Climatic Change

, Volume 113, Issue 3, pp 803–823

A method for incorporating climate variability in climate change impact assessments: Sensitivity of river flows in the Eden catchment to precipitation scenarios

Authors

    • Centre for Ecology and Hydrology
    • Walker Institute for Climate Systems ResearchUniversity of Reading
  • Christel Prudhomme
    • Centre for Ecology and Hydrology
  • Nigel Arnell
    • Walker Institute for Climate Systems ResearchUniversity of Reading
Article

DOI: 10.1007/s10584-011-0386-0

Cite this article as:
Ledbetter, R., Prudhomme, C. & Arnell, N. Climatic Change (2012) 113: 803. doi:10.1007/s10584-011-0386-0

Abstract

Interest in the impacts of climate change is ever increasing. This is particularly true of the water sector where understanding potential changes in the occurrence of both floods and droughts is important for strategic planning. Climate variability has been shown to have a significant impact on UK climate and accounting for this in future climate change projections is essential to fully anticipate potential future impacts. In this paper a new resampling methodology is developed which includes the variability of both baseline and future precipitation. The resampling methodology is applied to 13 CMIP3 climate models for the 2080s, resulting in an ensemble of monthly precipitation change factors. The change factors are applied to the Eden catchment in eastern Scotland with analysis undertaken for the sensitivity of future river flows to the changes in precipitation. Climate variability is shown to influence the magnitude and direction of change of both precipitation and in turn river flow, which are not apparent without the use of the resampling methodology. The transformation of precipitation changes to river flow changes display a degree of non-linearity due to the catchment’s role in buffering the response. The resampling methodology developed in this paper provides a new technique for creating climate change scenarios which incorporate the important issue of climate variability.

1 Introduction

Interest in the impacts of climate change is ever increasing. This is particularly true of the water sector where understanding potential changes in the occurrence of both floods and droughts is important for strategic planning. There are many case study examples in the literature of the impacts of climate change on specific catchments and regions. However there is increasing interest in quantifying the uncertainty associated with climate change impact studies, allowing for the creation of probabilistic scenarios.

In each component of an impact study certain assumptions are made by the investigator which leads to the formation of a cascade of uncertainty for a given emissions scenario (Schneider 1983; Wilby et al. 2008). The first decision is which climate model to use which is often dependent on the availability of data. However, it has been demonstrated that climate models provide the largest source of uncertainty in impact studies (Prudhomme et al. 2003; Kay et al. 2009; Vidal and Wade 2008). Climate model uncertainty originates from three main sources; firstly climate models require the parameterisations of processes that are not represented in the model or are physically poorly understood, which can be explored using perturbed physics ensembles (Murphy et al. 2004; Stainforth et al. 2005). However perturbed physics ensembles are seldom undertaken due to computational expense and time. The second source relates to different climate models having different physical structures and methods for simulating atmospheric, oceanic and land surface processes and interactions, leading to a large variation in output between different models. This uncertainty between climate models can be addressed though using as many different climate models as possible in an impact study. The final source of uncertainty is linked to the natural climate variability inherent in each climate model. The climate variability can counteract and enhance any climate change signal over different time scales. The influence of each of the components of climate model uncertainty have been shown to vary between regions, variables and over time (Hawkins and Sutton 2009; Hawkins and Sutton 2010).

The next component in the cascade of uncertainty is due to the difference in scales of the impact study and that from global scale models. Hydrological catchments in the UK are typically at km scale, requiring at least daily data. Climate model projections are grid averaged outputs over several degrees of latitude and longitude often at a monthly time step. This discrepancy in the spatial and temporal scale is overcome through downscaling the global scale values to the local scale (see extensive downscaling reviews in Xu 1999; Fowler et al. 2007). Downscaling can be either dynamical, where a higher resolution climate model is nested with a global scale model (Frei et al. 2006), or statistical, where empirical methods are used to derive relationships between the global and local scale (Wood et al. 2004; Haylock et al. 2006). One of the simplest methods is the use of change factors (Hay et al. 2000; Diaz-Nieto and Wilby 2005) which are advantageous when using multiple climate models as it removes the biases within the different models. The latest climate change projections for the UK are in the form of change factors in UKCP09 (Murphy et al. 2009).

The final component of uncertainty in hydrological impact studies is in the transformation of precipitation to runoff through hydrological modelling. Similarly to climate models, hydrological models use different methods and processes in representing the physical system. This results in a different transformation of the same rainfall inputs to different flow outputs (Jones et al. 2006; Kay et al. 2009). The chosen hydrological model is then typically calibrated to fit observed data, meaning there are a series of parameters to control catchment process. Although the final parameter set provides an adequate representation of the system, there are other possible parameter sets that may provide an equally valid representation (Beven 2006). This uncertainty can be explored though the use of multiple valid parameter sets (Cameron et al. 2000; Wilby 2005).

