Atmospheric Research 77 (2005) 203–217

www.elsevier.com/locate/atmos

Improving the accuracy of tipping-bucket rain

records using disaggregation techniques

A. MoliniT, L.G. Lanza, P. La Barbera

University of Genova, Department of Environmental Engineering, 1, Montallegro-16145 Genova, Italy

Received 4 May 2004; received in revised form 15 November 2004; accepted 7 December 2004

Abstract

We present a methodology able to infer the influence of rainfall measurement errors on the

reliability of extreme rainfall statistics. We especially focus on systematic mechanical errors affecting

the most popular rain intensity measurement instrument, namely the tipping-bucket rain-gauge

(TBR). Such uncertainty strongly depends on the measured rainfall intensity (RI) with systematic

underestimation of high RIs, leading to a biased estimation of extreme rain rates statistics.

Furthermore, since intense rain-rates are usually recorded over short intervals in time, any possible

correction strongly depends on the time resolution of the recorded data sets. We propose a simple

procedure for the correction of low resolution data series after disaggregation at a suitable scale, so

that the assessment of the influence of systematic errors on rainfall statistics become possible. The

disaggregation procedure is applied to a 40-year long rain-depth dataset recorded at hourly resolution

by using the IRP (Iterated Random Pulse) algorithm. A set of extreme statistics, commonly used in

urban hydrology practice, have been extracted from simulated data and compared with the ones

obtained after direct correction of a 12-year high resolution (1 min) RI series. In particular, the

depth–duration–frequency curves derived from the original and corrected data sets have been

compared in order to quantify the impact of non-corrected rain intensity measurements on design

rainfall and the related statistical parameters. Preliminary results suggest that the IRP model, due to

its skill in reproducing extreme rainfall intensities at fine resolution in time, is well suited in

supporting rainfall intensity correction techniques.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Rainfall; Measurement errors; Disaggregation; Depth duration frequency curves; Tipping bucket rain

gauge

T Corresponding author. Tel.: +39 010 3532485; fax: +39 010 3532481.

0169-8095/$ -

doi:10.1016/j.

E-mail add

see front matter D 2005 Elsevier B.V. All rights reserved.

atmosres.2004.12.013

ress: molini@diam.unige.it (A. Molini).

A. Molini et al. / Atmospheric Research 77 (2005) 203–217204

1. Introduction

Urban hydrology applications commonly rely on the processing of historic rain rate

data sets, recorded at a suitable measurement station located within or in the vicinity of the

investigated basin. Correct estimation of the return period of a given rain event for design

purposes is based on the prolonged and accurate measurement of rain data (Keifer and

Chu, 1957) and low accuracy in data collection can lead to poorly effective storm water

control within the considered basin.

At the same time, the measurement of rain intensity is affected by a number of errors,

due to both catching and counting inaccuracies, related to the positioning and mechanics/

electronics of the instrument employed (Marsalek, 1981; Fankhauser, 1997).

The measurement of rain intensity is traditionally performed by means of tipping-

bucket rain gauges (TBRs), the most popular and widespread type of rain gauge actually

employed worldwide (Fig. 1). These instruments are known to underestimate rainfall at

higher intensities (N100 mm/h) because of the rainwater amount that is lost during the

tipping movement of the buckets. The related biases are known as systematic mechanical

errors and result in the overestimation of rainfall at lower intensities (b50 mm/h) and

underestimation at the higher rain rates (Fankhauser, 1997; La Barbera et al., 2002).

Mechanical errors, although less important in terms of accumulated rainfall, have a

strong influence on the measurement of moderate to high rain intensities, with increasing

impact as far as the rain rate increases.

On the other hand, intense rain-rates are usually characterized by a short duration, so

that any possible correction of the uncertainty connected with mechanical errors strongly

depends on the available resolution in time of the considered time series (Lombardo and

Stagi, 1998).

Though a simple and effective correction technique exists for the bias induced by

systematic mechanical errors, namely dynamic calibration (Marsalek, 1981; Sevruk, 1982;

Fig. 1. The tipping-bucket mechanism (after Marsalek, 1981).

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 205

Sevruk and Hamon, 1984; Lombardo and Stagi, 1998; Luyckx and Berlamont, 2001), this

uncertainty is usually neglected in the hydrological practice, relying on the assumption that

it has little influence on the total recorded rainfall depth.

