Regional case studies
View of a Skull (Leonardo da Vinci) ENSEMBLES home page

Exploring inter-model uncertainties in weather extremes using the CRU weather generator and the PRUDENCE RCM ensemble

Work by Clare Goodess, Colin Harpham, and Phil Jones: Climatic Research Unit, UEA, UK


As part of the CRANIUM and ENSEMBLES projects, the CRU team has explored inter-model uncertainties in climate change projections using output from 10 different European regional climate models (RCMs) and a stochastic weather generator linked in a probabilistic framework. The RCM runs were undertaken as part of the PRUDENCE project. Most of the RCMs were forced by the Hadley Centre global climate model (GCM), but three of the RCMs were also forced by a second global model (ECHAM4) - giving a total of 13 RCM runs, all for the IPCC SRES A2 emissions scenario. Changes in mean temperature and precipitation, together with changes in their variability, were taken from each RCM run for the grid square nearest to each location of interest, and used to perturb the parameters of the CRU weather generator developed for the BETWIXT project (see BETWIXT Technical Briefing Notes 1 and 4). For each of the 13 RCM runs, the weather generator was run 100 times. Ten seasonal indices of mean and extreme temperature and rainfall (see table below) were then constructed from the daily time series. The scenario results are presented below, using a number of different formats to suit a range of different users.

It is important to note the following features of these probabilistic projections:

For the CRANIUM work, ten UK stations were used: Bradford, Coltishall, Elmdon, Eskdalemuir, Gatwick, Heathrow, Hemsby, Paisley, Ringway and Yeovilton. This work is reported in Goodess et al., 2007: Climate scenarios and decision making under uncertainty, Built Environment, 33, 10-30.

For the ENSEMBLES work, seven mainland-European stations were also used: Linkoeping, Karlstad, Saentis, Basel, Beograd, Kaliningrad and Timisoara.


Validation of the weather generator

Validation results for the UK stations are available here.

For the mainland-European stations, two sets of figures are provided here, as described below. Each figure is available as a GIF for immediate viewing, a PDF and EPS for high-quality, and a CSV with self-explanatory column headings for loading into a spreadsheet.

In all figures, observed values (blue crosses) are the mean for the period 1961-1990. The simulated values (red for the 1961-1990 control period) are the mean of 100 30-year weather generator runs (red dots). The red lines and bars show the variability of the 100 series (plotted as plus/minus two standard deviations around the mean).

Set 1: Precipitation and temperature statistics

Set 2: Extremes

Winter (DJF), spring (MAM), summer (JJA), autumn (SON) and the year as a whole (ANN) values for the following variables (which are defined in Table 3 of BETWIXT technical briefing note 4):

Control
1970s
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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The ENSEMBLES probabilistic projections: figures and tables

Probabilistic projections for the ten UK stations are available on the CRANIUM web pages, while those for the seven mainland-European stations are provided here.

The following acronyms are used to identify the ten seasonal indices of mean and extreme temperature and rainfall in the figures and tables below. All scenario results are for the 2080s (2071-2100).

Index Description User-friendly name
txav Mean Tmax Average maximum temperature
tnav Mean Tmin Average minimum temperature
tav Mean Tmean Average temperature
txhw90 Heat Wave Duration (days) Longest heatwave
txf90 % days Tmax > 90th percentile Number of hot days
tnf10 % days Tmin < 10th percentile Number of cold nights
tnf90 % days Tmin > 90th percentile Number of warm nights
pav Mean climatological precipitation (mm/day) Average daily rainfall
pxcdd Max number of consecutive dry days Longest dry period
pfl90 fraction of total rainfall from events > long-term 90th percentile Heavy rainfall proportion

Figures

Three sets of figures for seven stations and 10 indices/variables are provided, as described below. Each figure is available as a gif for immediate viewing, and as a pdf and eps for higher quality.

Histograms

In this set of figures, the weather generator output is plotted as histograms, with the number or magnitude of events on the horizontal axis and the probability of the event occurring in any one season on the vertical axis. Each individual histogram is constructed using 3000 values (i.e., 30 years x 100 weather generator runs)

The heavy black line in both left- and right-hand panels shows the weather generator results based on observations for the reference period 1961-1990. In the left-hand panel, each of the coloured lines represents weather generator results for the 2080s based on a different RCM run.

In the right-hand panel, the red line shows the ensemble average, i.e., the average of the coloured lines from the left-hand side.

For the A2 emissions scenario, 13 different RCM runs were used hence there are 13 coloured lines on the left-hand side.

Average temperatureTemperature extremesAverage
rainfall
Rainfall extremes
txav tnav tav txhw90 txf90 tnf10 tnf90 pav pxcdd pfl90
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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Interpretation of the histograms

See results for the UK stations

Probability Density Functions (PDFs) - A2 scenario changes

In this set of figures, changes for the A2 emissions scenario calculated from weather generator output are plotted as Probability Density Functions (PDFs). The magnitude of the change is shown on the horizontal axis and the density (frequency) of the change occurring in any one season on the vertical axis.

In the left-hand panel, each of the coloured lines represents scenario changes for the 2080s based on a different RCM run. Each individual PDF is constructed using 3000 paired changes (i.e., 30 years x 100 weather generator runs). The changes are calculated as the difference between each of the 3000 values for the 2080s and the equivalent control-period value.

