad Karesuado Lapplad Vsby arport Gotlad Karlsham Blekge Väersborg Västergötlad Karlstad Värmlad Västervk Smålad Katterjåkk (972-23) Lapplad Västerås Västmalad Krua Lapplad Växjö Smålad Krstastad Skåe Örebro Närke Kvkkjokk Lapplad Lköpg (closed 977) Östergötlad Östersud (closed 98) Jämtlad

16 Fgure 3.2. Statos that s used the sow statstcs. - 6

17 4. Theory. 4. Smple lear regresso. Regresso aalyss s used very frequetly to aalyse f there s ay depedece betwee two or more varables. Oe ca easly fd examples of meteorologcal varables that should be respectvely hardly should be sutable to perform regresso o. As examples of strogly depedet varables oe ca take wd drecto ad precptato o the wester sde of the moutas, the temperature at oe o clock p.m. (SNT) Stockholm ad Uppsala etc. Examples o two-dmesoal varables where t s dffcult to mage ay physcal coecto could be pressure ad humdty, temperature the 3:th of November ad 24:th of December ( Aders blazg Chrstmas slushg ). We wll here restrct us to two varables, so called lear regresso. Oe method to estmate f regresso s applcable o ths two-dmesoal dstrbuto s to plot the dfferet par of values (x,y) a dagram. From the scatter of these data pots oe ca the by free had try to sketch a straght le that as well as possble fts the observato materel. Oe more objectve but also more complcated method to ft a straght le a regresso le to a group of observatos pars s the so called least square method (the MK-method). Accordg to the MK-method the straght le should be estmated from to the gve data so that the sum of squares o the dstaces y-le betwee the observatos ad the straght le s mmzed. Fgure 4.. A schematc sketch of the MK-method. If we deote the regresso le; y a + b x, the the MK-method mples that the costats a ad b the equato for the le should be determed so that the sum of squares, 2 Q ( a,b) [ y ( a+ b )] () x s gettg so small as possble. The procedure of mmzg s performed the usual way wth the help of dervates: Q 2 a Q b ( y a b x ) ( 2) ; 2 x ( y a b x ) ( 3) - 7

18 - 8 By dvdg wth two ad develop the summatos the we get the followg ormal equatos (where the total umber of observatos): ( ) ( ) x b x a x y a x b y () 6 x b y a x b y s estmated from eq.(4): costat The a () 7 x x y x 2 2 x y put to (5): (6) s Eq. b The costat b s the slope of the le ad states how may uts y s chagg whe x s creasg oe ut. The resdual varace represets a measure o the scatterg alog the le of regresso, y a + b x: ( ) ( ) ˆ y 2 e y s 2 q By make use of the calculato rules for varace ad wth the requred assumpto that the observatos s depedet the oe ca show that the varace for the slope b ca be estmated wth the followg expresso: () 9 x x s s q 2 b The stadard devato for the slope of the straght-le s(b) s obtaed by takg the square root of the resdual varace. A radom sample does ever gve full formato about the populato. To estmate f the calculated slopes are sgfcatly separated from zero the we ca here set up the followg hypothess: : : b H b H - What cocluso could we draw about the estmated b-values f we wat the rsk to erroeously reject H to be at most.5? Soluto: Reject H o the sgfcat level α 5% f: ( ).96 ˆ 2 / > α λ b s b Z, where bˆ calculated value o the slope for the le of regresso.

