Precipitation patterns under climate change: Constructing statistical precipitation models using historical European persistence trends.

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MSc Thesis

Stijn Vredevoort – 10640592

Precipitation patterns under climate change:

Constructing statistical precipitation models using

historical European persistence trends.

Master Earth Sciences University of Amsterdam

Institute for Biodiversity and Ecosystem Dynamics 2017-2018

30ECTS

Supervisor: J.H. van Boxel Co-assessor: E.E. van Loon

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Abstract

Climate change is causing an increase in extreme weather events, but general circulation models fail to project precipitation patterns on a regional scale. Therefore, this research aims to assess 20th_{century changes in European precipitation patterns using persistence}

parameters. Also, first order Markov models are constructed to extrapolate persistence trends and generate future precipitation statistics.

Linear trends in persistence were derived from precipitation datasets provided by the European Climate Assessment & Database project. Furthermore, trends in occurrence of intense rainfall periods and prolonged dry and wet spells were calculated to identify precipitation extremes. Transition probabilities between dry, light, medium and heavy rainfall days were assessed for calibrating Markov transition matrices.

Historical persistence trends were found across Europe with large spatial heterogeneity. The trends corresponded with trends in occurrence of dry spells and occurrence of dry days. Regions in Northern Europe tend to get wetter, whilst climatic conditions in Southern Europe are getting dryer. Short periods with intense rainfall have increased in Northern Europe, indicating intensification of precipitation.

The first order Markov models generally generated realistic precipitation statistics but failed to simulate long dry and long wet spells. The model output displayed high agreement with historical observations and was subsequently extrapolated to project future precipitation statistics. Some historical datasets lacked reliable precipitation measurements, leading unrealistic future precipitation projections. Model improvements are required to simulate precipitation more accurately. Eventually, the Markov models can prove to be a simple tool, with low computational intensity, for generating precipitation statistics. If historical datasets are extensive and homogeneous, these statistics can be very useful for climate change impact assessments on a regional scale.

List of Abbreviations

ENSO El Niño–Southern Oscillation

ECAD European Climate Assessment & Database project

GCM General Circulation Model

HMM Hidden Markov Model

IPCC Intergovernmental Panel on Climate Change

RCM Regional Climate Model

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Figures and Tables

Table 1.1 Observed climatic changes since 1950 in Europe and the Mediterranean. Derived from Hartmann et al. (2013)....6

Figure 2.1 Latitudinal temperature (C) anomalies in the Northern Hemisphere (Bekryaev et al., 2010)...7

Figure 2.2 Global trends in wind speeds (u) based on 148 studies, revieved by McVicar et al. (2012)...8

Figure 2.3 Ridge elongation caused by polar amplification, dashed vs. solid line (Francis & Vavrus, 2012)...9

Figure 3.1 Overview of selected weather stations in Europe for precipitation analyses...13

Table 3.1 Example of data smoothening for a single missing value at De Bilt in 1906...14

Table 3.2 Transition values for four-state transition chain...16

Table 3.4 Transition Matrix for weather station Barcelona in 2014...16

Figure 4.1 Comparison of total annual precipitation (A) and division of dry and wet days (B), 1900 vs 2000...18

Figure 4.3 Trends in persistence (%/100yrs) of dry days for different precipitation thresholds in Europe...20

Figure 4.4 Trends in persistence (%/100yrs) of wet days for different precipitation thresholds in Europe...20

Figure 4.5 Trends in occurrence of 15-day dry and 10-day wet spells in Europe...21

Figure 4.6 Trends (%/100yrs) in occurrence of 25, 50 and 100 mm 5-day rainfall events within in Europe...22

Table 4.1 Percentile values and number of significant trends for transitions between states...22

Figure 4.7 Four-state Markov chains for Milan in 1901 and 1902...22

Figure 4.8 Comparison of validation and Markov simulations for Alicante and Kristiansand...23

Figure 4.9 Result of 36 year Markov (67:33) simulation for Milan...24

Figure 4.11 Mean state distribution in the 20th century compared to projected mean distribution 2041-2050...25

Figure 4.12 Percentage changes in state division from 20th_{century to 2041-2050...26}

Figure 4.13 Trends (%/100yrs) in occurrence of 25, 50 and 100 mm 5-day rainfall events within in Europe...27

Figure 5.1 Maps illustrating overview of changing precipitation conditions in Europe...29

Table 5.1 Occurrence and intensity of 90th , 95th and 99.9th single day precipitation events at wettest stations...29

Figure 5.2 Rainfall conditions for landslides in Europe (Guzzetti et al., 2007)...30

Table 5.2 Comparison of significant trends for state transitions in seasonal and annual data for Eelde...31

Figure 5.3 Future simulations for Kristiansand with reduced calibration set 1950-2009...32

Figure 5.4 Homogeneity of precipitation data according to Wijngaard et al. (2003)...32

Figure 8.1 Maps indicating 20th_{century trends for dry persistence in Europe for different thresholds...39}

Table 8.1 Persistence trends (%/100yrs) for different thresholds at the European weather stations in the 20th century...40

Figure 8.3 Occurrence of 5,10 and 15-day dry and wet periods with 20th_{century trends on top of bars...41}

Figure 8.4 Comparison of recurrence intervals for 10-day precipitation events at selected weather stations...42

Table 8.2 Trends (%/100yrs) in the transition matrices. Significant trends are shaded...43

Table 8.3 Means occurrence of dryness and rainfall events for European weather stations...44

Table 8.4 Average results of t-tests after 100 simulations for European weather stations [50:50 model]...45

Table 8.5 Average results of t-tests after 100 simulations for European weather stations [67:33 model]...46

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1. Introduction

Whilst the vast majority of scientists are acknowledging the fact that our climate is changing, it is very important to look at the consequences of climate change as well as mitigation measures. Global surface temperatures have risen, and the frequency of extreme precipitation events and heat waves has increased since 1950 (IPCC, 2013).

Climate change is also influencing European weather conditions. Table 1, derived from Hartmann et al. (2013), presents the observed changes of climate indices in Europe and the Mediterranean. A likely increase or decrease indicates a probability of 66-100%, while confidence is a qualitatively expressed based on the type, amount, quality and consistency of evidence (Stocker et al., 2013). The table implies that both climate variability and the occurrence of extreme weather events have increased in Europe. Such climatic trends are widely researched globally, providing evidence for anthropogenic climate change.

Extreme precipitation in table 1 is based on daily values, persistence of precipitation however has not been discussed in the 2013 IPCC report. In the report only the occurrence of heat waves, droughts and single precipitation events are addressed. In order to gain a more complete insight in changing precipitation patterns scientists have acknowledged the need for research on a more regional scale. General Circulation Models [GCMs] fail to accurately represent precipitation patterns and therefore downscaling is required (Maraun et al., 2010). Maraun et al. (2010) provide an overview of proposed methods for statistical downscaling in order to improve modelling of rainfall intensity, variability and consistency. Keller et al. (2015) used Markov chains to project precipitation statistics using a two-state method and were fairly successful in generating precipitation statistics. However, they highlighted the need for a multiple state Markov chain in order to project precipitation more accurately. Generating these chains, requires researching multi-day weather patterns. Therefore, precipitation persistence trends in Europe are analyzed in this research in order to generate probability matrices for Markov models.