One area of uncertainty which is not clearly included in Wilby et al’s (2008) cascade of uncertainty and has often been overlooked in impact studies is the effect of natural climatic variability. The climate of the UK and the North Atlantic European region in general is influenced by a number of competing climatic processes that result in the large variability in climate (Woollings 2010). The climate variability is predominately influenced by the North Atlantic Oscillation (NAO) (Hurrell et al. 2001) along with the Atlantic Meridional Overturning Circulation (MOC) (Marshall et al. 2001). Current climate models recreate these large scale processes of the climate but some physical processes and mechanisms influencing climate variability (i.e. jet stream variations, blocking) are known to be inadequately reproduced in global climate models (Parker et al. 2007; Woollings 2010). This leads to two issues relating to climate models and variability. Firstly, how to account for the fact that climate models may not reproduce the patterns or magnitudes of variability compared with the observed climate? Secondly, the climate variability that is produced in one climate model realisation may have been different in another realisation from the same model. With very few multiple runs available for a given climate model setup, impact studies are limited in the range of climate variability they can explore.

One method for addressing the role of climate variability in climate models is to use resampling techniques to analyse climate model outputs (Raisanen and Ruokolainen 2006; Ruokolainen and Raisanen 2007; Kendon et al. 2008; Prudhomme et al. 2010). The use of resampling methods allows for the inclusion of climate variability from just a few climate model realisations. Current resampling methods are based on sampling different averaging periods from an extended record window (Prudhomme et al. 2010) or by choosing paired averaging periods which provide the same change as a user defined pair (Raisanen and Ruokolainen 2006). Both of these methods maintain the variability produced in the original climate model realisation. An alternative approach to understanding climate variability is to analyse historical climate variability (also referred to as natural variability) which has previously been assessed in impact studies through the use of multiple realisations of climate model runs without external forcing (Arnell 2003; Arnell 2010), through the resampling of historic catchment precipitation (Kay et al. 2009), or by using a weather generator (Fowler et al. 2005; Jones et al. 2009). In all these methods, climate variability has been shown to play an important role in the cascade of uncertainty.

Understanding and quantifying these components of uncertainty allows for the production of probabilistic climate change scenarios. The development of probabilistic scenarios has recently been adopted in order to provide a broader characterisation of possible future changes, taking into account uncertainties. Previously, probabilistic studies have focussed primarily on climate model ensembles (New et al. 2007; Tebaldi and Knutti 2007), however probabilistic impact distributions have been created which incorporate other components of uncertainty within an impact study (Tebaldi and Lobell 2008; Wilby and Harris 2006). Providing this form of probabilistic impact analysis provides information on our confidence of our current range of projections.

This paper introduces a new, simple method for developing ensembles of climate change scenarios which incorporate climate variability. This is undertaken through applying a resampling procedure to climate model outputs to create multiple new precipitation realisations which are then used as input to a hydrological model; as demonstrated for the Eden catchment in Scotland. The paper is structured as followed: In Section 2 the resampling methodology is presented and the Eden catchment precipitation is analysed to inform this methodology. Section 3 describes the data used for the Eden case study with the results presented in Section 4 for the sensitivity of river flows to precipitation changes. Lastly the significance and implications of the results will be discussed in Section 5.

2 Methodology

2.1 Developing climate change scenarios

There are many different definitions of climate change scenarios. We refer herein to climate change scenarios as the climate time series to be input into the impact model. This refers to a single realisation of the climate, generated for either the baseline or future climate using regional climate models (RCMs) or global climate models (GCMs).

Climate change scenarios are typically constructed from climate model output by comparing one 30 year period (e.g. 2070–2099) to another (e.g. 1961–1990). However, these choices are somewhat arbitrary because a slightly different time period could equally be selected (e.g. 2071–2100 or 1960–1989). Furthermore the use of a different climate model realisation could give a slightly different time series for the same time period, due to the impact of natural variability.

Climate change impact studies are often informed using a single or few climate model realisations of baseline and future climates, thus limiting the inclusion of the impact of climate variability which has been shown to be important when assessing climate change impacts (Raisanen and Ruokolainen 2006). Incorporating climate variability in impact studies through using a weather generator or by statistically downscaling larger scale variables are still both informed using few climate model realisations.

The approach developed here incorporates climatic variability when building scenarios from a single climate model realisation using a simple resampling procedure.