19 We the assume that the data ths radom sample ca be approxmated wth the ormal dstrbuto whe s qute large (~ years). f H s rejected the the atural cosequece wll be a cofdece terval. Ths meas that we could just have looked at a 95 percet cofdece terval ad check f the value of the ull hypothess (b ) les sde or outsde ( reject H ) ths terval. H: b Fgure 4.2. A schematc sketch of the prcple for test of hypothess. 4.2 Defto of the correlato coeffcet. Assume that we have a radom sample (x,y ), (x 2,y 2 ),..,x,y ). As a measure of the lear relato betwee the two varables the radom sample oe ca calculate the coeffcet of correlato r: r SS SS x xy SS y ( ) The detaled summatos eq. () s defed as follows: SS xy x y ( x y ) ( ), SS x x ( x ) ( 2), SS y y ( y ) ( 3) SS xy > postve correlato of the radom sample. SS xy < egatve correlato of the radom sample. - How strog s the relato? Oe ca show that: - r +. r mples that all the observatos s lyg o the regresso le whle r meas that there s ot ay relato at all. The coeffcet of correlato s thus measurg f there s a relato betwee two varables, that s f the relato betwee the varables could be descrbed wth for example a straght le. If we get a value of r close to ± the t could be sutable to descrbe the relato wth a straght le. If we, however, get a value close to zero we caot descrbe the relato wth a straght le. The coeffcet of determato (r 2 ) s aswerg the questo how much of the total varato the y-values that could be explaed by a certa model due to the varatos the x-values. r 2 s completely geeral ad ca be calculated for all types of models. The rule of thumb s tellg that r >.7, because we preferably wat that more tha 5% of the varato should be explaed by the lear relato. To exame f the correlato s statstcally sgfcat oe ca apply Pearso s test: ( 64 + ) ( 4) r > 8-9

20 4.3 Ma-Kedall s test. Cocerg the aalyss of sgfcat treds the observato materel the o-parametrc method, Ma-Kedall s test, have also bee appled. The advatage wth a o-parametrc test s that oe does ot eed to kow the true frequecy dstrbuto for the actual dataset. The test varable (T) s defed by the followg equato ( test for a dow slopg tred): T N ( 5) N the total umber of elemet the data set ( ths case umber of years). the umber of precedg elemet that s larger tha elemet x (,2, N). The algorthm s workg so that oe couts all precedg elemet x j (j,2 N-) that s larger tha elemet x ( 2,3 N). Appled o the metoed example below for Uppsala the we got the followg results: Ex: The maxmum sow depth for Uppsala durg the perod : År cm T T 8 The testvarable of Ma-Kedall s cotrast to the case wth regresso aalyss a odmesoal parameter, that s t does ot gve ay formato about the magtude of the tred the actual tme seres but s rather a measure of the correlato of x wth tme ad gves as such oly formato about the drecto of the observed tred (upward, dowward or uchaged). O the codto that the umber of elemet the data set s more tha te the we have that the test varable s early ormally dstrbuted. It s expected value, E(T), ad varace, V(T), s gvg by the followg eq.: E ( T ) N ( N ) 4 ( N )( 2N 5) N + ( 6), V ( T ) 72 The ormalsed test varable Z(T) ca ow be used to test the ull hypothess that the data the tme seres s radomly dstrbuted: Z ( T ) T V E( T ) ( T ) ( 8) By comparg wth the stadardzed ormal dstrbuto we ca ow determe the probablty α ( the below the curve fg.4.2 to the rght respectvely left of the crtcal borders λ(α/2)): α P( Z > Z(T) ) The ull hypothess s accepted or rejected o the sgfcat level α depedet o f we have that α > α or α < α. The sgfcat level for the ths test was set to 5%, whch correspods to the crtcal value Z.96. Whe the values of Z(T) s sgfcat the oe ca ether detect a ascedg or descedg tred depedet f Z(T) > or Z(T) <. ( 7) - 2

21 4.4 Calculato of fltered mea values. The may dfferet hstograms of maxmum sow depth ad umber of days wth sow cover as s preseted chapter 5 are dcatg large varatos from year to year. By calculatg a tme seres wth fltered mea values (fgure 5.4 ad 5.8) we may remove hgh frequecy fluctuatos ad oe ca easer dstgush ay accumulatos of wters wth hgh or small amouts of sow respectvely. The followg formula gves a cetred mea o year t, where S for example ca be maxmum sow depth (cm): S 2 () t ( *S (t- 3) + 6 *S (t- 2) + 5*S (t-) + 2 *S (t) + 5*S (t+ ) + 6 *S (t+ 2) + *S (t+ 3) ) 64 ( 9) S (t) mea values for dvdual years, S 2 (t) tme seres wth weghted meas for every seve years based o the 6:th row the tragle of Pascal. Pascal s tragle Fgure 4.3 shows a example for Stockholm how ths flterg works: a) Maxmum sow depth per year Stockholm Idvdual years b) Maxmum sow depth per year Stockholm weghted meas for every seve years Year Fgure 4.3. Hstogram that shows the maxmum sow depth durg the perod 95-23, for dvdual years (a) ad for the weghted case (b). - 2