1.1 Precipitation persistence

Meteorological persistence can be described as prolonged periods of the same weather type using parameters such as wind, precipitation and temperature. Persistence is often measured in order to predict or analyze the occurrence of prolonged periods of drought (Alam et al., 2013; Wilby et al., 2016; Yu et al., 2017). Although not specifically mentioned in the IPCC (2013) report, precipitation persistence has been assessed in multiple studies. Nissen & Uldrich (2017) for example conclude that under the more pessimistic Representative Concentration Pathways [RCPs] multi-day heavy rainfall events are likely to increase in most European regions. It is possible that persistence has increased due to changes in large scale atmospheric circulation patterns caused by polar amplification. This process is described more elaborately in the next chapter.

More persistent weather could potentially have large societal impacts. Especially food production highly depends on water availability, whilst an increase of floods and droughts could cause large socio-economic losses. Identifying persistence trends can thus provide a valuable source of information not only for farmers, but also for insurance companies, engineers and energy producers (Maraun et al., 2010).

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Table 1.1 Observed climatic changes since 1950 in Europe and the Mediterranean. Derived from Hartmann et al. (2013).

Climate Index Observed Changes

Warm days High confidence: Likely overall increase Cold days High confidence: Likely overall decrease Warm nights High confidence: Likely overall increase Cold nights / Frosts High confidence: Likely overall decrease

Heat waves / Warm spells High confidence: Likely increases in most regions

Extreme precipitation High confidence: Likely increases in more regions than decreases but_{regional and seasonal variation} Dryness / Droughts Medium confidence: Spatially varying trends_{High confidence: Likely increase in Mediterranean}

1.2 Research Aim

Identifying persistence trends could signify a changing climate and provide useful input for precipitation models on a smaller geographical scale. The aim of this research therefore is to determine precipitation persistence in Europe over the past century and the trends therein and to construct statistical precipitation models that can be used to simulate these persistence trends and project future precipitation patterns.

The statistical models can help to accurately project short-term future climatic conditions, which could prove to be valuable for different stakeholders. If trends in persistence are found, models describing the statistical properties of the climate for the near future can be build. Several research questions were constructed to reach the aim of the research. The main question is:

 How has precipitation persistence changed in Europe since 1900 and can trends be used to design small-scale stochastic precipitation models?

In order to provide a comprehensive answer to this question several research sub-questions have to be addressed. The sub-questions are:

 How have precipitation persistence rates changed in Europe since 1900?

 To what extent has the frequency of extreme persistent periods changed in Europe since 1900?

 How are persistence trends spatially distributed in Europe?

 How are persistence rates expected to change in the near future with continuation of anthropogenic induced climate change?

The majority of the research consists of analyzing precipitation data in order to identify persistence trends. In the next chapter the theoretical framework of the research is provided in which the broader context of the research is described. The chapter elaborates on the necessity of identifying persistence trends as well as the use of Markov models to simulate precipitation models. Thereafter the methodology for this research is described, followed by the results, discussion and conclusions.

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2. Theoretical framework

In this chapter, the theoretical background required for this research is described extensively. First of all, the processes that might lead to increased persistence are described, followed by the consequences of increased persistence, a brief introduction of Markov modelling and hypotheses. These hypotheses are derived from the theory and focused on the research questions stated in the previous chapter.

2.1 Polar amplification

An increase in persistence parameters is expected as a consequence of climate change. Global mean surface temperature is rising but temperature increase rates are spatially heterogenic (Hartmann et al., 2013). Polar amplification is causing the poles to warm quicker than tropical regions (figure 1., Bekryaev et al., 2010). Regions at higher Northern Hemisphere latitude are warming twice as fast compared to lower latitudes (Cohen et al., 2014). This amplification is caused by different drivers such as the positive snow and ice albedo feedback, sea ice thickness, cloud coverage and ocean heat transport (Holland & Bitz, 2003). According to Cohen et al. (2014) September sea-ice extent has declined by 50%, leading to a 40% loss of thickness and even bigger losses in volume.

Cohen et al. (2014) describe three pathways linking Arctic amplification to changes in Northern Hemisphere mid-latitude weather patterns. First of all, Arctic amplification may alter the North Atlantic Oscillation [NAO] and storm tracks. Due to variability in sea-ice extent and snow cover the amplitude and phase of the NAO can be altered, leading to either more severe or milder winters in Eurasia. The NAO however has a much larger natural variability and therefore it is highly uncertain if Arctic amplification influences the NAO and subsequently weather patterns on temperate latitudes (Cohen et al., 2014).

Secondly Arctic amplification could have an impact on the Jet stream due to a decreasing meridional temperature gradient. The stronger warming in polar zones causes a reduction of the difference in air pressure between the polar high and the equatorial low-pressure zones, resulting in alterations of the prevailing winds (Vavrus et al., 2017). However, due to a lack of historical data and high uncertainties in re-analysis data, no significant changes in surface wind speeds were reported by the IPCC (Hartmann et al., 2013).

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Several studies did find trends in wind speeds over the past decades. A review by McVicar et al. (2012) concluded that in both tropical and mid-latitudes average wind speed is declining by 0.014 m s−1_a−1_{, leading to a reduction of 0.7 m s}−1_{over 50 years, if a linear trend is}

assumed. The review was based on 148 studies with varying spatial and temporal distributions and the results are visualized in figure 2 (McVicar et al., 2012). It is important to identify such trends for example for finding locations suitable for wind energy production (Pryor & Barthelmie, 2010).

Figure 2.2 Global trends in wind speeds (u) based on 148 studies, revieved by McVicar et al. (2012) The decreasing wind speeds found by McVicar et al. (2012) might implicate weakening of the westerlies on mid-latitudes and therefore alterations of pressure systems. This idea is shared by Francis & Vavrus (2012), who concluded that Rossby wave movement is slowed down by a combination of two consequences of Arctic amplification.

First of all, the weakening of zonal winds described above is causing Rossby waves to move eastwards more slowly. Secondly amplified arctic warming causes the 500 hPa heights in high-latitudes to rise compared to mid-latitudes. This process, known as ridge elongation, leads to larger Rossby wave amplitudes and therefore slower eastward movement of the wave. The process of ridge elongation is schematically presented in figure 3 (Francis & Vavrus, 2012), where the dashed line represents the wave amplitude related to polar amplification and the arrows represent eastward velocity of the wave. This theory, although disputed by Barnes (2013), is often used to explain the increasing frequency of extreme weather events (Francis & Vavrus, 2012; Petoukhov et al., 2013; Screen & Simmonds, 2014). Mann et al. (2017) suggest that anthropogenic warming causes Rossby wave resonance and consequently more frequent weather extremes in summer.

