Estimation of extreme wet and dry days through moving totals in

Analysis of extreme precipitation in different time intervals using moving precipitation totals Tiina Tammets1, Jaak Jaagus2 1

Estonian Meteorological and Hydrological Institute 2

Department of Geography, University of Tartu

Outline • Introduction, precipitation regime and extremes in Estonia • Overview of the characteristics used for description of precipitation extremes • Objectives of the study • Using of moving precipitation totals as characteristics of precipitation regime • Extreme precipitation in Estonia in dependence of a number of days and months in observed period • Extreme precipitation in Estonia in case of very wet and dry conditions during 1957-2006 • Trends in precipitation extremes in Estonia during 19572006 • Conclusions

Annual curve of monthly mean, maximum and minimum precipitation in 1966-2009, mean of the meteorological stations in Estonia 160 140

average

precipitation, mm

120

min

max

100 80 60 40 20 0 I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

Precipitation in July and August 1966-2009, mean of the meteorological stations in Estonia 180

August

2008

July

160

1987

1978

1988

1990

2005

120

1996, 1994 1997

100

2002

1983

2006

80 60 40 20

2008

2006

2004

2002

2000

1998

1996

1994

1992

1990

1988

1986

1984

1982

1980

1978

1976

1974

1972

1970

1968

0

1966

precipitation, mm

140

JUNE

PRECIPITATION 2009 IN ESTONIA AUGUST

JULY

Characteristics used for description of precipitation extremes • quantiles of precipitation amounts; • maximum number consecutive wet days (R>= 1 mm; 10 mm); • maximum number of consecutive dry days with the threshold of 0.1 mm; 1 mm precipitation; • number of heavy precipitation days in a month or year (R>=10 mm); • number of very heavy precipitation days (R>=20 mm); • number of dry and wet days in a month or in a year with chosen threshold; • mean wet-day and dry-day persistencies; • hydrothermical coefficient.

hydrothermical coefficient (HTK) : HTK = Precipitation / 0,1* Temperature Hydrotermical coefficient, average of Estonian meteorological stations June-August 1961-2009

90 80

1998 1962

1978

70

1981

1987

HTK, mm/°C

1990

1961 1974

1965

1964

1971 1967

2001

1986 1984

1970 1973 1968 1975 1969

1983

0

2005

2003

1979 1982 1977 1976

2007

1995 1994 1992

20 10

2009

1985

40 1963 30

2008 2004

60 50

1993

HTK = R/0,1*T

2002 1999 2006

For many purposes it is essential not to show how much it rains in a day

but

to show how much has been rained till this day A day will be extreme day, if the amount of precipitation till this day has been too small or too large.

Objectives • To define characteristics describing continuous dry and wet spells with various duration, which doesn’t divide time into months or 10-day periods • To elaborate a method characterising climatology of extreme precipitation totals for any time periods (number of following days, months or years using moving totals) • To detect the most severe wet and dry spells in Estonia during last 40-50 years and to analyse trends in days with precipitation extremes

To find the number of extreme days we have to calculate the moving total or average of precipitation time series

CALCULATING MOVING TOTALS (AVERAGES) Mathematically the sequence of moving totals (averages){sj(n),1  j  N-n+1} is derived from a sequence {ai, 1  i  N} obtained by taking the totals (averages) of the subsequent n terms: i n1

sj(n)=  aj (by moving averages j i

in1

sj(n)=1 n

aj),where N is the total number of days ji

in the precipitation time series and n the number of days through which the moving average is calculated. We find drought and wet days by calculating sj(n) with time period n for each day i in the time series and choosing the days with values of sj(n), that are smaller or larger than the given threshold t.