2.2 Resampling methodology

The aim of the resampling procedure is to change the sequencing and repetition of values in a climate time series originally produced by a climate model. While the procedure does not generate events that are not simulated by the climate model, through modifying the sequencing and frequency of events a new climate realisation is created. Given that the model simulation and synthetic realisation contain mostly the same information it is assumed they are both equally valid representations of the climate. However, the manner in which a variable can be resampled is dependent on its temporal structure.

2.2.1 Resampling climate model precipitation

The precipitation time series of monthly totals simulated by the climate model is split into two sets of thirty year sub-series for a baseline (1961–1990) and a future period (2070–2099). These time series will form the basis for the resampling process, each being resampled independently. To create a new baseline time series the 1961–1990 time series is split into twelve monthly groups with thirty members each. A new thirty year time series is generated by randomly selecting a value from its corresponding monthly group and placing it in the new time series. The method samples with replacement so the value is returned back to its group for reselection. For example the same January value could occur thirty times in a thirty year time series, although this is unlikely to happen. The process is repeated until a new thirty year time series is constructed. The same procedure is then repeated for the future period of 2070–2099. A key assumption made in this resampling strategy is that precipitation can be treated as independent from month to month, which is tested in the following section.

2.2.2 Observed precipitation-temporal structure

Understanding the temporal properties of precipitation is a critical step to inform the resampling procedure. Analysis is undertaken for the observed precipitation time series for the Eden catchment.

Autocorrelation is the measure of correlation between time series observations at different temporal spacing, and was applied to the precipitation time series of monthly totals (Fig. 1, top), with each month correlated with the following twenty three months. The autocorrelation result (not shown) displays a seasonal cycle, due to winter precipitation being oppositely correlated with summer precipitation. The time series was de-trended by removing monthly means from each monthly value, leaving the autocorrelation of monthly anomalies (Fig. 1, bottom). The autocorrelation of the monthly anomalies indicates that there is no significant correlation from one month to another.
https://static-content.springer.com/image/art%3A10.1007%2Fs10584-011-0386-0/MediaObjects/10584_2011_386_Fig1_HTML.gif
Fig. 1

Monthly precipitation totals for the Eden catchment (top) with autocorrelation coefficient and corresponding correlogram for monthly precipitation anomalies (bottom). Correlogram has 95% confidence limits (dashed lines) at ±2/√N, where N is the number of observations. There is no correlation between months

The autocorrelation test informs us that there is no regularly occurring cycle within the precipitation structure, but this does not provide information on the possibility of any intermittent persistence of either a wet or dry period. It is therefore important to identify if there is persistence of high, medium or low magnitudes of precipitation occurrences. A further test is conducted by separating the time series into twelve monthly groups. Each monthly group is then further divided into five categories of equal size according to the magnitude of each precipitation value, category one being the lowest 20% of values and category five being the highest 20% of values. Each precipitation value in the time series is then assigned the value of its associated category (Fig. 2), resulting in a time series of integers. The sequence of the time series of magnitude groups is summarised as a contingency table in Table 1, where the number of occurrences of transitions from one monthly group to another is summarised. The contingency table is evaluated using the Chi-Squared test with a null hypothesis (h0) that the sequencing of monthly groups is independent and an alternate hypothesis (h1) that month to month sequences have some degree of correlation. This test results in an Χ2 value of 16.56 compared with a test statistic of 26.30 at the 5% confidence level based on 16 degrees of freedom. The null hypothesis is not rejected as the Χ2 value is less than the test statistic (p = 0.41), suggesting there is no evidence for correlation between months.
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Fig. 2

Sequencing of persistence in observed precipitation magnitude. Magnitude groups of monthly precipitation (top), 1 being the lowest and 5 the highest category

Table 1

Contingency table for precipitation group magnitudes in Fig. 2, showing the sequencing of groups. Rows show the group at a given time step and columns show the group at the preceding time step. Based on 25 combinations and 240 time steps, perfect random sequencing would be 9–10 counts in each combination

 

Magnitude group at time step i + 1

Totals

M1

M2

M3

M4

M5

Magnitude Group at time step i

M1

8

14

9

12

5

48

M2

11

9

5

11

12

48

M3

9

10

11

4

13

47

M4

8

7

13

10

10

48

M5

12

8

10

10

8

48

Totals

48

48

48

47

48

 

The autocorrelation and the analysis of sequencing and persistence of events demonstrate that precipitation is independent between months at this location. This property of month-to-month independence can be exploited within the resampling methodology.