These extreme events are often a consequence of prolonged periods of constant weather, for example droughts, heat waves and floods. The extreme events are related to blocking highs: stationary atmospheric fields that retain the same location for multiple days or even weeks causing a prolonged period of constant weather. Although an increase in blocking frequency is not proven (Barnes et al., 2014) it is important to investigate whether weather persistence is increasing.

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Figure 2.3 Ridge elongation caused by polar amplification, dashed vs. solid line (Francis & Vavrus, 2012) The third pathway linking Arctic Amplification to changing weather on temperate latitudes described by Cohen et al. (2014) is also based on changes in Planetary wave movement. This pathway links a reduction of sea-ice extent and Eurasian snow cover to an increasing amplitude of Planetary waves. Due to melting of sea-ice and snow the Polar vortex weakens and Planetary waves are altered. This theory however has a lot of shortcomings and lacks statistical significance as well as robust evidence (Cohen et al., 2014).

Vavrus et al. (2017) concluded that increasing wave amplitudes lead to weakening of zonal winds in North America and consequently they expect changing weather patterns leading to extreme drying and heating in central North America. Their climate models also projected changes in precipitation patterns. For Europe, such a research has not been conducted and therefore it will be interesting to investigate precipitation patterns.

2.2 Consequences and relevance

Based on the theory described above it seems likely that Polar amplification is impacting climate on more temperate latitudes including Europe. The focus in this research is precipitation persistence. But why is it necessary to address persistence?

First of all, a trend in weather persistence changes could be a good indicator for identifying the frequency of extreme weather events. Due to atmospheric warming, the hydrological cycle is intensifying leading to more extreme precipitation events (Allan & Soden, 2008). On the other hand, the frequency of droughts is likely to increase in Europe (Hartmann et al., 2013). Higher persistence parameters for both precipitation and dryness are good indicators for finding extreme precipitation and drought events. Such events can have large socio-economic impacts on European society.

Information on precipitation persistence can for example be very valuable for farmers to prevent crop failure caused by prolonged periods of the same weather such as dryness or

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extreme precipitation (Roque-Malo & Kumar, 2017). Besides, extreme events leading to crop failure increased persistence may also require revision of irrigation schemes and crop selection. Changing precipitation persistence could impact the growing season and soil conditions and thus it is very important for farmers to learn about changing climatic conditions on a more regional scale. Furthermore, insurance companies might be interested in persistence trends. Not only because of potential losses in food production, but also in order to identify areas prone to extreme precipitation and dryness events, which could cause substantial economic damage.

Municipalities and water boards may also require information on precipitation persistence trends when designing urban drainage systems, identifying floodplains or anticipating high water levels. Horton et al. (2014) also underline that stagnating weather can cause severe air pollution in large cities. Low wind speeds and precipitation allow accumulation of pollutants in densely populated areas, which may cause health issues (Horton et al., 2014). Prolonged periods of intense rainfall can also contribute to landslides due to soil saturation (Guzzetti et al., 2007). Other parties that are potentially interested in persistence data are wind and solar energy producers, who might be able to improve their efficiency if meteorological patterns are better understood.

Europe is located on the temperate latitudes and climate is largely influenced by the westerlies and Atlantic Ocean current coming from the west. Changes in the Rossby wave activity are likely to have an effect on the European climate, especially in Western Europe. Therefore, persistence trends in Europe may have severe socio-economic consequences. When looking at historical weather data it is also important to keep in mind that certain climatic cycles may play a role in persistence fluctuations. Variations in persistence patterns could for example correlate with El Niño Southern Oscillation [ENSO]. Precipitation patterns in more southern located countries such as Spain may be influenced by El Niño and therefore persistence rates in these years may be different (Rodo et al., 1997).

2.3 Statistical downscaling

Due to the scales used in GCMs it is not possible to simulate precipitation patterns accurately. Scientists therefore emphasized the need for statistical downscaling of precipitation models (Maraun et al., 2010). In order to improve precipitation modelling statistical downscaling is required. Therefore, Regional Climate Models [RCMs] are designed to meet the end user requirements of precipitation models. Maraun et al. (2010) differentiate two types of end user requirements for RCMs: Short-term and long-term precipitation projections. Short-term projections need to be assessed in order to analyze crop yields, whilst long-term projections are needed for infrastructural planning and water resource assessments.

RCMs are still relatively complicated models that require many input variables for modelling grid sizes down to 50 km. A more efficient manner to project precipitation is using weather generators. Statistical models allow for generating precipitation datasets with unlimited length based on historical precipitation observations. These datasets can be used for impact assessments on a regional scale (Maraun et al., 2010). Weather generators can either be conditional or unconditional. Unconditional weather generators only use local observations from a single weather station, whilst conditional weather generators use larger scale conditions similar to GCMs and RCMs (Maraun et al., 2010). Quality and quantity of observations determine the performance of statistical models.

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Markov models can be used to generate precipitation statistics. In a Markov model, probabilities determine the transition between the current state and following state. In this way, a temporal sequence can be constructed where states are solely determined by the previous state and none of the other prior states (Ghahramani, 2001). For precipitation, a two-state model can be created using the probabilities for having dry and wet days or a multi-state model with different precipitation intervals. For example, having a day with no precipitation in the current state gives a 70% probability for having another dry day in the next state and a 30% probability for a rainy day. These probabilities can be ordered in a stochastic transition matrix. Using this matrix, a dynamic Bayesian network can be generated which assigns a value for each state in time (Ghahramani, 2001). Markov models are not only used in natural sciences, but also in marketing, economics and programming (Ching & Ng, 2006). Examples of applications are random walk modelling, consumer behavior modelling and webpage ranking algorithms used by Google.

The statistical models are suitable for impact assessments on a small scale. From these models, metrics such as rainfall intensity, distribution and variance as well as dry and wet spells can be derived. Projecting future precipitation statistics can be very helpful for both long- and short-term impact assessment and therefore the focus of this research is mainly on statistical modelling.

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3. Materials and Methods

In this chapter, an overview is provided of the different methods used during this research. The methods are divided over several subchapters that are presented in chronological sequence in order to maintain a clear research overview. First of all, the process of data acquisition is described, followed by the data processing, threshold determination, data analysis and a results section. All calculations during the research were performed in Matlab R2017a and no additional materials were required.

3.1 Data acquisition

Historical weather data was acquired from the European Climate Assessment & Dataset Project [ECAD] (Klein Tank et al., 2002). The datasets contain weather observations from weather stations across Europe. Daily precipitation observations are collected from ECAD. Blended data is used to ensure optimization of the datasets. The countries included in this research were chosen based on data availability. Most of the stations are located in Western Europe, with a maximum longitude of 17E.