In the right-hand panel, the red line shows results for all 39,000 paired changes (i.e., 30 years x 100 weather generator runs x 13 RCM runs). Thus it represents an ensemble average.

In order to estimate probabilities of change from these plots, it is necessary to integrate the area under the part of the curve of interest. However, these PDFs do provide a clear visual picture of the most likely change (indicated by the peak or mode of the distribution) and the uncertainty (indicated by the shape and spread of the distribution).

Average temperatureTemperature extremesAverage
rainfall
Rainfall extremes
txav tnav tav txhw90 txf90 tnf10 tnf90 pav pxcdd pfl90
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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Cumulative Density Functions (CDFs) - A2 scenario changes

This set of figures is exactly the same as for the PDFs, except that here, cumulative density functions (CDFs) are plotted.

This allows the cumulative probability of particular changes to be easily read. Where the changes are positive, the cumulative probability for a change greater than any particular value on the horizontal axis is read as 1 minus the value on the vertical scale.

Average temperatureTemperature extremesAverage
rainfall
Rainfall extremes
txav tnav tav txhw90 txf90 tnf10 tnf90 pav pxcdd pfl90
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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Interpretation of the PDFs and CDFs

See results for the UK stations

Tables

In the two tables below, probability values derived from the figures above are shown.

The CDF percentiles give lower (10th percentile), mean (50th percentile) and upper (90th percentile) estimates of changes derived from the PDFs/CDFs shown above.

The class probabilities give estimates of the probability of changes lying within fixed classes or bins. About 10 classes are used for each index, with the same ranges or bin sizes used for all stations, depending on the variable considered:

CDF
percentiles
Class
probabilities
LinkoepingComma-Separated ValuesComma-Separated Values
KarlstadComma-Separated ValuesComma-Separated Values
SaentisComma-Separated ValuesComma-Separated Values
BaselComma-Separated ValuesComma-Separated Values
BeogradComma-Separated ValuesComma-Separated Values
KaliningradComma-Separated ValuesComma-Separated Values
TimisoaraComma-Separated ValuesComma-Separated Values

Interpretation of the percentile/class probability tables

If the 10th, 50th and 90th percentile changes for a particular station/season/variable have the same sign (positive - an increase, or negative - a decrease), we can have more confidence in the projected direction of change.


A preliminary exploration of weighting schemes

As a preliminary exploration of how a weighting scheme could be introduced into this probabilistic framework, a simple approach has been tested. The weighting scheme is based on the ability of the RCMs to reproduce present-day half-monthly values of (1) mean temperature, (2) mean precipitation, (3) temperature variability, and (4) precipitation variability, for the model grid box in which each station is located. Plots for mean temperature and precipitation are shown below. For variability (plots not shown) the standard deviation of daily values is used.

The weights are calculated as the product of the four values, and are used to determine how frequently each weather generator-RCM pairing is sampled to construct the ensemble average. Thus better performing models should contribute more to the PDF.

Results are shown immediately below for the UK and then for the mainland-European stations. In most cases, very little difference can be seen between the weighted (black) and unweighted (red) PDFs. This may well be because the majority of RCM runs use boundary conditions from the same GCM, which dominates the weighting scheme.

UK weighted PDFs

Average temperatureTemperature extremesAverage
rainfall
Rainfall extremes
txav tnav tav txhw90 txf90 tnf10 tnf90 pav pxcdd pfl90
Bradford
53.82N 1.77W
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Coltishall
52.77N 1.35E
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Elmdon
52.45N 1.73W
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Eskdalemuir
55.32N 3.2W
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Gatwick
51.15N 0.18W
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Heathrow
51.48N 0.45W
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Hemsby
52.68N 1.68E
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European weighted PDFs

Average temperatureTemperature extremesAverage
rainfall
Rainfall extremes
txav tnav tav txhw90 txf90 tnf10 tnf90 pav pxcdd pfl90
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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UK RCM validation

Mean
Air Temp.
Mean
Precip.
Bradford
53.82N 1.77W
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Coltishall
52.77N 1.35E
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Elmdon
52.45N 1.73W
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Eskdalemuir
55.32N 3.2W
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Gatwick
51.15N 0.18W
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Heathrow
51.48N 0.45W
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Hemsby
52.68N 1.68E
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European RCM validation

Mean
Air Temp.
Mean
Precip.
Linkoeping
58.4N 15.53E
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Karlstad
59.35N 13.47E
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Saentis
47.25N 9.35E
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Basel
47.55N 7.58E
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Beograd
44.8N 20.47E
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Kaliningrad
54.72N 20.55E
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Timisoara
45.77N 21.25E
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Future work

As part of the ENSEMBLES project, partners are developing more sophisticated weighting schemes for both the GCMs and RCMs used in the project. It is planned to use these new weights, together with output from the new ENSEMBLES RCM ensemble which should become available in late 2007, to improve on the first probabilistic projections presented here. Despite their shortcomings, these projections nonetheless demonstrate the utility of combining a weather generator and RCM output in a probabilistic framework.


Last updated: June 2007 - Clare Goodess. Thanks to Mike Salmon and Colin Harpham for help in constructing this page.