In a previous work (Molini et al., 2005), we demonstrated that since the error increases

with rainfall intensity, this assumption is not acceptable for the assessment of design

rainfall in urban scale applications. In this case, indeed, the high resolution required for the

monitoring of rainfall intensities (due to the very short response time of urban catchments)

amplifies the influence of mechanical errors on the derived statistics of rainfall extremes

(La Barbera et al., 2002).

We then propose a simple procedure for the correction of low resolution rain records

after disaggregation at a finer scale so that evaluation of the influence of systematic errors

on the statistics of rainfall extremes becomes possible. In the case study discussed below,

we downscale hourly rainfall data at a resolution of 1 min, using the outcomes of a

disaggregation technique based on the IRP (Iterated Random Pulse) algorithm

(Veneziano, 2002; Veneziano and Iacobellis, 2002; Veneziano et al., 2002).

After a brief summary of measurement errors in TBRs and the available data set

(Section 2), in Section 3 we review the properties of the IRP process, focusing on its

application to disaggregation techniques. Then we use the model to produce ensembles of

corrected rain rates, starting from a 40-year long (1961–2000) rain intensity series,

recorded at hourly resolution at the Meteorological Observatory of Chiavari in North West

Italy. To produce such synthetic time series, the Chiavari data set is disaggregated down to

a 1 min, corrected and then re-aggregated at the original hourly resolution.

Correction parameters are derived from the dynamic calibration of the historical

instruments used in recording the considered rain data in the period from 1961 to 2000.

Finally, DDF (depth–duration–frequency) curves are derived for both the original and

corrected time-series and the results are discussed in Section 4.

2. TBRs measurement errors

Rainfall measurements are affected by several sources of error, due to both catching and

counting inaccuracies, related to both the positioning and mechanics/electronics of the

adopted instrument. Most of the errors due to the catching problem have a limited

influence on rain intensity figures, being on the other hand important for rain accumulation

measurements at the daily, monthly or longer time scales (Adami and Da Deppo, 1986;

Marsalek, 1981). These are commonly categorised as wind induced, wetting, splashing,

and evaporation errors, all of them occurring within or at the top of the water collector

implemented to convey rainfall from a standardised orifice into the measuring device.

The error always results in this case in some underestimation of the total amount of

rainfall. A wide literature exists about the assessment and correction of catching type

errors, mainly concerned with climatologic studies and light to moderate precipitation (see

e.g. Sevruk, 1982; Sevruk and Hamon, 1984; Legates and Willmott, 1990).

On the other hand, mechanical errors due to the inherent characteristics of the counting

device, although less important in terms of accumulated rainfall, have a strong influence

on the measurement of the rain intensity, with increasing impact as far as the rain rate

A. Molini et al. / Atmospheric Research 77 (2005) 203–217206

increases. In fact, the measurement of rain intensity, traditionally performed by means of

tipping-bucket rain gauges, is affected by underestimation of rain rates at high intensities

because of the rainwater amount that is lost during the tipping movement of the bucket.

Though this inherent shortcoming can be easily remedied by dynamic calibration (see

later in this section), the usual operational practice in hydro-meteorological services and

instrument manufacturing companies relies on single-point calibration, based on the

assumption that dynamic calibration has little influence on the total recorded rainfall depth

(Fankhauser, 1997).

In two recent papers, the bias introduced by systematic mechanical errors of tipping

bucket rain gauges in the estimation of return periods and other statistics of rainfall

extremes was quantified in very general terms (La Barbera et al., 2002; Molini et al.,

2001), basing on the error figures obtained after laboratory tests over a wide set of

operational rain gauges from the network of the Liguria region in Italy. An equivalent

sample size was also defined as a simple index that can be easily employed by

practitioner engineers to measure the influence of systematic mechanical errors on

common hydrological practice and the derived hydraulic engineering design (La Barbera

et al., 2002).

The bias, estimated in average at about 10–15% for rain rates higher than 200 mm/h, is

strongly specific of the single rain gauge, depending on the manufacturer, the date of

production and the type of wearing (as a function of the existing environmental conditions)

(Becchi, 1970; Marsalek, 1981; Adami and Da Deppo, 1986).

The relevance of such losses, affecting each single tipping of the bucket, increases with

rainfall intensity and is a function of the total time DT requested for the bucket to complete

its rotation. According to Marsalek (1981) the theoretical relationship between the

recorded (Ir) and actual (Ia) intensities as a function of DT is given by:

Ir=Ia ¼ hn= hn þ IaDTð Þ ð1Þ

where hn is the nominal rainfall depth increment per one tip. Note that Ir/Ia=1 only in the

case of DT=0 and that DT is a function of rainfall intensity.