The actual weather stations were selected based on two criteria. First of all, elevation of the weather station should be lower than 500 meters to overcome topographical influences. Besides, datasets had to be longer than eighty years, because longer datasets are more suitable for trend analysis. To make a selection a text file was obtained which contained the elevation and dataset length for precipitation of all weather stations in the ECAD database. In Matlab, these files were analyzed and weather stations with datasets longer than eighty years and elevation below 500 meters were selected. The text file proved to be unreliable and therefore some datasets were downloaded and selected through a trial and error process. The 34 weather stations that were eventually chosen are visualized in figure 3.1. The coordinates of the stations are listed in appendix II.

3.2 Data processing

The obtained data files were imported into Matlab. For each station at least four files are available: Elements, sources, metadata and the actual observations. The elements file contains information on the measuring methods available for precipitation observations, while the sources file provides information on the location of the weather station. In the metadata file a description is given of the local surroundings and available measuring devices at the station. The desired data is embedded in the file named after the station ID. This file contains the source ID, station ID, date, observations and a quality code. This quality code is very important because it provides an indication of the reliability of the observations. If the quality code equals 0 the data can be considered as valid. Data with a quality code of 1 corresponds with suspect data and a quality code of 9 indicates missing data. Sometimes this quality code proved to be very misleading. For example, the dataset for Kristiansand contained a ten-year period with quality code 1 and precipitation values of 0. A ten-year drought in a relatively wet climate in Norway is extremely unlikely and therefore these values were removed for analysis. Once the data is imported into Matlab some data cleaning steps were performed.

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First of all, missing values were identified. In the datasets, missing observations have a value of -9999. Missing values can occur for example due to technical problems or more serious matters such as the second world war. For the weather station de Bilt for example, precipitation data for the entire month December in 1905 is missing. This means that persistence rates cannot be calculated for the entire year. Approximately 8% of data points are missing and this will influence not only persistence rates for this period but also the days before and after the missing values. Therefore, it is decided that if a prolonged period of observations is missing, persistence rates for the entire year are not recorded for the trend analysis. A similar method was used by Zhai et al. (2005).

By using the blended data option single missing values are mostly filled in using regression based on data from weather stations located within 12.5 km and with a maximum altitude difference of 25 m (Klein Tank et al., 2002). Similar regression methods are often used for imputation of missing values and have proven to be reliable (Tardivo & Berti, 2012; Schneider, 2001). If data points are still missing and no weather stations are located nearby, another method was used for imputation of single data values.

Single missing data points rarely occurred. For these data points kernel smoothening was used as described by Lee & Kang (2015). Lee & Kang explored different smoothening methods, and Tricube smoothening based on the four nearest neighbors demonstrated the best results. Equation 3.1 was used for this method, where M is the missing value, x1 to x4

precipitation values of the two days before and after the missing data point and K the kernel values. K(1) for the two furthest neighbors was set to 0.301 and the for the two nearest neighbors K(2) to 0.772. An example of such a calculation is given in table 3.1 for a 5-day period of precipitation at weather station de Bilt in 1906. The value for the 19th_{of May is}

calculated as 2.9 mm, whilst the actual value is 2.8 mm. If multiple values within this 5-day period are missing, the missing values are deleted and left out for calculations. After all cleaning steps, the remaining data was analyzed.

Table 3.1 Example of data smoothening for a single missing value at De Bilt in 1906.

Date 17-05-1906 18-05-1906 19-05-1906 20-05-1906 21-05-1906 Prec. [mm] 1 0.3 2.8 13.3 2.7

Weight (K) 0.301 0.772 0.772 0.301

New prec. [mm] 0.301 0.232 10.268 0.813

Estimation 2.9

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3.3 Persistence

First of all, trends in annual precipitation sums and the division of dry and wet days was calculated to get a rough indication of the climate at each weather station. Thereafter, persistence of dry and wet days was calculated for all stations separately at different thresholds to indicate how persistence at different rainfall intensities has changed over the 20th_{century. The thresholds used for identifying dry days are: Dry <0.1, <0.2, <0.5, <1.0,}

<2.0, <5.0 <10.0, <20.0 and <50.0 mm. However, persistent periods with daily precipitation over 20.0 mm barely occur in Europe and therefore calculations for these higher thresholds are left out of this report.

Based on the thresholds, data points were given the value 0 for a dry day and 1 for a wet day. Using this division, day to day conversions could be calculated using equation 3.2, where C is the conversion on day d and X the value

on a day, which is either 0 or 1. The outcome of the formula is either 0, 1, 2 or 3. A conversion of 0 means a dry to dry conversion, whilst a conversion of 3

indicates a wet to wet conversion. The annual number of each of these conversions was then used to calculate annual persistence of wet and dry days by dividing the conversion by the total number of dry or wet days. Persistence rates are displayed as percentages of total dry or wet days. For example, a dry day persistence of 80% means that 80% of all days following a dry day are also dry.

A linear regression analysis of annual persistence values was then conducted to indicate whether persistence rates have changed through time. A significance level of 5% was used to indicate whether a trend was significant. Linear regression is widely used in climate research, including by the IPCC, for trend identification (Barnes & Barnes, 2015). Livezey et al. (2007) stated that recent climate trends generally have at least a substantial linear component and therefore linear regression can be used for analysis and even extrapolation into the future. Trends are compared and mapped to see whether persistence is changing uniformly across Europe.

3.4 Dry and wet spells

According to the IPCC, occurrence of dry spells and extreme rainfall has also increased in Europe. Trends in the occurrence of dry and wet spells were calculated by counting annual occurrences of 10 and 15-day periods of dryness or rain. Zolina et al. (2010) calculated that wet spells of 10 days contribute to approximately 2% of all wet days in Europe and are thus very rare. It is interesting to see how occurrence of these periods has changed through time. Dry spells can be defined in many different ways. In this research, dry spells are defined as periods of 10 days without precipitation. Another definition for dry spells could be 10-day periods with less than 1 mm of rainfall (Huth et al. 2000). Calculations for dry and wet spells were made by calculating moving sums of binary chains over the specified amount of days. For example, if a rainy day has a value of 1 and the moving sum reaches the value of 10 within 10 days, a wet spell is registered. The moving sum is then set back to 1 and continues in order to register multiple wet periods in a prolonged wet period.

A wet spell does not give information about persistence, but not the intensity of the precipitation. If 0.2 mm of precipitation occurs ten days in a row, only 2 mm of rain falls in this long period. This will not cause any large fluctuations in for example river water levels.

C_d=2 ∙ X_d−1+X_d

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Therefore, annual occurrence of intense rainfall within short periods was calculated for all stations. Using moving precipitation sums 25, 50 and 100 mm rainfall events within 5 days were registered for each year and trends in occurrence were calculated. Recurrence rates are calculated based on these trends. The recurrence rates are plotted at different precipitation intensities and different moments in time to indicate whether intense rainfall events occur more often at the beginning or the end of the century.

