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9th International Conference Zaragoza-Pau

on Applied Mathematics and Statistics

On heat wave definitionAbaurrea J., Cebrián A.C., Asín J., Centelles A.

19-21 September 2005

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Introduction (1)Heat waves have not a standard operational definition

Usual approach to define them:

• An excess of daily maximum temperature, Tx, over a fixed threshold (POT)

Other conditions required:

• A minimum duration of the event

• The daily minimum temperature exceeds another threshold

Problems and evidences not considered:

• Greater effects on morbidity and mortality of heat waves occurring in the early summer

• Possibility of longer heat waves including intermediate “cool” days

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• Kysely (2000):

A group of consecutive days is considered a heat wave if:

a) Tx ≥ T1 for, at least, three days

b) Tx ≥ T2 for every day

c) Mean (Tx) ≥ T1

Tx: Daily maximum temperature

T1: Threshold for hot days

T2: Threshold for warm days

For Central Europe T1 = 30ºC and T2 = 25ºC

Introduction (2)

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a) and b) as Kysely

c) Mean(Tx) T1 for the whole period and for each partial sequence, HC, HCHC, etc., where H stands for a hot spell and C a cool spell

d) The length and the area (the accumulated sum of differences to T1) for each cool spell included in the wave, must be lower than the corresponding 90th percentile in the reference period

T1 and T2 are, respectively, the 95th and 50th percentiles of Tx values observed in June, July and August, in the reference period 1961-1990

A time period is considered a heat wave if:

Introduction (3)• Abaurrea et al. (2004):

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Heat wave: A period of arbitrary length where Tx exceeds a “shot temperature”Shot temperature = extraordinary increase of mortality

– Madrid (36.5ºC)– Barcelona (30.3ºC)

Introduction (4)• Díaz et al. (2003):

–Sevilla (41ºC)

–Lisboa (33.5ºC)

These thresholds are the 95th percentiles of the corresponding Tx value distributions in JJAS, 1991-2002

In this way, they obtain the heat wave thresholds for main Spanish towns: Zaragoza (37.3ºC), Huesca (36.1ºC)

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Data and preliminary analysis

 

•Zaragoza and Huesca

•Daily Tx and Tn data for 1951-2004

•Daily mortality data for 1975-2002 (people aged 65 or more years)

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Temperature

• Tx and Tn evolution during the studied period

1951-75 stability 1976-90 increase

1991-96 stability 1997-2004 increase

Data and preliminary analysis

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• Tx evolution in different summer periods

TemperatureData and preliminary analysis

Lowess (40) of Tx data in 7 overlapping 5-week intervals

9 Lowess (30) of Mr corresponding to seven overlapping 10

year long intervals

Mr decreases between 1975 and 2002

Change in the seasonal profile

MortalityData and preliminary analysis

• Mr: Daily mortality rate per 1000 inhabitants

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•The effect of hot temperatures on mortality occurs in the short term (1-3 days) (Díaz et al. 2005)

•For daily variables, the correlation between Tx and Mr is maximum with a 24 hour delay

•The greatest correlation between 3 days averaged values is also obtained for a 24 hour delay

Temperature-Mortality relationshipData and preliminary analysis

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Data and preliminary analysis

The impact on Mr of a fixed high temperature changes in time and along the summer

To show this property we select a temperature value, 33.3ºC, the 90th percentile of daily Tx values in June, 1975-81

•1975-02 is divided into four 7-year periods and we consider observations from June, July and August

Temperature-Mortality relationship

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Data and preliminary analysis

•Decrease of Mr 90th percentile and mean values in time and along the summer

•33.3ºC is a critical value, regarding the Mr response, for the first period and it is not for the last one

Temperature-Mortality relationship

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Data and preliminary analysis

•Decrease of Mr 90th percentile and mean values in time and along the summer

•33.3ºC is a critical value, regarding the Mr response, for the first period and it is not for the last one

Temperature-Mortality relationship

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Mortality ExcessWe define the mortality excess, Mex(t), in day t as the difference between the number of deaths, Mf(t), and its expected value, Me(t)

Mex (t) = Mf(t) –Me(t)

The expected mortality is obtained by fitting a regression model including:

a) Time terms until the second order (long term evolution)

b) Harmonic terms until the fourth order (seasonality)

c) Dummy variables for indicating the periods 75-86, 87-96 and 97-02, in order to fit different seasonal patterns

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Expected and observed mortality lowess

Mortality Excesss

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•We try to identify the ‘shot temperature’ for each 7-year period and summer interval, looking for the change point in the lowess smoother of Mex vs. Tx

PROBLEMS

Smoothed curves are frequently erratic because of small sample sizes

A proper shot temperature doesn’t appear in many graphs

Threshold selection

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Threshold selection

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Threshold selection

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High excess crossing temperatures increase in time but remain constant when they are transformed to a percentile scale

Threshold selection

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Threshold selection processThe process to define T1 threshold needs several steps

a) Analysed interval: 14-May to 16-September in 1975-2002

b) Four 7-year periods (1975-81, 1982-88, 1989-95, 1996-2002)

c) Several divisions of the 14/5-16/9 interval using different

length cells: 3-weeks, 4-weeks, month,...

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d) Identifying 1.25-excess crossing temperature percentiles

Threshold selection process

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Threshold selection process

e) Percentile-Threshold allocation to 11 selected dates along the summer

1.25-excess crossing temperature percentile values

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f) Transformation of the percentile-threshold into its equivalent temperature-threshold (T1) using an adequate probabilistic distribution

Threshold selection process

Probabilistic distributions:

N: Normal

LN: Lognormal

W: Weibull

EV: Extreme Value

L: Logistic

LL: Log-Logistic

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g) Estimation of the daily T1 threshold for each 7-year period

Threshold selection process

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•4th June: 32.3-34ºC•27th August: 37-39.8ºC

•The increase of T1 along the period 1975-2002 is about 2ºC

•The bigger slope of the 3rd period is due to temperature warming in August and July, whereas the smaller slope of the 4th period is due to strong temperature increase in June

Threshold selection process

T1 thresholds for the period 1975-2002

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in comparison with the T1-Díaz performance

Results and conclusions

Evaluation of T1- threshold results

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References Abaurrea, J., et al. (2004). Modelling hot extreme temperature events using a non homogeneous Poisson model. 6th World Congress of Bernoulli Society for Mathematical Statistics and Probability, Barcelona.

Díaz, J., et al. (2002). Effects of extremely hot days on people older than 65 years in Seville (Spain) from 1986 to 1997. Int. J. Biometeorology, 46, 145-149.

Díaz, J., Linares, C., García-Herrera, R. (2005). Impacto de las temperaturas extremas en la salud pública. Futuras actuaciones. Rev. Esp. Salud Pública, 79, 145-157.

Kysely, J. (2002). Temporal fluctuations in heat waves at Prague, the Czech republic, from 1901-97 and their relationship to atmospheric circulation. Int. J. Climatol., 22, 33-50.

Robinson, P. J. (2001). On the definition of a heat wave. J. of Applied Meteorology, 40, 762-75.