The relationship presented by Marsalek (1981) between DT and Ia shows significant

durations of the bucket movement ranging between 0.3 and 0.6 s for the instruments

analysed. However, the uncertainty involved in the measurement of the time of tipping–

due to the very slow initiation of the bucket rotation–made the comparison of experimental

and theoretical calibration curves hardly appreciable in the author’s work. Sophisticated

measurement of DT allows better success in comparing the experimental calibration curve

with its theoretical expression.

For example, in Luyckx and Berlamont (2001), a theoretical derivation of the

calibration curve is proposed based on a mean value for DT.

However, direct estimation of the calibration curve is far more reliable than its

theoretical derivation as it does not involve sophisticated measurements of very short

intervals in time as a function of varying rain rates. A simple hydraulic apparatus can be

used to this aim, which allows high precision measurements and reliable dynamic

calibration of TBRs (see e.g. Calder and Kidd, 1978; Marsalek, 1981; Niemczynowicz,

1986; Pagliara and Viti, 1994; Lombardo and Stagi, 1998).

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 207

The objective is that of providing the gauge receiver with a constant rain rate at a

number of calibration points in the (Ia, Ir) space. This is achieved by connecting a

constant water level tank with the receiver after interposition of a nozzle with specified

diameter. By modifying the water head over the orifice and the nozzle diameter, constant

flows can be generated at various flow rates as desired (see Humphrey et al., 1997;

Lanza and Stagi, 2002).

Calibration curves reflecting the so-called dynamic calibration of the gauge can be

expressed by means of a power law formulation as:

Ia ¼ a Ibr ð2Þ

where Ia and Ir are again the actual and recorded rain intensities and a, b are calibration

parameters strictly related to the mechanical and wearing characteristics of the considered

TBR. In the practice, Ir is the rainfall intensity recorded during a generic calibration test,

while Ia derives from a more precise measurement device (e.g. a precision balance) placed

in series with the TBR bunder testQ.The two parameters a and b are therefore sufficient to characterise the mechanical

behaviour of the instruments in hand, and to allow correction of the recorded data sets in

order to increase their accuracy.

The associated relative measurement error e can be defined as:

e ¼ Ir � Ia

Ia100 ð3Þ

so that e b0 indicates underestimation rather than overestimation (eN0) of the actual rain

rates.

As an example we report here the results of the dynamic calibration exercise performed

on the three rain gauges that will be used in the following sections to demonstrate the

impact of measuring errors on the estimation of design rainfall. These are the TBR of the

University of Genoa station (available for the period 1990–2002) and the two ones

(manufactured by SILIMET and SIAP) used on successive time spans at the

Meteorological Observatory bAndrea BianchiQ of Chiavari, located about 40 km east of

the town of Genoa along the coastline, and operating since 1883. Concerning the

Meteorological Observatory bAndrea BianchiQ series, a 40-year sub-series is used in this

study (1961–2000). The two series will be hereinafter called the DIAM and the Chiavari

series, respectively. The DIAM data are publicly available online from the University of

Genoa at the following web address: http://www.diam.unige.it/.

In all cases the rain gauge in use was accurately calibrated in the laboratory using the

automatic qualification module for rain intensity measurement instruments developed by

Table 1

Calibration parameters a and b for the three gauges analysed

Station Rain gauge a h

DIAM-University of Genoa CAE (1990–2002) 0.79 1.06

Observatory Andrea Bianchi of Chiavari SIAP (1961–1989) 0.76 1.07

SILIMET (1990–2000) 0.76 1.05

0 50 100 150 200 250 300 3500

50

100

150

200

250

300

350

Recorded Rainfall Intensity Ir [mm/h]

Rai

nfal

l Int

ensi

ty I

[mm

/h]

CAE (DIAm Station)SIAP (Observatory of Chiavari, 1963-1989)SILIMET (Observatory of Chiavari, 1990-2000)

Fig. 2. Calibration curves for the tipping-bucket rain gauge of DIAM-University of Genoa (CAE) and the two

gauges employed at the Meteorological Observatory bAndrea BianchiQ of Chiavari (SIAP and SILIMET).

A. Molini et al. / Atmospheric Research 77 (2005) 203–217208

Lanza and Stagi (2002). The estimated calibration parameters a and b for the three gauges

are reported in Table 1, while calibration curves of the three instruments are reported in

Fig. 2.