22 5. Results. 5. Average umber of days wth sow cover. I wll here order troduce hstograms for the whole tme seres (95-23), the latest 43 years (some more statos tha the log tme seres), cosecutve meas for every te years ad a tme seres wth smoothed mea values. The startg pot for the separate case was partly govered by the fact that the global mea temperature has creased qute substatally durg the latest 3-4 years ad that t has bee relatvely easy to provde data from dgtal meda at SMHI (Swedsh Meteorologcal ad Hydrologcal Isttute) from 96. Addtoal calculatos of correlato coeffcets ad aalyss of treds usg smple lear regresso ad Ma-Kedall s test are show the followg tables. I have ot metoed correlatos uder secto 5..3 as these values oly dffer sgfcatly from the cotets table 5.5. The results wll be dscussed the followg sectos. Defto of troduced abbrevatos: t tme ( ths case umber of years). Y average umber of days wth sow cover per caledar year (cm). X mea temperature for the wter the orther hemsphere (devatos related to the referece perod 96-9). Calculated for caledar years wth respect to the perod (Ja - Apr + Nov ad Dec). X2 the Swedsh wter mea temperature (calculated accordg to the same prcples as the global case!). r correlato coeffcet ( - r +). I also tred to perform my calculatos based o the average temperature for the whole globe, partly for the etrely year ad partly for the actual wter perod. Results from these correlato calculatos dd ot dffer much from the results below. - 22

23 5.. The complete tme seres umber of days a) Average umber of days wth sow cover orther Norrlad umber of days umber of days umber of days umber of days b) Average umber of days wth sow cover souther Norrlad c) Average umber of days wth sow cover Svealad d) Average umber of days wth sow cover Götalad e) Average umber of days wth sow cover Swede Year Fgure 5.. Hstogram that shows the average umber of days wth sow cover (S,SB,BS) per year durg the perod

24 Table 5.. A lst of statos used fgure 5.. N Norrlad () S Norrlad (6) Svealad (9) Götalad (5) Karesuado, Rksgräse/Katterjåkk, Krua, Gällvare, Kvkkjokk, Jokkmokk, Haparada, Pteå, Hemava/Täraby, Stesele ad Umeå. Storle/Vsjövale, Östersud/Frösö, Härösad, Sveg, Delsbo/Bjuråker ad Gävle. Sära, Säle, Gustavsfors/Ko, Falu, Karlstad, Örebro, Västerås, Uppsala ad Stockholm. Lköpg, Skara, Väersborg, Borås, Ulrceham, Jököpg, Västervk, Göteborg, Halmstad, Växjö, Kalmar, Karlsham, Krstastad, Lud ad Vsby. The formato fgure 5. s based o aalyss of data from all 4 statos. I have tred to focus o as log tme seres as possble but t has ot bee easy to fd statos that have qualfed for ths purpose as the data materal s of very chagg completeess ad qualty. As see fgure 3. the desty of statos s cosderably lower orther Norrlad tha the rest of Swede. Malug ad Gäddede are examples of old statos, startg 879 ad 95 respectvely, that ufortuately dropped out of the statstcs because of bad qualty o the orgal observato materal. To get a more represetatve mea value for the coutry as whole I have my calculatos left out data from Ulrceham ad Kalmar (marked talcs table 5.). Table 5.2. Raks of the fve logest ad shortest years wth sow cover the statstcs brackets. The formato ths table s based o the data fgure 5.. N Norrlad S Norrlad Svealad Götalad Swede logest 968 (229.2), 992 (222.6), 927 (222.), 932 (22.6), 97 (22.) shortest 953 (68), 937 (73), 98 (76), 9 (82.4), 9 (82.5) logest 94 (96), 985 (94), 988 (92.5), 955 (9.5), 927 (89) shortest 93 & 953 (29.2), 96 (29.8), 92 & 938 (37.2) logest 985 (72), 97 & 95 (64), 94 ad 99 (59) shortest 2 (77), 989 (78), 99 (8), 99 (8), 93 (88) logest 985 (32), 97 (27), 969 (26), 97 (2), 94 (2) shortest 989 (4), 99 (7), 974 (9), 9 (), 949 (26) logest 985 (7), 97 (66), 969 (65.), 97 (64.4), 94 (62.6) shortest 99 (98.7), 989 (2.2), 953 (2.5), 2 (3.7), 99 (5.) The extremes the umber of days wth sow cover for Norrlad s farly well scattered durg the tweteth cetury. The year wth by far logest hghest sow cover orther Norrlad s 968 whle the stuato s more complex souther Norrlad wth the logest sow year 94 tghtly followed by 985 ad 988. Cocerg the fve shortest years wth sow cover the 953 takes a leadg posto the statstcs for as well orther as souther Norrlad. The statstcs for Götalad ad Svealad s more smlar, where the sow average stayed logest durg 985 respectvely 97. O the other had both 989 ad 99 were charactersed by extreme lack of sow. I Svealad four of the fve shortest years wth sow cover has occurred after 989 whle Götalad, qute remarkable, had t -s four lowest otes durg the latest 3 years. Table 5.2 shows that the extreme case for the coutry as whole s cocdg very well wth the sow stuato Götalad ad Svealad. Aga we see that 985 ad 97 had very loglastg sow cover whle a sequece of less sowy wters has occurred after