2.2.3 Climate model scale to catchment scale

Climate model outputs are available in the format of gridded cells that are typically measured in degrees, with time series available at the monthly time step. When undertaking an impact study it is rare for the element of interest to be at such a large temporal or spatial scale. This leads to the large scale scenario needing to be converted to the local scale.

In this study the widely used change factor method has been adopted which is consistent with the UK’s latest climate change projections, UKCP09 (Murphy et al. 2009). In this method, the difference between the baseline and future projection is expressed as monthly percentage change factors. These precipitation change factors are then used to perturb the observed values in a catchment precipitation time series. This creates a new precipitation time series that is representative of the future climate, but at the local scale appropriate to the impact analysis. The use of climate change factors is beneficial in this study as it removes the biases within different climate models, allowing for the easy calculation of future changes.

2.2.4 Distribution of future precipitation change factors

When generating climate change factors from resampled climate time series the question of how many synthetic time series are necessary to completely capture the full range of climate variability arises. The resampling procedure allows for the creation of an unlimited number of realisations, so that impact studies are no longer limited to a few realisations as dictated by climate modelling outputs. However, some impact applications may be computationally intensive and might not easily run several thousand scenarios (e.g. distributed hydrological modelling (Bell et al. 2007)) Therefore the number of new baseline and future time series created needs to be a compromise between efficient impact modelling whilst ensuring that the final distribution of change factors fully represent the effects of climate variability. Considering too few time series could potentially skew a final distribution, while too many time series would increase the computational effort for little gain.

The resampling methodology was initially tested for precipitation from one GCM (HadCM3) using 10, 20, 30, 40, 50 and 60 baseline and future resamples resulting in 100, 400, 900, 1600, 2500 and 3600 precipitation change factor ensembles (difference between all baseline and future combinations). The distribution of the January precipitation change factor varies as the ensemble size increases (Fig. 3, top). Smaller ensembles produce a more variable distribution of precipitation change, whilst larger ensembles create a more consistent normal distribution of precipitation change. The resampling methodology is repeated for each ensemble size 100 times to confirm how the variability reproduced by each ensemble size changes. These 100 distributions (i.e. 100 versions of Fig. 3 top) have been summarised using the median and 5th and 95th percentiles of the precipitation changes (Fig. 3, middle). It can be seen that there is a clear convergence of the distribution of the median and 5th and 95th percentiles as the ensemble size increases (Fig. 3, middle and bottom). For smaller ensemble sizes there is in some cases an overlap between the distribution of the median and the 5th or 95th percentiles; in these cases the resampled variability is highly conditional on the choice of ensemble size. It is therefore important to consider a larger ensemble size to consistently capture the full range of variability. However the convergence of percentiles (Fig. 3 middle and bottom) indicates there may be a threshold where increasing the ensemble size no longer increases the range of resampled variability.
https://static-content.springer.com/image/art%3A10.1007%2Fs10584-011-0386-0/MediaObjects/10584_2011_386_Fig3_HTML.gif
Fig. 3

Distribution of January change factor from HadCM3 for a single repetition of the resampling methodology for different resampling sizes (10, 20, 30, 40, 50, 60) from left to right (top) with the median in bold and 5th and 95th percentiles in dashed. The resampling methodology is repeated 100 times with the median, 5th and 95th for each of the 100 repeated distributions plotted for each resample size (middle). The distribution of each percentile for each different number of resamples is then calculated (bottom)

An ensemble containing the combination of 60 resamples for both baseline and future provides the most consistent distribution (Fig. 3) and is taken as reference. Q-Q plots compare the distribution of the percentiles for each ensemble size (i.e 10, 20, 30, 40 & 50 resamples) with the reference ensemble size (60 resamples) and show the point at which increasing the number of resamples adds little benefit to the distribution of precipitation changes (Fig. 4). This occurs from 40 resamples onwards for HadCM3, with a close to one to one fit indicating the distribution from 40 resamples is very similar to that produced by 60 resamples (Fig. 4).
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Fig. 4

Quantile-Quantile plot for HadCM3 comparing the percentiles across the 5th percentile of 100 ensemble distributions of precipitation change from repeated resampling. Y-axis is a 60 resample ensemble and x-axis is 10, 20, 30, 35, 40, and 50 resample ensembles from left to right. Dashed lines are 5th and 95th percentiles of precipitation change distributions, with lines at 10% increments (median in bold). As distributions become similar they adopt a line similar to x = y. The transition from 35 to 40 resamples shows this trend

The same assessment was repeated for two GCMs, one with similar resolution to HadCM3 and one with a finer resolution (IPSL-CM4 and CNRM-CM3 respectively), and different monthly change factors. The conclusion from this suggests an ensemble size of changes from at least 40 resamples of both baseline and future (i.e. 1600 members) is sufficient to accurately represent the change factors across different months and GCMs.