Counting of moving total

if there are no precipitation on a day and previous n days the day has been counted as a

droughtday

n

days 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

days 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

17 18 19 20

17

21

21 22 23

22 23

N days

18 19 20

if the average of precipitations on a day and previous n days is M mm and more the day has been counted as a

p

wetday

n

Presentation of the extreme precipitation in any number of days, months or years 600

Jõgeva max Jõgeva min Poly. (Jõgeva max) Poly. (Jõgeva min)

precipitation, mm

500

400

300

200

100

0 0

20

40

60

80

100

number of days

120

140

Precipitation stations in Estonia

Extreme totals of precipitation for any number of days during 1966-2009 has been found in Tallinn, Vilsandi, Väike-Maarja, Võru Tartu and Pärnu stations

Dependence of maximum and minimum precipitation on the number of successive days at six stations in Estonia in 1966-2009 Extreme precipitation totals in Estonian climate stations in 1966-2009

1200

TALLmax

V-MAARmax

PÄRNUmax

TÕRAmax

VILSmax

VÕRUmax

TALLmin

V-MAARmin

PÄRNUmin

TÕRAmin

VILSmin

VÕRUmin

precipitation, mm

1000 800 600 400 200 0 0

50

100

150

200

250

number of days

300

350

400

Dependence of maximum and minimum precipitation on the number of successive months at six stations in Estonia in 1966-2009 Extreme precipitation totals 1966-2009 in Estonian climate stations 4500

pärnumax v-maarjamax tallinnmax võrumax vilsandimax tõraveremax

4000

precipitation, mm

3500 3000

pärnumin v-maarjamin tallinnmin võrumin vilsandimin tõraveremin

5 years

4 years 3 years

2 years

2500 1 year

2000 1500 1000 500 0 0

10

20

30 number of months

40

50

60

Extremely wet and dry days for Estonia In agrometeorological studies of Estonia, the criterion of extremely wet conditions - mean daily precipitation 10 mm or more during successive 10 days is used. If the moving average for a 10-day period sj (10)>= 10 mm, then the last day of the period is regarded as a wet day. Extremely dry conditions for field plants mean that there is no precipitation during successive 20 days; then sj (20) = 0 and the last day of the period has been counted as a dry day.

number of day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

wet

dry

criteria:

average 10 mm in a day

without precipitation

• extremely wet conditions: when the mean daily amount of precipitation is 10 mm and more during 10 consecutive days

1. wet day

1. dry day

• extremely dry conditions: no precipitation during 20 consecutive days

Monthly relative number of wet days and days with precipitation ≥10 mm during 1957-2006, mean of the meteorological stations in Estonia wetdays

days with precip.10mm and more

0,40 0,35 0,30 0,25 0,20 0,15 0,10 0,05 0,00 I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

Monthly relative number of dry days and days without precipitation during 1957-2006, mean of the meteorological stations in Estonia 0,25

drydays

days without precipitation

0,20 0,15 0,10 0,05 0,00 I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

Maximum number of dry days in Estonia from May to August during 1957-2006 16

14

24 12

13 13

24

11

26

23 10

15

14 14

9

22

10

21

8

15

12

10 10

15 7

8

10

10

26

17 23

17 26

22 22

22

14 17

5

7

13

10 18

8

23

18

15 8

11

23

12

10 10 30

wetdays

0,14

12

drydays

0,12

10 8

relative number of extremes Linear (relative number of extremes)

0,10 0,08

6

0,06

4

0,04

2

0,02

0

0,00

Relative number of extreme (dry+wet) da ys

14

1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Number of days

Number of wet and dry days (mean of 56 stations) and relative number of extreme (wet+dry) days in 1957-2006

Conclusions The method of moving precipitation totals allows to 1. present maximum and minimum precipitation in different periods (from 1 day to 4-5 years) on graph, which gives complete information about precipitation extremes of a station. It allows also to compare extreme precipitation amounts in different stations for every time period. 2. connect precipitation extremes with the dynamics other characteristics of hydrological regime (for example soil moisture content, ground water level, river runoff etc.) and find the best predictants of precipitation regime for extreme situations of environment 3. extract the time intervals of extreme precipitation events to relate them to atmospheric circulation

Conclusions Using of the method of moving precipitation totals for the analysis of precipitation extremes in Estonia demonstrated that • maximum and minimum precipitation in case of any number of successive days and months on the coast of open sea (Vilsandi) is significantly lower than in the continental Estonia • occurrence of wet days is the highest in July and August while the number of dry days is maximal only in August and much lower in July • maximum number of days without precipitation has been observed in May

• total number of extreme (wet and dry) days in Estonia has increased significantly during 1957-2006