3.5 Markov models

Markov models were constructed in order to generate weather statistics for the future. For constructing models, the historical observations were divided into four precipitation states: dry, 0.1 mm to percentile 33.33 [light precipitation], percentile 33.33 to percentile 66.67 [medium precipitation] and percentile 66.67 or higher [heavy precipitation]. For each station these states differed because the states are calculated from percentile values. The 33th_and

67th_{percentile values were derived from all precipitation values over the entire dataset for a}

weather station. Values of 0, which indicate dry days were not included in the percentile calculations. The 33th_{and 67}th_{percentile values were thus only based on wet days.}

Transitions were calculated slightly different compared to the calculations for dry and wet days. A base 4 number system was included to calculate transitions for the four different states: dry, light precipitation, medium precipitation

and heavy precipitation. In table 3.2 the value for each transition is provided. The occurrence of every value was counted for each and converted to a fraction for each state following equation 3.3. Frdl

is the fraction of conversions from dry to light precipitation, which is calculated as the sum of all conversions dry to light divided by the sum of all dry states.

Table 3.2 Transition values for four-state transition chain.

Next state → Dry 0 Light prec. 1 Medium pre. 2 Heavy prec. 3 Current State ↓ Dry 0 0 1 2 3 Light prec. 4 4 5 6 7 Medium prec. 8 8 9 10 11 Heavy prec. 12 12 13 14 15

Having calculated all fractions, a probability transition matrix can be generated for a Markov model. An example of such a matrix is provided in table 3.3. Linear trends were calculated for each transition probability in order to create a heterogeneous Markov model, with a changing matrix every year following the transition trends. The trends where thus applied to the matrix in order to generate a different transitions matrix for every modelled year.

Table 3.4 Transition Matrix for weather station Barcelona in 2014

Next state → Dry Light prec. Medium pre. Heavy prec.

Current State ↓ Dry 0.80 0.09 0.07 0.04 Light prec. 0.52 0.15 0.09 0.24 Medium prec. 0.61 0.07 0.11 0.21 Heavy prec. 0.56 0.09 0.06 0.29 Fr_{d →l}=ΣC_{d → l}÷ Σ S_d Equation 3.3

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The dataset for each station was then divided into two parts to create a calibration and validation set. Two models were constructed based on the calibration/validation ratio. Firstly, data was divided in odd and even years [50:50 model]. Secondly out of every three years the first two years were used for calibration and the third year for validation [67:33 model]. The calibration sets were used for creating the transition probability matrices. Markov chains where then generated for the same years as the validation set and compared. For every station 100 Markov simulations were performed and means for different precipitation periods were compared using a two-sample t-test. This test was conducted for occurrence of 30 different precipitation periods during each simulation. The occurrence of single dry, rainy, light precipitation, medium precipitation and heavy precipitation days was tested, as well as occurrence of 2, 3, 5, 10 and 15 periods of these rainfall types. The test decided whether means of the Markov and validation populations were equal. A result of 0 means that populations are equal, whilst a result of 1 indicates that means are significantly different. The sum of the t-test results after 100 simulations was used to indicate whether Markov simulations were accurate. If the sum of t-test results after 100 simulations was less than 5, the simulation for a certain precipitation period was considered accurate. If the sum was lower than 5 the model projected that the occurrence of a precipitation period was not significantly different in at least 95% of the simulations.

This analysis was performed for both the 50:50 model and the 67:33 model. The model that yielded the highest overall accuracy was then used for extrapolations into the future. From these extrapolations average occurrence of precipitation periods for the decades 2021 to 2050 were calculated. These averages will give an indication of precipitation patterns in the near future, assuming that linear trends continue in the coming years.

Additionally, hidden Markov model was used for extrapolations. This model not only provided precipitation state outputs, but also generated a sequence with precipitation values. The model is calibrated with the actual precipitation values that belong to a state and provides two output sequences. The first sequence contains the state, which is either dry, light precipitation, medium precipitation or heavy precipitation. The second sequence consisted of 11 different states. State 1 still corresponded to a dry day and state 2 to 11 gave the average precipitation values between each 10th_{percentile interval of all precipitation}

values. From these values total annual precipitation can be calculated and compared to annual precipitation trends. Furthermore, intense rainfall periods were analyzed from these generated precipitation values.

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4. Results

This chapter contains the results that were derived from the analyses described in the previous chapter. The chapter is divided based on the different research questions that were stated in paragraph 1.2. First of all, persistence results are presented, followed by extreme weather events. Furthermore, the results of the Markov simulations are stated as well as an indication of future persistence rates.

4.1 Persistence rates in Europe

In order to obtain an overview of weather conditions for the different weather stations, a graphic representation of the division of wet and dry days (B) and annual precipitation (A), is provided in figure 4.1 The figure compares the precipitation conditions in 1900 and 2000 based on linear regression analyses. When looking at the precipitation sum, no homogeneous pattern can be recognized with some significant positive and a few significant negative precipitation trends over the 20th_{century. All significant positive trends (p<5%) are}

found at latitudes higher than 50° and negative trends below this latitude, in Palermo and Salzburg.

Fig. 4.1B shows the division of dry and wet days over the 20th_{century. For 23 stations there}

was a significant trend in de division of days. For some stations the amount of dry days has increased, for others the amount of wet days. A clear division based on latitude cannot be made in this case. There is however a general linear relation between the amount of precipitation and the number of wet days, as can be seen in equation 4.1.

¿annual=%WD ∙11.37 +271.09 P=0.002∧R2=0.257

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Figure 4.1 Comparison of total annual precipitation (A) and division of dry and wet days (B), 1900 vs 2000. P-values for trends are given on top of the bars. The stations on the x-axis are listed from North to South. Persistence rates for different thresholds were calculated for all weather stations. The results of this analysis are partly listed in figures 4.3 and 4.4. Linear trends are presented together with the persistence percentage. For example, in Fig. 4.3A 72% of the dry days in Steigen in 1900 were followed by a dry day. This percentage however has decreased by 7% leading to 65% dry to dry conversions in 2000. The stations are again ranked from North to South. Dry day persistence decreases more often at more Northern located stations, whilst it tends to increase in the South. This pattern is clearly visible in figure 4.2, where blue dots indicate a decrease in dry persistence and red dots an increase. For each station seven dry and seven wet persistence trends were calculated using the different thresholds. Dry persistence maps for all thresholds are listed in appendix I.

In total, 33.6% of the trends were significant at a 5% significance level. For the stations A Coruna, Armagh, Bremen and Frankfurt less than two significant trends were found. For the stations Kristiansand and Steigen in Norway more than ten significant trends were found, indicating a clear change in

precipitation persistence. In general, more significant trends were found at higher latitudes. The largest trend was found in Tranebjerg, where wet day persistence (dry < 0.1mm) increased by 17.5% over the 20th_{century. This trend is}

remarkable, because no significant trend in annual precipitation was found for this weather station.