3 Case study data

3.1 Future climate data

The monthly precipitation time series outputs from thirteen different CMIP3 GCMs (Meehl et al. 2007) used in the IPCC Fourth Assessment Report were used in this study (Table 2). The suite of GCMs covers a range of different spatial resolutions from 1.50° (NCAR-CCSM3) to 4.00°/5.00° (GISS-ER). Outputs are available for a 20th century control run with observed anthropogenic forcing and a future under an SRESB1 emissions scenario.
Table 2

Grid cell location and Resolution information on thirteen IPCC AR4 GCMs used in this study. Information taken from IPCC data distribution centre website (www.ipcc-ddc.org) and Meehl et al. (2007)

GCM

Modelling group

Grid cell centre

Atmospheric resolution

Oceanic resolution

Lat

Lon

Lat

Lon

Lat

Lon

CCSM3

NCAR

56.73

−2.81

1.40

1.40

1.125

0.27

CGCM3.1

CCCma

57.52

−3.75

3.75

3.75

1.80

1.80

CM3

CNRM

54.41

−2.81

2.80

2.80

0.50–2.00

2.00

ECHAM5

MPI

56.89

−3.75

T63

L31

1.5

L40

MK3.0

CSIRO

56.89

−3.75

T63

L18

0.84

1.875

CM2.0

GFDL

57.00

−3.75

2.00

2.50

1.00

1.000

CM2.1

GFDL

55.62

−3.75

2.00

2.50

1.00

1.00

ER

GISS

54.00

−2.50

T30

L19

T42

T42

HadCM3

UKMO

57.50

−3.75

2.75

3.75

1.25

1.25

CM3.0

INM

56.00

−5.00

4.00

5.00

2.00

2.50

CM4

IPSL

57.04

−3.75

2.50

3.75

2.00

2.00

MIROC3.2

NIES

54.42

−2.81

T42

L20

0.50–1.40

1.40

CGCM2.3.2

MRI

57.21

−2.81

2.80

2.80

2.00

2.50

3.2 Case study catchment

The Eden Catchment (NRFA station number 14001) is located in Eastern Scotland with latitude 56.3o, longitude −2.9o and an area of 307.4 km2 (Fig. 5). It is a low-lying, gently sloping catchment between two estuaries with the Firth of Forth to the South and the Firth of Tay to the North. The catchment is underlain by a mixed geology with no single geology dominating. The river has a base flow index (BFI) of 0.63, indicating a mixed flow routing response. Mean annual precipitation is 812 mm while mean annual runoff is 405 mm. Mean annual river flow is 3.94 m3s−1, while the peak record flow is 69m3s−1.
https://static-content.springer.com/image/art%3A10.1007%2Fs10584-011-0386-0/MediaObjects/10584_2011_386_Fig5_HTML.gif
Fig. 5

Helmsdale catchment location. Catchment boundaries provided by Morris and Flavin (1990) with 1:50,000 watercourse from Moore et al. (1994). © NERC (CEH). Contains Ordnance Survey data © Crown copyright and database right 2011

The catchment provides a good case study for this demonstration of the resampling method as it has been found to have a fairly neutral response to changes in its inputs (Prudhomme et al. 2010). This avoids mixing the assessment of climate variability and the resampling methodology with a more complex catchment response.

3.2.1 Catchment data

A daily flow record and daily catchment precipitation was provided by the national river flow archive (NRFA) for the period from 1967 to 2001. Potential evaporation used is the UK Met Office MORECS monthly data that is assumed equally distributed across each month. Temperature data is taken from the UKCP09 gridded climate observations (https://ukclimateprojections.defra.gov.uk).

3.2.2 Hydrological model

River flows are simulated using the probability distributed moisture model (PDM) (Moore 2007). PDM is a lumped conceptual model that represents catchment processes using simple mathematical steps to control flow storage and routing. Soil moisture storage in the catchment is controlled by a probability distribution, routing flow between slow and quick routes. An elevation and temperature dependent snowmelt module (Bell and Moore 1999) is applied as a pre-processor to catchment rainfall. If snow fall occurs then a lag is introduced to the precipitation time series to simulate this impact.

The PDM is run at the daily time step and was calibrated for the Eden catchment by Crooks et al. (2010), and results in Nash Sutcliffe (Nash and Sutcliffe 1970) values of 0.66 and 0.96 when calculated for single and thirty day averaged flows respectively.