25 Table 5.3. Results of the test wth smple lear regresso appled o the umber of days wth sow cover durg the perod 9-23 (see fgure 5.). N Norrlad S Norrlad Svealad Götalad Swede Slope of the tred le b (Y a + b*t) Stadard devato for the slope of the tred le, s(b) Normalsed test varable Z (b ) / s(b) - For whch cofdece level may we reject the ull hypothess, H : b. Z >λ(β) << 95% << 95% << 95% << 95% << 95% The appled regresso les fgure 5. are early costat over the whole tme seres. The magtudes o the estmated slopes are so small that oe caot dstgush ay apprecable chage. From table 5.3 t also becomes clear that the stadard devatos s so large wth respect to the slope of the tred les that oe of the cases s sgfcat o the cofdece level 95 %. Table 5.4. Ma-Kedall s test appled for maxmum sow depth durg the perod N Norrlad S Norrlad Svealad Götalad Swede T (x < x j ), where,2 N- ad j 2,3 +. Normalsed test varable Z(T) (T E(T)) / (V(T) - For whch cofdece level (β) may we reject the ull hypothess? (H : completely radom tme seres) Z > λ(β) β<< 95% β<< 95% β<< 95% β<< 95% β<< 95% The test show table 5.4 gves about the same formato as table 5.3, e we ca mpossbly prove ay sgfcat treds for the umber of days wth sow cover. The test statstc T, defed by eq. (5), couts for all precedg elemets that s larger tha the value the pot x (, 2 N). The terpretato of the dfferet values o the test varable T must always be doe from the expected value for the actual tme seres (the perod 9-23). The expected value provdes a measure o the cetre for a certa dstrbuto ( our case approxmated wth ormal dstrbuto). Wth umercal data put to eq. (6) we get that E(T) Depedet o whch sg the umerator the has eq. (8) we ca ether dstgush a upward or dowward tred. Thus, f we have postve values o the ormalsed test statstc Z(T) t dcates a decreasg tred whle egatve values correspods to a creasg tred. Table 5.5. Calculato of correlatos betwee the average umber of days wth sow cover ad the Swedsh respectvely the orther hemsphere s wter mea temperature durg the perod Test of correlato Rego N Norrlad S Norrlad Svealad Götalad Swede - Is the correlato statstcal sgfcat? r > P.345 r (X,Y) No, all cases s below P. r (X2,Y) Yes, wth excepto for N Norrlad. r (X,X2) No. The estmated correlato coeffcets table 5.5 above are too small to dcate ay lear relato the global case, but we ca however detect a strog correlato souther Swede betwee the presece of the umber of days wth sow cover ad the average Swedsh temperature for the wter moths. -