Since mechanical errors affecting high rain rates are usually recorded at very short

intervals in time, the recovery of rain records by means of suitable correction is only

possible at very fine resolution in time. Unfortunately, most of the historical information is

stored in the form of accumulated rainfall depth over intervals not finer than 30–60 min

and the details of the rain process at finer time scales are irremediably lost. In those cases

correction can be performed based on suitable downscaling of the recorded figures at least

down to a resolution in the order of 5 min, where the rain rate is higher and significant

biases arise. Obviously correction would result in a statistical sense, and no deterministic

assessment can be performed of the actual impact of the error on design values.

3. Rain intensity correction after downscaling

Reconstruction of the original variability at sub-hourly scales is therefore necessary, at

least down to a resolution in the order of 1–5 min, since at lower scales sampling errors

may become also relevant. This can be achieved by downscaling coarse data using a

suitable disaggregation technique, at least able to reproduce the structure and the

amplitude of intense rainfall at high resolution.

This is not a trivial issue, since e.g. the well-known family of disaggregation

techniques, namely random cascades, is strongly sensitive to climatic factors. For instance,

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 209

disaggregation schemes basing on the classical multiplicative random cascade can produce

unrealistic rain intensities when calibrated on mid-latitudes data (Guntner et al., 2001;

Mouhous et al., 2001), then making statistical correction less effective.

In this section we apply the correction procedure to the coarse resolution rain intensity

data of the Chiavari series after downscaling based on the IRP (Iterated Random Pulse)

algorithm. After a brief review of the model, the Chiavari data set, is disaggregated at 1-

min resolution, corrected using the parameters obtained after dynamic calibration of the

involved TBRs and therefore re-aggregated at hourly resolution. The calibration curves of

the two TBRs used at the Chiavari station in the period 1961–2000 are reported in Fig. 2.

The basic parameters of the model, the co-dimension and the contraction factor, have been

respectively obtained from the literature (Veneziano and Iacobellis, 2002) and after

accurate calibration of the model on the data of the DIAm series.

The procedure has been repeated 1000 times, so that an ensemble of as much 40

year2long synthetic series was obtained. Traditional DDF curves and extreme statistics

have been calculated in order to assess the influence of the applied correction. To infer

DDF curves, independence was assumed for annual maxima and the related parameters

were derived after fitting an extreme value distribution (EV1 or Gumbel).

The best fit of the Gumbel model is shown in Fig. 3, where the EV1 for the original

time series of Chiavari and DIAm stations are respectively represented.

Finally, results obtained for the synthetic series have been compared with those

deriving from the original data of Chiavari and with the figures deriving from the direct

correction of the high resolution DIAm series.

3.1. Implementation of the IRP model

Iterated random pulse (IRP) algorithms due their definition to the hierarchical clustering

of their pulse location. They have been largely investigated by Veneziano (2002) and

Veneziano et al. (2002) and recently, these same authors have proposed to apply the IRP

scheme to rainfall simulation at the sub-synoptic scale and to sub daily resolution

disaggregation (Veneziano and Iacobellis, 2002). For different scales the pulses present

amplitudes with a cascade-like dependence, though the produced fine resolution lacunarity

is non-fractal.

The applied downscaling procedure is therefore as follows: first, hourly data are

assimilated to events at the synoptic scale and indicated as h(t� t0), with t0 a location

parameter.

Each rain event is then replaced by a random number N of offspring pulses contracted

by a factor r N1 with respect to the original pulse. These N offspring pulses have random

time offsets relative to the location parameter and randomly scaled intensities, so that:

h t � t0ð Þ ZXN

i¼1

gih r t � tið Þð Þ ð5Þ

where the number N is Poisson distributed with E[N]= r, the locations ti are independent

and identically distributed random variables with a probability density function dependent

on the rescaled parent pulse h(t� t0) and the gi are independent replications of a non-

Fig. 3. Fitting of the Gumbel distribution of rainfall extremes for the rain series of Chiavari (a) and DIAm (b).