3.2.3 Hydrological simulation

The PDM requires time series inputs of precipitation and potential evaporation. The observed catchment precipitation series is processed using the snowmelt module which is then used in conjunction with the potential evaporation data to simulate the baseline flow series. A future precipitation time series is created by perturbing the historic baseline with each monthly precipitation change factor. The snowmelt module is applied in the same manner as to the baseline but using the historical temperature time series so that results focus solely on changes in the precipitation regime. This generates a river flow series for the baseline period and a river flow series for the change factor scenario. The climate change impact is the difference between the two river flow time series.

With a 40-resample ensemble containing 1600 precipitation change factors for each GCM, 1600 future synthetic precipitation series are input to PDM. This results in a 1600 member ensemble of future flow changes per GCM.

4 Application to change in future river flows

The resampling methodology outlined previously is applied to the Eden catchment using a baseline period from 1961–1990 and future period of 2070–2099 forced using the SRESB1 emissions scenario. A 40-resample ensemble is used to incorporate the climatic variability obtained within a single GCM. In the analysis the results for HadCM3 and the resulting sensitivity of mean monthly flows to precipitation variability is discussed in Section 4.1.

In Section 4.2 the same methodology is repeated for twelve other GCMs with the resulting distributions of all thirteen GCMs combined with equal weighting in a single ensemble of 20800 (13 × 402) climate change factors.

4.1 Single GCM-HadCM3

4.1.1 HadCM3—precipitation change factors

In this section the resampling methodology is applied to just a single GCM, HadCM3. Monthly mean precipitation change from HadCM3 follows a distinct seasonal cycle, with increases between October and April and declining across the summer months (Fig. 6, left). Incorporating climatic variability through resampling of the single realisation results in a range of possible future changes each month. The largest range, describing the largest variability in precipitation change (Larger box and whiskers, Fig. 6, right), occurs in spring months. Summer months show the least variability in precipitation change. The seasonal cycle is maintained after resampling, although in some instances there is uncertainty in the direction of change. For example the median value of change for May is close to 0, indicating climate variability could lead to either an increase or decrease in precipitation in the 2080s.
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Fig. 6

Precipitation monthly change factors derived from HadCM3 for the Eden catchment. Comparison between using a single realisation (left) which produces a single precipitation change for each month and the resampling methodology (right) which generates 1600 precipitation changes for each month. Box plot whiskers indicate full data range, the box shows the quartile range and the median is marked in bold

4.1.2 HadCM3—mean flows

When considering precipitation change factors from a single realisation of HadCM3, the resulting river flow in the River Eden in the 2080s is predicted to increase in magnitude in all months with the exception of July, August and September (Fig. 7, left). With the resampling methodology however, the range of predicted values for each monthly flow change increases (Fig. 7, right). Median changes retain a similar structure to the single realisation, while uncertainty in the direction of change in many months is highlighted, particularly in June and September.
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Fig. 7

Simulated mean monthly flow changes for the Eden catchment in the 2080s using the 40-resample ensemble of precipitation changes from HadCM3. Comparison of a single realisation (left) and the resampling methodology (right). Box plot whiskers indicate full data range, the box shows the quartile range and the median is marked in bold

The role of the Eden catchment characteristics in generating a response to a given climate change input plays an important role. The precipitation change factors have a distinct seasonal cycle (Fig. 6) which is conserved in the monthly flow changes. However there is a greater level of variability apparent in the precipitation change factors compared to the smoother cycle in the flow change. For example September precipitation change has a range of 50% and a median change of 15%, when this is transformed to flow change the range increases and the median change is 0. This is a result of the catchment processes reducing the month to month variability when transforming the precipitation change to changes in flow. The Eden catchment has a fairly mixed hydrological response, where the catchment acts as a buffer in the rainfall to runoff response change. This buffering is linked to the catchment storage capacity, typically the higher (lower) the BFI of a catchment the greater (lesser) it is able to buffer any runoff response to precipitation.

4.2 Multiple GCMs

4.2.1 Multiple GCMs—precipitation change factors

The previous section applied the methodology to just a single GCM, here the methodology has been repeated for twelve additional GCMs. This provides 40-resample ensembles of precipitation change factors for each GCM, which gives a total of 20800 precipitation change factors across all 13 GCMs. Assuming that each of these scenarios is equally probable, the precipitation change factors are combined in a single multi-GCM distribution. Each GCM can also be considered separately as in the previous section, and compared to the full range of change.