26 5..2 The perod umber of days a) Average umber of days wth sow cover orther Norrlad umber of days umber of days umber of days umber of days b) Average umber of days wth sow cover souther Norrlad c) Average umber of days wth sow cover Svealad d) Average umber of days wth sow cover Götalad e) Average umber of days wth sow cover Swede Year Fgure 5.2. Hstogram that shows the average umber of days wth sow cover (S,SB,BS) per year durg the perod

27 Table 5.6. A lst of statos used fgure 5.2. N Norrlad (2) S Norrlad (9) Svealad () Götalad (6) Karesuado, Rksgräse/Katterjåkk, Krua, Gällvare, Kvkkjokk, Jokkmokk, Pajala, Haparada, Pteå, Hemava/Täraby, Stesele ad Umeå. Gäddede, Jusele, Storle/Vsjövale, Östersud/Frösö, Härösad, Sveg, Söderham, Delsbo/Bjuråker ad Gävle. Sära, Säle, Malug, Gustavsfors/Ko, Falu, Karlstad, Örebro, Västerås, Uppsala ad Stockholm. Lköpg, Skara, Väersborg, Borås, Ulrceham, Jököpg, Västervk, Göteborg, Halmstad, Växjö, Kalmar, Karlsham, Krstastad, Lud, Vsby ad Hoburg. The formato fgure 5.2 s based o a slghtly larger selecto of statos compared to the log tme seres (fgure 5.). The ew added statos are marked wth talcs table 5.6. Table 5.7. Results of the test wth smple lear regresso appled o the umber of days wth sow cover durg the perod (see fgure 5.2). Slope of the tred le b (Y a + b*t) Stadard devato for the slope of the tred le, s(b) Normalsed test varable Z (b ) / s(b) - For whch cofdece level may we reject the ull hypothess, H : b. Z >λ(β) N Norrlad S Norrlad Svealad Götalad Swede β << 95% β << 95% β 96% β 97.8% β 95.5% A separate study of the latest 43 years shows a clear dowward tred Götalad, Svealad ad the coutry as a whole, whch also s statstcally sgfcat o the 95% level. Oe ca here see the fluece from the latest 2-3 years predomately warm wters souther Swede. Roughly oe ca say that the umber of days wth sow cover average has decreased wth 36 days Götalad ad days Svealad after 96 (compare wth fgure 2.2). Table 5.8. Ma-Kedall s test appled for the umber of days wth sow cover durg the perod (see fgure 5.2). T (x < x j ), where N- ad j +. Normalsed test varable Z(T) (T E(T)) / (V(T) - For whch cofdece level (β) may we reject the ull hypothess? (H : completely radom tme seres) Z > λ(β) N Norrlad N Norrlad Svealad Götalad Swede β << 95% β << 95% β 87% β 96.2% β 95.5% The alteratve method Ma-Kedall s test gves about the same respose as table 5.7 but oly sgfcat treds (dowward) for Götalad ad all statos together. Table 5.9. Calculato of correlatos betwee the average umber of days wth sow cover ad the Swedsh respectvely the orther hemsphere s wter mea temperature durg the perod Test of correlato Rego N Norrlad S Norrlad Svealad Götalad Swede - Is the correlato statstcal sgfcat? r > P.473 r (X,Y) No, all cases s below P. r (X2,Y) Yes, wth excepto for N Norrlad. r (X,X2) No. The correlato betwee the umber of days wth sow cover ad the temperature o a global scale s stll dcatg a weak relato, however, t s somewhat larger values compared to the log tme seres. It s, however, clear that the Swedsh wter temperature s a mportat parameter for the durato of sow cover as far orth as Jämtlad ad Ågermalad. I orther parts of Norrlad, o the other had, the total umber of days wth sow cover s farly depedet of the presece of warm or cold wters.