A. Molini et al. / Atmospheric Research 77 (2005) 203–217210

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

2

4

6

8

10

12

Meteorological Observatory of Chiavari, Genova – Simulated rainfall depth cumulated on 1 minute (mm): year=1995

month

Rai

nfal

l dep

th (

mm

) –

Agg

rega

tion=

1 m

inut

e

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

2

4

6

8

10

12

14

Dept. of Environmental Engineering, University of Genova – Rainfall depth cumulated on 1 minute (mm): year=1995

µ= 0.0032 mmσ2= 0.0019 mm2

rainy periods= 1.07 %lost data= 3.56 %

µrr>0= 0.286 mm

σrr>0= 0.095 mm2

max on 1 minute= 9.4 mm

month

Rai

nfal

l dep

th (

mm

) –

Agg

rega

tion=

1 m

inut

e

–––

–––

µ= 0.0018 mmσ2= 0.0010 mm2

rainy periods= 0.68 %

µrr>0= 0.269 mm

σrr>0= 0.077 mm2

max on 1 minute= 7.6 mm

–––

–––

a

b

2

2

Fig. 4. Sample of original (a) and IRP simulated (b) high resolution (1 min) rainfall intensity data set. Original

data have been extracted from the DIAM high resolution series for year 1995. The synthetic record has been

obtained by the downscaling of the hourly series recorded in Chiavari. Each record is 1 year long; l represents the

sample mean, while r is the standard deviation.

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 211

0 3 6 9 12 15 18 21 2430

40

50

60

70

80

90

100

duration (hours)

rain

fall

dept

h (m

m)

T=2 years

0 3 6 9 12 15 18 21 2460

70

80

90

100

110

120

130

140

150

160

170

duration (hours)

rain

fall

dept

h (m

m)

T=10 years

0 3 6 9 12 15 18 21 2460

80

100

120

140

160

180

200

duration (hours)

rain

fall

dept

h (m

m)

T=20 years

0 3 6 9 12 15 18 21 2480

100

120

140

160

180

200

220

240

duration (hours)

rain

fall

dept

h (m

m)

T=50 years

0 3 6 9 12 15 18 21 2480

100

120

140

160

180

200

220

240

260

duration (hours)

rain

fall

dept

h (m

m)

T=100 years

0 3 6 9 12 15 18 21 24100

120

140

160

180

200

220

240

260

280

duration (hours)

rain

fall

dept

h (m

m)

T=200 years

a b

c d

e f

Fig. 5. Original (bold with triangular markers) and ensemble of corrected DDF curves (light grey belt) after

disaggregation via the IRP procedure for the Chiavari station at various return periods from T=2 to T =200 years.

The bold grey line indicates the average corrected curve while the two thin dashed lines are the limits containing

90% of the simulations. In this case, in fact, confidence limits can not be derived under the hypothesis of

Gaussianity due to the strong asymmetry of the light grey belt around the average curve.

A. Molini et al. / Atmospheric Research 77 (2005) 203–217212

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 213

negative random variable g with mean value 1. The process is then iteratively reproduced

at all the successive disaggregation steps.

Moreover, according to Veneziano and Iacobellis (2002), the distribution of g was

assumed lognormal, so that only two parameters have to be estimated: the contraction

factor r (here assumed equal to 4) and the co-dimension C1=0.5 logr(Etg2b) (here assumed

equal to 0.1, i.e. the same value estimated by Veneziano and Iacobellis, 2002 on the long

duration time series of Florence).

The value of the contraction factor r has been obtained from the calibration of the

model on the DIAm high resolution series. In Fig. 4 a qualitative comparison between the

year 1995 sub-series from DIAM and 1 year of IRP simulated high resolution (1 min)

rainfall depths, is reported.

The ensemble of DDF curves (for 1000 simulations) obtained after suitable correction

and re-aggregation of the IRP disaggregated data is reported in Fig. 5 for different return

periods T.

The original data are represented by the bold line with triangular markers, while the

light grey belt is the ensemble of corrected DDF curves after disaggregation using the IRP

procedure. The bold grey line indicates the average corrected curve while the two thin

dashed lines are the limits containing 90% of the simulations.

4. Discussion of the results

The accuracy of the proposed correction procedure of historical rainfall time series is

obviously dependent on the reliability of the adopted disaggregation technique. It is

therefore evident that in case the downscaling procedure should produce unrealistic

rainfall intensities at finer scales, the validity of the corrected figures actually breaks

down. In a previous work (Molini et al., 2005), we proposed correction of historical

rainfall data, based on the canonical random cascade algorithm for rainfall downscaling.

That model generally overestimates high rainfall intensities at fine resolution, due to its

tendency to concentrate extreme intensities on very short time durations. This fact

directly derives from the parameter estimation procedure, where the weights deriving

from the down-scaling of low to medium events–i.e. the most frequent occurrences–

assume a more relevant role than the generators coming from the disaggregation of

extreme events (marginally probable) presenting a more complex correlation structure.