The trends can be roughly divided into two types of trends: Trends that tend to lead to a wetter climate and trends that lead to a dryer climate. The first group contains significant negative dry day persistence trends and positive wet day persistence trends. The other group includes significant positive dry day and negative

wet day persistence trends. An overview of all trends is provided appendix II, where the first group is shaded yellow and the second group is shaded green. A total of 103 trends can be designated to the first group, whilst 57 trends can be designated to the second group.

Fig ure 4.2 Map indicating 20th century dry persistence trends in

Europe: Dry < 0.5 mm.

Size of the dots indicates the magnitude of the trend. Filled dots represent a significant trend.

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Figure 4.3 Trends in persistence (%/100yrs) of dry days for different precipitation thresholds in Europe. Significant trends are darker and exceed the significance threshold. An asterisk indicates a trend that exceeds

the threshold but is not significant. Dry conversions at the specified threshold are listed on top of the graph.

Figure 4.4 Trends in persistence (%/100yrs) of wet days for different precipitation thresholds in Europe.

C A B B C A

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4.2 Dry and wet spells

Besides persistence rates, the occurrence of dry and wet spells was analyzed to indicate whether weather extremes in Europe are occurring more or less frequently. Furthermore, the occurrence and recurrence rates of 5, 10 and 15-day precipitation events were calculated for all weather stations.

Figure 4.5 Trends in occurrence of 15-day dry and 10-day wet spells in Europe. Larger dots indicate higher trends and filled dots represent significant trends.

In figure 4.5, the trends for occurrence of 10-day wet and 15-day dry spells are visualized. Generally positive trends for dry spells correspond to negative trends for wet spells and the other way around. This implies that either dry or wet persistence is changing and not both parameters. An overview of 5, 10 and 15-day spells for all stations is provided in appendix III. An increase of wet spells does not necessarily lead to an increase of intense rainfall events. Eelde, de Bilt, Frankfurt and Bamberg are among the stations where the occurrence of wet spells has significantly decreased. However, recurrence intervals for intense rainfall events have also decreased for some of those stations, which is visualized in appendix IV.

To indicate whether short periods with intense rainfall have changed over the 20th_century,

precipitation sums were calculated for periods of 5, 10 and 15 days. Figure 4.6 shows the trends for occurrence of 25, 50 and 100mm rainfall events. The specified amounts of rainfall were observed within a period of 5 days, meaning that dry days can also occur in such a day period. Especially in coastal regions, occurrence of these events has increased. Negative significant trends were only found in Salzburg and Palermo.

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Figure 4.6 Trends (%/100yrs) in occurrence of 25, 50 and 100 mm 5-day rainfall events within in Europe

4.3 Markov models

In order to construct Markov chains, transition matrices were required. These matrices were based on observations and contained the probabilities for state transitions. For every year all 16 probabilities were calculated for transitions between the four states: Dry, light precipitation, medium precipitation and heavy precipitation. Trends for each transition were calculated with a linear regression model. The percentile values and number of significant transition trends for each station are provided in table 4.1. Trends range from -0.21% to 0.21% per year and in total 39.1% of all trends are significant (appendix V).

Table 4.1 Percentile values and number of significant trends for transitions between states

Based on these trends, heterogeneous transitions matrices were created in order to generate Markov chains. An example of such a chain is given in figure 4.7, in which precipitation states for Milan in 1901 and 1902 were simulated.

Figure 4.7 Four-state Markov chains for Milan in 1901 and 1902. Chains move between the four states: dry, light, medium and heavy rain.

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From the generated Markov chains persistent periods were calculated. As an example, comparisons were made between observed data and generated data for the stations Alicante and Kristiansand. These are the stations with least (0) and most (13) significant trends for transitions between precipitation intervals. Figure 4.8 displays average occurrence of rainfall and dry periods for the validation and Markov sets, using the 50:50 calibration/validation ratio. For Alicante 40 years were simulated, whereas for Kristiansand 48 years were simulated. For both stations the Markov models seem to underestimate the occurrence of long dry periods, whilst other periods are projected more accurately.

Figure 4.8 Comparison of validation and Markov simulations for Alicante and Kristiansand.

To estimate the accuracy of both Markov models, means of precipitation events were compared 100 times for each station. The results of the t-tests are listed in appendix VI, where the means are listed as well. The 50:50 model was clearly outperformed by the 67:33 model. The 50:50 model yielded a t-test result of zero for 57% of the precipitation periods in over 80% of the simulations, whilst the 67:33 model produced equal means for 77% of the precipitation periods in at least 80 simulations. The Markov model generally projected equal means for precipitation periods, except for 10 and 15-day periods for both rainfall and dryness. Occurrence of such long periods are mostly underestimated by the Markov models. An example of the results is given in figure 4.9 for a 36-year simulation in Milan. The regression coefficients show that the means of each prolonged event are time dependant.

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Figure 4.9 Result of 36 year Markov (67:33) simulation for Milan.

Occurrence of prolonged rainfall events, regression coefficients for these events and results of the t-test are visualized in the different graphs. The red line in the bottom graph indicates the significance threshold of 5%.

4.4 Future projections

The best performing model [67:33] was used for extrapolation in order to project precipitation events in the coming decades. In figure 4.10 the results of a simulation for weather station de Bilt are presented. Dry periods are clearly increasing, whilst rainfall periods decrease. Heavy rainfall periods generally increase, as does annual precipitation.

Figure 4.10 Results of future simulations for de Bilt 2020-2050.

Top graph compares occurrence of rainfall events with the 20th_{century observations. Bottom graphs shows the} minimum, mean and maximum occurrence of events in the 2040-2050 decade.

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In the 20th_{century, annual precipitation at de Bilt increased by 0.99 mm per year and}

Markov simulations for 2001-2050 yielded an increase of 1.00 mm per year. Recurrence rates of 10-day rainfall events with over 75 mm of precipitation dropped to approximately 1 year in 2050, whist recurrence in 2000 was approximately 1.4 years. In appendix VII occurrence of rainfall events in 2040-2050 is compared to mean occurrence of these events in the observational sets for all weather stations. It must be noted that precipitation sums are based on the hidden Markov model, which only reproduces percentile values for precipitation.

Figure 4.11 Mean state distribution in the 20th_{century compared to projected mean distribution 2041-2050.} Thresholds are 0.1 mm, the 33th_{and 67}th_{percentile for precipitation in the 20}th_century.

In figure 4.11 the state distribution in the 20th_{century is compared to the projected}

distribution in 2041-2050 for all weather stations. The difference between the means for the different periods are listed in appendix VII. Maps indicating the percentage differences between the two periods are provided in figure 4.12. In general, the amount of dry days and days with medium rainfall are decreasing, whilst the amount of days with light and heavy rainfall will increase. Spatial differences are large and no homogeneous pattern for Europe can be derived from the map.

For the 2041-2050, a linear relation is found between the percentage of wet days and projected precipitation sums (equation 4.2). This relation is similar to the one found in the observational dataset, but this time the annual precipitation increases faster with the percentage of wet days.