28 5..3 Cosecutve mea values for every te year. a) Average umber of days wth sow cover per decade orther Norrlad umber of days b) Average umber of days wth sow cover per decade souther Norrlad umber of days c) Average umber of days wth sow cover per decade Svealad umber of days d) Average umber of days wth sow cover per decade Götalad umber of days e) Average umber of days wth sow cover per decade Swede umber of days Decade Fgure 5.3. Hstogram that shows cosecutve meas for every te year for the umber of days wth sow cover each rego. - 28

29 5..4 Tme seres wth weghted mea values. umber of days a) Average umber of days wth sow cover orther Norrlad weghted meas for every seve years umber of days umber of days umber of days umber of days b) Average umber of days wth sow cover souther Norrlad c) Average umber of days wth sow cover Svealad - 29 weghted meas for every seve years weghted meas for every seve years d) Average umber of days wth sow cover Götalad weghted meas for every seve years e) Average umber of days wth sow cover Swede weghted meas for every seve years Year Fgure 5.4. Hstogram that shows smoothed meas of the umber of days wth sow cover (based o the formato fgure 5.).

30 Cosecutve mea values for every te year (fgure 5.3). The ew calculatos for the umber of days wth sow cover as cosecutve meas for every te years show that the shortest wters geeral occurred durg the 93 s ad 99 s except for orther Norrlad where we have extremely small dffereces betwee the decades. The mea umbers for Götalad durg these decades are aroud 5-6 days, Svealad -2 days, souther Norrlad 5-6 days ad orther Norrlad slghtly less tha 2 days. Log wters wth stable sow cover were commo Götalad ad Svealad durg the 96 s ad the 98 s. For Svealad (fgure 5.3 c) oe ca also see that there were relatvely log wters durg the perod 9-3. The legth s the 85 days Götalad ad about 4 days Svealad. The dffereces the umber of days wth sow cover betwee the decades ths study are everthelessly relatve small, as most up to 35 days. The statstcs for the etre coutry (fgure 5.3 e) dcates that t was average least sow durg the 3 s ad 9 s ad most sow the 6 s ad 8 s. Weghted mea values for every seve years (fgure 5.4). From fgure 5.4 a ad b t s clear that we have small ampltudes for orther Swede regardg varatos the umber of days wth sow cover durg the tweteth cetury. For Götalad ad Svealad, where the patter s more varable, we ca see that there were some strog depressos the sow statstcs the mddle of the 97 s ad the begg of the 99 s. The secod part of the 96 s as well as the ed of the 97 s were, however, charactersed by of log wters, most clear Götalad (fgure 5.4 d). The very cold war wters the begg of the 94 s ca also be dscered as a small hump the smoothed tme seres, at least for Götalad ad Svealad. I orther Norrlad there s a weak tedecy to that the umbers of days wth sow cover has creased durg the latest 2-3 years. - 3

31 5.2 Average maxmum sow depth. I wll here order troduce bar charts for the whole tme seres (95-23), the latest 43 years (some more statos tha the log tme seres), cosecutve meas for every te years ad a tme seres wth smoothed mea values. The startg pot for the separate case was partly govered by the fact that the global mea temperature has creased qute substatally durg the latest 3-4 years ad that t has bee relatvely easy to provde data from dgtal meda at SMHI from 96. Addtoal calculatos of correlato coeffcets ad aalyss of treds usg smple lear regresso ad Ma-Kedall s test are show the followg tables. I have ot metoed correlatos uder secto as these values oly dffer sgfcatly from the cotets table 5.4. The results wll be dscussed the followg sectos. Defto of troduced abbrevatos: t tme ( ths case umber of years). Y2 average maxmum sow depth per caledar year (cm). X mea temperature for the wter the orther hemsphere (devatos related to the referece perod 96-9). Calculated for caledar years wth respect to the perod (Ja - Apr + Nov ad Dec). X2 the Swedsh wter mea temperature (calculated accordg to the same prcples as the global case!). r correlato coeffcet ( - r +). - 3