The distribution of precipitation change factors from the thirteen GCMs (equally weighted) display a range of future changes for each month (Fig. 8, right), larger than that of a single GCM (Fig. 6, right). There is a modest seasonal cycle in median precipitation change with higher increases in winter/spring, whilst median summer changes indicate no change. This is a much reduced cycle compared with the results from just using HadCM3 (Fig. 6). This indicates that the seasonal structure of precipitation changes given by other GCMs is different in its timing or its strength of cycle compared to HadCM3. This is confirmed when looking at the single realisation precipitation change factors from each GCM (Fig. 8, left). The greatest consensus of change is in autumn/winter months between September and December (Fig. 8, right), although the full range of variability in these months could still lie between −25% and 50%, displaying a large range of uncertainty.
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Fig. 8

Monthly precipitation change factors from 13 IPCC GCMs in the 2080s for the Eden catchment. Precipitation change factors are derived from a single GCM realisation (left) and through combining resampled realisations (right). Box plot whiskers indicate full data range, with the box showing the quartile range and the median is marked in bold

Histogram distributions provide a powerful visualisation of the distribution of the precipitation change factors, and are shown for two months in Fig. 9. The direction of change in June precipitation (Fig. 9, left) is uncertain with a median value close to 0%, implying that either an increase or decrease in precipitation is equally probable. The June distribution is also skewed, with a large tail towards higher increases. In contrast precipitation changes in December (Fig. 9, right) adopt a normal distribution, with a median change of 5–10%. The range (5th–95th percentiles, i.e. 90% of the probability distribution) of precipitation changes in June is almost double that of December, showing considerably larger variability in precipitation and uncertainty in the climate change signal for summer precipitation in the Eden catchment.
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Fig. 9

Histograms of June (left) and December (right) precipitation change factors from 13 IPCC GCMs in the 2080s for the Eden catchment. The median is shown with the bold line and the 5th and 95th percentiles in dashed lines

4.2.2 Multiple GCMs—mean flows

The combined impact of precipitation change and variability on annual flow in the Eden catchment is assessed using the 40-resample ensemble of precipitation change factors from the 13 GCMs. When all GCMs are combined with equal weight, the annual flow change produces a near normal distribution that has a long positive tail with a median change of 10% (Fig. 10, right). The median to 95th percentiles has a smaller range than that from the median to the 5th percentile, reflecting the skew to larger increases. An overall increase in annual flows in the 2080s is probable at the 95th percentile of the scenarios.
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Fig. 10

Sensitivity of mean annual flow in the Eden catchment in the 2080s using precipitation climate change factors derived from 13 IPCC GCMs. Changes are derived for each GCM from a single realisation (points-left), resampled realisations (boxplots-middle) and combined in a single distribution (histogram right). The histogram median is shown with the bold line and the 5th and 95th percentiles in dashed lines

Results for each GCMs 40-resample ensemble individually (Fig. 10, middle) show that the large tail of the full ensemble (all GCMs together) is created largely by just a single outlying GCM (GFDL-CM2.0). The impact of precipitation variability varies between each GCM as demonstrated by the varying range of each boxplot (Fig. 10, middle). However the variability in the flow change does not display direct linearity with the variability in precipitation for a given GCM. In addition to the catchment properties that act as a buffer and could delay the response to seasonal precipitation changes, variations in the timing of precipitation changes between GCMs (Fig. 8, left) would also influence how annual river flow changes are distributed.

The median changes in monthly flow as a result of precipitation change and variability is seen to increase in eleven out of twelve months, with a greater chance of a decrease in flow in summer months with the August median change close to 0 (Fig. 11, right). Maximum flow increases are predicted from October through to December, with October having the largest range of possible future change. In comparison to the precipitation change factors in Fig. 8, the seasonal cycle is more pronounced but much smoother in the monthly flow changes. Winter increases in precipitation are enhanced by catchment processes to create larger corresponding increases in the flow. Similarly spring and summer decreases in precipitation are not reflected as dominantly in flow change as the rainfall-runoff response transformation is buffered by the catchment.
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Fig. 11

Monthly flow changes from 13 IPCC GCMs in the 2080s for the Eden catchment. Change factors are derived from a single GCM realisation (left) and through combining resampled realisations (right). Box plot whiskers indicate full data range, with the box showing the quartile range and the median is marked in bold

The impact of the catchment properties in transforming monthly precipitation changes to monthly flow changes can be seen when comparing the distributions of monthly precipitation change factors (Fig. 9) to the corresponding monthly flow changes (Fig. 12). In June, the precipitation distribution is slightly skewed, while the skew is much larger in the distribution of flow changes (larger tail towards increases in flow). In December the distribution of changes in both precipitation and flow have similar shapes, but is shifted towards larger magnitude changes in flow than precipitation. This suggests that the catchment processes and characteristics lead to an enhancement of the December precipitation change when transformed to a flow change.
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Fig. 12