¿annual=%WD ∙14.00+163.55 P=7.1× 10−5∧R2=0.394

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Figure 4.12 Percentage changes in state division from 20th_{century to 2041-2050.}

A percentage increase means that more days are designated to a certain class in 2041-2050 compared to the 20th_{century. Larger dots indicate larger percentage changes.}

Trends in occurrence of intense precipitation for five-day periods were calculated from the hidden Markov models over the period 2001 to 2050. The trends give an indication of simulated extreme events across Europe. A visualization similar to figure 4.6 is made to indicate if Markov chains project continuation of historical trends. The trends are displayed in figure 4.13. More significant trends are found in the 21st_{century compared to the 20}th

century, especially for 25 mm events.

Figure 4.13 Trends (%/100yrs) in occurrence of 25, 50 and 100 mm 5-day rainfall events within in Europe Trends are calculated from Markov models that generated data for 2001 to 2050.

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5. Discussion

In this chapter the results of the research are discussed, and recommendations are given for future research. The chapter follows the same structure as the methodology and results chapters. In the following chapter the research questions are assessed, and conclusions are drawn for this research.

5.1 Data processing

Data acquisition and processing methods were executed in order to obtain clean datasets for all stations. The minimum length for datasets after clean-up steps was 80 years. However, datasets for two stations still contained impurities. For the Kristiansand station 11 years of drought were found from 1940 to 1950. A quality code of 1 was assigned to the observations, whilst it should have been a 9. The missing interval was excluded for the research.

For the Stornoway weather station, no observations less than 1.0 mm were found up to the year 2002. It is not clear whether precipitation values between 0.1 and 1.0 mm were set to 0 or 1 (Klein Tank et al., 2002). Data analysis was conducted for the station, but results are heavily biased. The large increase of annual precipitation implicates that values below 1 mm were probably set to 0. Inhomogeneity of data can be caused by relocation, even if relocation distances are very small (Zhai et al., 2005). Relocation was not assessed in this research and therefore datasets could contain imperfections. Wijngaard et al. (2003) tested the quality of the ECAD precipitation datasets and concluded that 75% of all stations with dataset length over 79 years show no significant signal of inhomogeneity. These datasets are considered sufficient for trend analysis.

5.2 Precipitation persistence

Climatic conditions have clearly changed in Europe. Due to global warming the water holding capacity of the atmosphere has increased, leading to higher amounts of water vapor in the atmosphere and increased precipitation (Trenberth, 2011). Most significant annual precipitation trends found in this research are positive, which corresponds with findings in the IPCC report (Hartmann et al., 2013). Negative significant trends were only found in Salzburg and Palermo. These trends were also found in datasets from the Climate Research Unit, Global Historical Climatology Network and Global Precipitation Climatology Centre (Hartmann et al., 2013). Generally, the European climate has become wetter.

For the annual percentage of dry days significant trends were mostly negative, leading to a wetter climate. At some stations precipitation intensifications has occurred. Especially in the Netherlands this process is clearly visible. Annual precipitation sums have increased by 0.81 to 0.99 mm per year over the 20th_{century for the three Dutch stations, but the percentage}

of dry days has also increased by 0.05% to 0.09% per year for this period. A similar pattern was found in Copenhagen.

The trends in annual percentage of dry days correlate to the trends in persistence of dry days for all stations (Coefficient = 0.91, P = 5x10-14_{) and also to the trends in occurrence of}

10-day dry spells (Coefficient = 0.80, P = 8x10-9_{). This implicates that persistence is related to}

occurrence of droughts. The pattern of these trends is noticeable in figure 5.1. Correlation between trends in occurrence of 10-day wet spells and percentage of dry days is weaker

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(Coeff. = -0.65 and P = 3x10-5_{) and no correlation was found between trends in percentage of}

dry days and the occurrence of intense rainfall events (25, 50 or 100 mm within 5 days).

Figure 5.1 Maps illustrating overview of changing precipitation conditions in Europe. The size of the dots indicates the magnitude of trends. Dots for significant trends are filled.

Lambert et al. (2003) defined that a system tends to be persistent if the sum of dry to wet and wet to dry conversions is less than 100%. If the sum exceeds 100%, the system is more fluctuating. For all stations the weather system can be considered as persistent. Not a single station showed a significant positive trend for both dry and wet day persistence. Generally, when dry day persistence increased, wet day persistence decreased. The weather stations Armagh, Dublin, Cambridge, Uccle, Vlissingen, Prague and Palermo generated relatively large positive trends for both dry and wet day persistence (dry < 0.1mm), with at least one trend being significant. At these stations precipitation persistence has clearly increased.

At thresholds ≥ 0.5 mm a clear distinction for significant persistence trends can be made based on latitude. South of the 50° latitude mark only positive trends for dry day persistence and negative trends for wet day persistence are found. North of the 50° mark all significant dry day trends are negative and wet day trends are positive. This roughly corresponds to the trends in occurrence of intense rainfall events as shown in figure 4.6. To illustrate the severity of these events, percentile values for single-day precipitation events at some of the wettest stations are listed in table 5.1. Dry days were excluded for calculating the percentile values. The 99.9th_{percentile values thus occur approximately once every 5 years at these}

stations and range between 51.4 and 90.4 mm on a single day. An increase of rainfall events of 50 mm and 100 mm in a short period could lead to problems with river discharge, landslides and crop failure.

Guzzetti et al. (2007) determined thresholds for landslides in central and southern Europe by looking at historical events. Figure 5.2 shows the rainfall conditions that lead to landslides in this region. The researchers stated that 5 days of rainfall with an average of 0.2 mm per hour is likely to trigger landslides. Increased rainfall persistence, which was for example found in Salzburg could lead to increased occurrence of landslides in the Alps.

Table 5.1 Occurrence and intensity of 90th_{, 95}th_{and 99.9}th_{single day precipitation events at wettest stations.} Data was derived from the entire datasets for the different weather stations.

Steigen Kristiansand Salzburg San Sebastian

Prec. (mm) Occ. (/year) Prec. (mm) Occ. (/year) Prec. (mm) Occ. (/year) Prec. (mm) Occ. (/year) Perc. 90.0 14.0 21 16.1 22 17.3 19 21.6 19 Perc. 95.0 18.5 10.5 22.0 11 24.0 9.5 29.7 9.5

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Perc. 99.9 51.4 0.21 67.8 0.22 78.0 0.19 90.4 0.19

Figure 5.2 Rainfall conditions for landslides in Europe (Guzzetti et al., 2007)

Filled symbols resulted in landslides. Landslide types: square = debris flow, diamond = soil slip, dot = shallow landslide and triangle = unknown type of landslide. Larger symbols represent multiple events.