32 5.2. The complete tme seres a) Average maxmum sow depth orther Norrlad b) Average maxmum sow depth souther Norrlad c) Average maxmum sow depth Svealad d) Average maxmum sow depth Götalad e) Average maxmum sow depth Swede Year Fgure 5.5. Hstogram that shows the average maxmum sow depth durg the perod

33 Table 5.. A lst of statos used fgure 5.5. Norther Norrlad () Souther Norrlad (7) Svealad (9) Götalad (3) Karesuado, Rksgräse/Katterjåkk, Krua, Gällvare, Kvkkjokk, Jokkmokk, Haparada, Pteå, Hemava/Täraby, Stesele ad Umeå. Gäddede, Storle/Vsjövale, Östersud/Frösö, Härösad, Sveg, Delsbo/Bjuråker ad Gävle. Sära, Säle, Malug, Falu, Karlstad, Örebro, Västerås, Uppsala ad Stockholm. Lköpg, Skara, Väersborg, Borås, Jököpg, Västervk, Göteborg, Halmstad, Växjö, Karlsham, Krstastad, Lud ad Vsby. Table 5.. Raks of the fve most respectvely less sowest years wth addtoal average maxmum sow depth brackets reported cm. N Norrlad S Norrlad Svealad Götalad Swede most sowy 96 (7), 997 (4), 953 (), 936 (), 965 (8). least sowy 933 (5), 932 (56), 93 (6), 92 (65), 947 (65). most sowy 966 (), 988 (3), 98 (98), 96 (93), 982 (9). least sowy 93 (3), 933 (32), 99 (37), 939 (4), 932 (44). most sowy 966 (92), 95 (8), 977 (), 982 (74), 93 (69). least sowy 95 (24.2), 99 (24.3), 996 (24.4), 989 (.4), 9 (26.4) most sowy 979 (53), 966 (49), 977 (45), 985 (42), 97 (4) least sowy 949 (7.), 99 (7.2), 989 (7.8), 96 (9.6), 974 (.) most sowy 966 (83.7), 977 (72.4), 982 (69.3), 988 (67.8), 987 (66.4) least sowy 933 (3), 932 (34), 93 (35), 964 (37), 92 (4). The formato table 5. shows that Svealad ad souther Norrlad has absolute records maxmum sow depth from 966, Götalad 979 tghtly followed by 966 whle the patter for orther Norrlad s slghtly more dffcult to terpret wth the years 96 ad 997 the top of the statstcs. The fve sowest years for the last-metoed rego have a hgh level of ucertaty because of the small umber of statos (9). The record for the coutry as whole dates from 966. There s o doubt about that t was a exceptoally sow year! Amog the 4 statos that are cluded ths vestgato there were eghtee places that could report a maxmum sow depth o cm or more. A farly uque record for Swedsh sow statstcs. O secod place ths regard came 936 wth te statos. Mld wters occurred orther Swede the begg of the 93 s where orther ad souther Norrlad had ther lowest depths 93 ad 933. I Götalad ad Svealad oe ca, however, ot pot out ay specal extreme year, as the dffereces betwee the fve least sowy years are small. For Götalad t stads betwee 949 ad 99 whle we for Svealad we ca meto the years 95, 99 ad 996. Whe t cocers the coutry, as a whole 933 s the least sowy year. It should here also be oted that we wll have slghtly dfferet results Svealad the case wth the least sowy years depedg f we are vestgatg the souther (Karlstad, Örebro, Västerås, Uppsala ad Stockholm) or orther part (Sära, Säle, Malug ad Falu). The wter of were cotrast to 989 ad 99 relatvely cold souther Swede but at the same tme dry, so the sow depth dd ot crease apprecably. It was less sow souther Svealad durg the years 9 (.5 cm), 989 (3.5 cm) ad 99 (6.5 cm) compared to 95 (5 cm) ad 996 (5 cm). The umercal data brackets refer to the average maxmum sow depth. I orther Svealad the stuato was o the other had the opposte; 95 & 996 (37 cm), 989 (4 cm), 9 (46 cm) ad 99 (47 cm). 2 Source: The magaze of SMHI, Väder och Vatte, umber -4/