This model is therefore more suitable for arid zones, where convective events

constitutes the 90% of total events, rather than for the considered mid-latitude regions,

characterized by both convective and frontal events, with very different characteristics

(Guntner et al., 2001). We then concluded that comparison of different algorithms

would be desirable although it is quite reasonable that the resulting correction on the

statistical parameters will be basically determined by the imposed variance of the inner

scale process.

This observation is confirmed by the results obtained here from the IRP based

disaggregation model where, even if the substantial underestimation of return periods and

extreme statistics is still evident, the influence of measurement errors seems to be less

pronounced.

1

1.02

1.04

1.06

1.08

1.1

01E+00 10E+00 01E+02

duration (hours)

h cor

rect

ed/h

orig

inal

T=2

T=10

T=20

T=50

T=100

T=200

Return PeriodT (years)

Fig. 6. Synthetic representation of the bgainQ obtained after correction of the high resolution realisations obtained

from downscaling hourly records from the Chiavari station using IRP.

A. Molini et al. / Atmospheric Research 77 (2005) 203–217214

At the same time, the ensemble average curve for the IRP simulated data appears

shifted towards the zone of the curves that is more affected by correction, producing a sort

of low correction tail below the curve of the original data. This fact, combined with a

10-2 10-1 100 101 1021

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

duration (hours)

h cor

rect

ed/h

orig

inal

Return Period

T (years)

T=2

T=10

T=20

T=50

Fig. 7. Representation of the bgainQ obtained after direct correction of the high resolution data by the DIAM time

series.

A. Molini et al. / Atmospheric Research 77 (2005) 203–217 215

wider dispersion of IRP based series, is probably due to the skill of IRP processes in better

representing strongly correlated events (that are also the ones with higher volumes) and, at

the same time, in preserving the variance of the process at fine scales (low tail).

The assessment of the relative error on maximum depths as a function of duration in time,

is represented for the IRP synthetic data in Fig. 6. Here the deviation of corrected data from

the original ones is represented in the form of a bgainQ varying with duration and seems to

suggest the presence of a strong underestimation of total maximum volumes for the lowest

traditionally considered durations (the most relevant in urban hydrology applications).

In Fig. 7, the bgainQ is reported as a function of duration, for the 1 min DIAM series

after direct correction using the parameters in Table 1 has been performed. The corrected

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1 10 100 1000T (years)

Tor

igin

al/T

corr

ecte

dT

orig

inal

/Tco

rrec

ted

IRP SimulatedDIAM high resolution series

duration=1 hour

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1 10 100 1000 T (years)

IRP SimulatedDiam high resolution series

duration=24 hour

a

b

Fig. 8. The influence of systematic mechanical errors on the assessment of the return period for the 1 h (a) and 24

h (b) duration: comparison of the results obtained for IRP based and the directly corrected DIAM dataset. The

error bars represent the mean standard error for simulated data.

A. Molini et al. / Atmospheric Research 77 (2005) 203–217216

DIAM series constitute an important reference for the performance of the correction

procedure.

Again, the underestimation of maximum depths in IRP synthetic data for T=50 years

and 1 h duration is about 8–9%, denoting a good agreement with directly corrected data

(8%).

Finally, in Fig. 8(a) and (b) the influence of systematic mechanical errors on the

assessment of the return period for the 1 h and 24 h durations is represented for the IRP

and directly corrected data. The error bars represent the mean standard error for simulated

data.

In particular, for directly corrected data, the induced bias can be quantified as an error

of 80% on the assessment of the return period of design rainfall for duration 1 h, when the

return period is in the order of 200 years, against the 60% of IRP simulated records.

Obviously, in analysing these results the fact that the two series (Chiavari Observatory

and DIAM) were recorded at different locations must be properly taken into account.

Acknowledgements

The authors express their sincere thanks to Roberto Picasso, Director of the

Meteorological Observatory bAndrea BianchiQ of Chiavari, for his kindness in providing

the rain data collected over the period 1961–2000 and to the whole group of volunteers at

the observatory, particularly to Alberto Ansaloni, for the precious contribution provided in

the reconstruction of the history of the observations and of the various rain gauge

instruments employed.

We also wish to thank Vito Iacobellis for his precious suggestions about the IRP

algorithm and its application to rainfall disaggregation.

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