Extreme weather events can also affect agricultural productivity in several ways. Heat and drought stress may reduce photosynthesis and respiration (Porter & Semenov, 2005), whilst it enhances development of pests and diseases (Tubiello et al., 2007). More frequent occurrence of heavy precipitation on the other hand can cause crop damage through excessive soil moisture and difficulties with field operations (Van der Velde et al., 2012). Furthermore, changing precipitation and temperature patterns have to be assessed for adjusting irrigation requirements (Tubiello et al., 2007). Both wet and dry spell occurrence have changed in Europe at different rates and weather generators can be used to assess the impact of these changes on crop productivity. Furthermore, the generators can be used to project river discharge extremes, which are likely to occur more frequently in Europe in the future (Dankers & Feyen, 2008).

5.3 Markov models

Four-state Markov models were constructed to simulate historic and future precipitation patterns. The models were calibrated using trends in transitions between the different states. Using these trends, the transition probability matrix for the Markov chain changed for every simulated year. On average 6.2 out of the 16 trends between the states were significant. Insignificant trends were generally small. The insignificant trends were applied to the transition matrix in order to retain a complete matrix.

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Using a larger set of calibration data (67% of observations) clearly generated more accurate Markov chains in comparison to the smaller calibration set (50% of observations). Although precipitation data seem valid, the model failed to simulate precipitation states accurately for the Stensele weather station. The problem is likely caused by big differences in observed trends between the validation and calibration sets. For example, persistence for heavy precipitation increased with 9% in the calibration set, while it only increased by 1% in the validation set. A longer dataset is required for this station in order to create more accurate simulations.

The Markov models generally underestimated the occurrence of 10 and 15-day dry periods. Such prolonged dry periods occur regularly in Spain and Milan but are not often projected by the Markov models. This problem was also identified by Akyuz et al. (2012). In a first-order Markov model chances for a prolonged period of drought decrease exponentially and are therefore very rare. For example, the chance of having a dry period of 10 days, with dry day persistence of 70%, is equal to 0.710_{or approximately 3%. A higher order Markov model, in}

which the current state depends on multiple previous states, is more suitable for predicting long droughts (Akyuz et al., 2012). A higher order Markov model is more complex, especially when multiple precipitation states are incorporated.

Another way to improve the Markov chains is including seasonality. Persistence rates often differ largely throughout a year and sub-yearly transition matrices could potentially improve precipitation simulations. However, the number of transitions in such a model largely decreases and therefore the occurrence of significant trends will also decrease. Furthermore, it is difficult to determine seasonality. Table 5.2 illustrates how seasonality affects the significance of the transition matrix for weather station Eelde. Trends are less significant in shorter periods but could lead to more accurate precipitation simulations.

Table 5.2 Comparison of significant trends for state transitions in seasonal and annual data for Eelde. Significant trends are given as a percentage of total 16 transitions

5.4 Future projections

The 67:33 model was used for simulating future precipitation patterns for the European weather stations. Extrapolation of linear trends lead to some very extreme projections for the 2041-2050 decade (appendix VII). Besides the Stornoway and Stensele stations, which lack reliable calibration input, extreme changes were also projected for Kristiansand, Pesaro and Tranebjerg.

Kristiansand experienced an enormous increase in annual precipitation of 5.24 mm/yr, over the 20th_{century. The amount of dry days decreased by 16% over the 20}th_{century and wet}

day persistence increased by 12.5%. According to the simulations, the decrease in dry days will accelerate and cause an enormous increase in light and heavy rain days. Wijngaard et al. (2003) detected significant data breaks around 1950 and 1965, often caused by relocation and changes in measuring equipment for European weather stations. Such an intervention may have occurred in Kristiansand, where a large data gap is found between 1940 and 1950.

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Figure 5.3 Future simulations for Kristiansand with reduced calibration set 1950-2009.

Average occurrence of prolonged rainfall events are given for different periods in the future and observed data. When simulations for Kristiansand are calibrated with observations between 1950 and 2009, future projections become less extreme (figure 5.3). Annual precipitation still increased by 5.03 mm/yr in this period but the amount of dry days only decreased by 8% in this period, leading to more realistic projections. However, all trends in the transition matrix become insignificant, proving the difficulty of modelling with a very short calibration set.

The extreme results in Pesaro (Italy) and Tranebjerg (Denmark) can also be attributed to the large negative trend in dry days. For both stations the 33th_{percentile precipitation value after}

1950 decreased by at least 0.3 mm compared to the 33th_{percentile value for the entire}

dataset. This might indicate that low precipitation values were registered more often after an unknown data breakpoint. Hofstra et al. (2009) interpolated the assessment of precipitation data homogeneity by Wijngaard et al. (2003). The map in figure 5.4 illustrates the results of the homogeneity assessments. The stations Kristiansand, Stornoway, Pesaro and Stensele are located in red and blue areas. Tranebjerg is located in a green area, indicating that data is most likely homogeneous. The locations of the weather stations can be found in figure 3.1.

Generally, simulations project a decrease of days with medium precipitation intensity across Europe (figure 4.12). On higher latitudes the model projects more days with heavy precipitation leading to an increase of annual precipitation. The amount of dry days also decreases often in coastal regions corresponding with reduced historical dry day persistence. The Netherlands forms an exception, with increasing dry day persistence. Occurrence of heavy precipitation will also continue to rise in the Netherlands, leading to more prolonged periods of both dryness and heavy precipitation.

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The assessment focused on observational data for the period 1950-2006.

The model fails to simulate long periods of drought and rainfall, leading to an underestimation of dry and wet spells. Climate models project an increase of wet spells in Northern European regions, whilst droughts will likely occur more frequently in Southern Europe in the future (Heinrich & Gobiet, 2012). This indicates that recent trends are continuing towards the end of the 21st_{century (Zolina et al., 2010). The Markov models}

project no spatial variations for changing frequencies of dry spells. Wet spells do seem to increase more in Northern regions, which shows agreement with simulations by Heinrich & Gobiet (2012). Incorporation of climatic cycles such as NAO could improve modelling and projections of long wet and dry spells.

Precipitation values were assigned to the simulations, using the mean between every 10th

percentile of precipitation observations. The hidden Markov model generated 11 different output possibilities for each year in the simulation and precipitation sums were calculated for each year. The weather stations with suspected inhomogeneous data generated very unrealistic changes in annual precipitation means (last column in appendix VII). Comparing generated and actual precipitation sums could therefore provide a method for testing data homogeneity. For many stations 21st_{century annual precipitation trends seem to be}

overestimated. A way to improve the model is using statistical methods to determine the number of possible output states (Robertson et al., 2004). Due to time restrictions such a method was not applied in this research.

Five-day intense rainfall periods were calculated for Markov simulations for the period 2001-2050. Trends in the occurrence of these periods were found for most stations, especially for 25 mm precipitation intervals. Significant dry trends were again found for Palermo and Salzburg. The Markov model seems to make realistic simulations for these intense periods, but the precipitation states only include mean values for every 10th_{percentile. Improving}

this method would give more accurate simulations and generate more realistic precipitation statistics for impact assessments.

Precipitation patterns under climate change: Constructing statistical precipitation models using historical European persistence trends.

MSc Thesis

Stijn Vredevoort – 10640592