Histograms of June (left) and December (right) simulated flow from 13 × 40-resample ensembles of precipitation change factors derived from 13 IPCC GCMs. The median is shown with the bold line and the 5th and 95th percentiles in dashed lines

5 Discussion and conclusions

A resampling procedure applied to GCM monthly precipitation time series has been developed, providing a new method for incorporating climate variability within climate change scenarios of precipitation. It was applied to the Eden catchment to produce changes in mean monthly precipitation and resulting changes in mean flows (annual and monthly). Through resampling the precipitation outputs of a GCM for both baseline and future time periods, ensemble distributions of precipitation change factors can be generated which incorporate changes in both climate variability and signal. The resampling process incorporates climate variability by altering the sequence and repetition of the original model output in the new resampled realisations. A sensitivity analysis showed that 40 resamples for both baseline and future are enough to accurately describe the full range of precipitation variability and change (i.e. 1600 change factors). When applied using the perturbation method with hydrological simulation, distributions of flow changes can also be constructed.

Climate variability has been shown to play a significant role when assessing the potential impacts of precipitation changes in the Eden catchment. Applying the resampling procedure to a single GCM shows uncertainty in the direction of future change for both monthly precipitation and river flow, which is not accounted for when using just a single realisation. The ensembles of change for each GCM were generated independently allowing for a comparison of the changes from each GCM. Through this comparison, both the climate change signal and the magnitude of precipitation variability were seen to differ between GCMs. Each GCM displays a different range of precipitation variability through the resampling which in turn creates a different range of sensitivity in mean river flows. This further confirms the importance of using multiple climate models in impact analysis to capture both variations in the mean and ranges between models.

Multi model ensembles were produced through combining the 40-resample ensemble of each GCM in a single distribution ensemble using an equal likelihood assumption (Weigel et al. 2010). This creates a probabilistic impact distribution incorporating uncertainty from different climate models and precipitation variability. In this example each climate model is given equal weighting, some impact studies have chosen to apply different weightings to each model (Wilby and Harris 2006). There remains a great deal of debate as to the best practice for combining multiple climate models which is becoming more widely discussed (Knutti et al. 2010a, b), however in practice it may not have a significant effect on the end result (Chiew et al. 2009; Christensen et al. 2010).

One of the main assumptions in how the resampling methodology has been implemented here is the independence of monthly precipitation, as identified for the UK. In different climatic regions this assumption may not be valid, for instance in a monsoon climate, as once the monsoon starts it could not be stopped and then restarted. As well as the influence of location, analysing a different climate variable could require a different resampling strategy (e.g. temperature). The methodology provides the opportunity to account for these factors as well as incorporating multiple variables through altering the resampling strategy. The temporal time step of the resampling is dictated by the highest temporal level of correlation for all the considered variables. For example if including both precipitation and temperature simultaneously, the resampling of both variables may be undertaken for seasonal blocks due to the stronger month to month correlation of temperature compared with precipitation. In light of this the resampling methodology allows for multivariate, spatially coherent and temporally coherent scenarios to be created through applying the same resampling procedure simultaneously to all variables and locations of interest.

In the absence of climate model ensemble projections or full probabilistic climate change scenarios, the resampling of a single climate model realisation provides a useful tool for developing climate change scenarios within a probabilistic framework. The development of probabilistic scenarios and the assessment of their impact allows for better characterisation of uncertainty, including that of climate variability. However it is important to note that probabilistic scenarios are not probability forecasts and only summarise a number of assumptions and uncertainties dependent on the methods used to construct them (Beven 2011).

From a hydrological impact modelling perspective, increasing the number and range of scenarios, allows for a detailed assessment of the non-linearity in catchment response, which has been shown to be an important factor when assessing the potential impacts of climate change. The role of the catchment in transforming changes in precipitation to changes in flow highlights the importance of hydrological simulation, the use of full ensemble probabilistic climate change scenarios and the need for climate change impact studies.

The next stage in developing this methodology is to separate the climate change signal from that of climatic variability. If future climate change can be assessed in the context of current climate variability it would help to provide present day context to strategic decisions made for the future.

Acknowledgements

This research was funded by the Water Science programme of the NERC Centre for Ecology and Hydrology, who also fund the PhD project that this work is part of. Thanks to Alison Kay for providing calibrated PDM parameters. The authors would also like to thank the three anonymous reviewers for their constructive comments; in particular for suggestions regarding the analysis of precipitation sequencing.

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© Springer Science+Business Media B.V. 2011