Climate predictability beyond traditional climate models Rasmus E. Benestad & Abdelkader Mezghani Rasmus.benestad@met.no
More heavy rain events?
More heavy rain events? Heavy precipitation events with more than 20 mm/day
The number of heavy rain events
Predicting number of heavy rain events
Some clues...
Different quantities Mean = (wet-frequency) (wet-mean) x = fw µ
What information can we use?
Simple model for wet-day amount
Simple model for wet-day amount Heavy precipitation
More heavy rain events?
Probabilities for all days -x/µ Pr(X>x) = fwe
How often does it rain? fw (fraction)
How often does it rain?
Not much trend in frequency...
The 24-hr precipitation amounts -x/µ Pr(X>x) = fwe
How much does it rain when it rains? µ (mm/day)
How much does it rain when it rains?
PRELIMINARY RESULTS The question: more heavy rain events? Observations: annual mean µ - Downscaled from 107 CMIP5 GCMs (RCP4.5)
Conclusions Rain is more than just rain... Frequency and magnitude Wet-day mean µ is key Empirical-statistical downscaling land-sea contrast Wet-day mean is sensitive to changing conditions
Thank you for your attention Rasmus.benestad@met.no The R-package 'esd: 'https://www.facebook.com/rclimateanalysis
Other aspects: duration and intervals
The common source of information ENSEMBLES DMI-HIRHAM5_A1B_ECHAM5_MM_25km-CRU_pr
The common source of information ENSEMBLES DMI-HIRHAM5_A1B_ECHAM5_MM_25km-CRU_pr Monthly totals for Copenhagen
Climate predictability beyond traditional climate models Rasmus E. Benestad & Abdelkader Mezghani Rasmus.benestad@met.no Abstract: Reliable predictions of local climatic characteristics are often needed in decision-making and the adaptation to climate change. The mainstream approach to predicting local climate change involves downscaling results from a global climate model (GCM) with a regional climate model (RCM). This approach only makes use of part of the available information. An alternative way to provide a description of the local climate is to use empirical-statistical downscaling (ESD), which makes use of an additional and independent source of information: empirical data. However, we argue that past efforts have not made fully use of a third independent available source of information. Statistics provide a valuable theoretical reference frame for validating model results, making sense out of data, and designing statistical models. We propose a combination of these various information sources that will enhance our ability to predict local climate change. To demonstrate this, a strategy for predicting the statistical distribution, frequency of wetdays, and duration of events for 24-hr precipitation is presented. This approach is used to predict heavy precipitation events, both in terms of intensity, and frequency. Results are presented for consecutive wet and dry days and number of events per year exceeding a given threshold. We also propose a strategy for validating and estimating the skill-score of the predictions in terms of relevant figures: the number of intense events per year and number of cases falling outside the 90% confidence interval are assessed using a binomial distribution with known probabilities. Furthermore, we present an assessment of GCMs based on common empirical orthogonal functions (EOFs). All these results are derived using a new freely available open-source R-package (esd) and are a part of the work carried out for projects like EU-SPECS, COST-VALUE, and CORDEX-ESDM.
More heavy rain events? Let's take a look at the historic rainfall amounts in copenhagen. One notable feature is the spikes, with the highest showing the recent record-breaking rain event. Question: will there be more heavy rain events in the future? How do we find the answer?
More heavy rain events? Heavy precipitation events with more than 20 mm/day First we need to specify what we mean by 'heavy rain event' or 'extremes'. Let's say it is days when it rains more than 20 mm/day. We can estimate the probabilities for such cases for the past by counting events, assuming that the probability is fixed. A change in the statistics of heavy precipitation implies a change in its probability. Our mission is to predict the probability of such events.
The number of heavy rain events We can look at the number of days with heavy precipitation per year, as shown here. Typically, the number fluctuates, and there are between 1 and 4 of these days per year, but with slightly more since the 1990s. There are also some individual years with more days with intense rain. I will argue that it is possible to some extent to predict the variations in the number of heavy rain days.
Predicting number of heavy rain events Indeed, this figure shows the observed and predicted number of heavy precipitation days per year. The grey-hatched area shows the 90% confidence interval. The predictions are based on probability estimates. What's the story behind these results?
Some clues... Let's first start to look at some different aspect of precipitation to find some clues. The curves here show how different rain statistics typically varies with the season it's their climatology. Notice the more pronounced annual cycle in the wetday mean (red) compared to the monthly mean for all days (blue) and the wet-day frequency (green). The wet-day mean is more sensitive to the well-known and systematic differences in the seasons than the mean and frequency. This is a clue.
Different quantities Mean = (wet-frequency) (wet-mean) x = fw µ We know that the mean for all days is the product of the frequency and the wet-day mean. But how do the means and wet-day frequency relate to the probability of a heavy precipitation event?
What information can we use? There is more relevant information. We can look at the histogram of the precipitation amounts for the days when it rains, and we see that its shape is similar to an exponential distribution. Here the histogram of the data is shown in grey. The xaxis represents the amounts and the y-axis indicates how often there have been cases with a certain amount. The higher the column, the more frequent a specific amount has been recorded. The red curve here shows an exponential distribution that uses the wet-day mean - mu as it's only parameter.
Simple model for wet-day amount These statistical distributions are also known as 'probability distribution functions' and quantify the probabilities that the daily rainfall exceeds any given threshold amount. The exponential distribution is also very nice, since it only has one parameter and is easy to solve for the probability and any quantile analytically. So let's take the daily precipitation to be exponentially distributed for the sake of simplicity.
Simple model for wet-day amount Heavy precipitation Now we can make some statement about changes in the probability, because that will only involve a change in mu. The figure here shows the original probability distribution in red and a new distribution for when mu has increased by 50% (grey). It's a given that the area under the curve is 1 the probability must always add up to one. The point is that the probabilities must add up to one, and a change in the curve sets the change in the tail. Traditional: return values: only look at the tail. Assume stationarity... The probability of a 'heavy' event is the area under the curve to the right of the threshold. We see that the area of the grey curve shows an increase with an increase in mu.
More heavy rain events? Here is an example of how the annual wet-day mean can be used to estimate upper annual wet-day percentiles. Note, there is a slight long-term trend
Probabilities for all days Pr(X>x) = fwe-x/µ There is more than just the exponential distribution for wet days. We also need to factor in the frequency of rainy days in order to estimate the probability of a day with heavy rain.
How often does it rain? fw (fraction) The question is: how often does it rain? The curve here shows the annual mean wet-day frequency in Copenhagen. The black curves show the observed frequency and the red curve shows predicted frequency. The frequency of rainy days varies from year to year, and is typically between 1/4 and 1/3. The predictions capture a good part of the year-to-year variations.
How often does it rain? So what's behind these predictions? The map shows mean sea-level pressure anomalies associated with the wet-day frequency variations. Typically, low pressure over western Norway brings rain to Copenhagen. This map shows the predictor choice in the empirical-statistical downscaling, used to predict the local precipitation statistics.
Not much trend in frequency... There is not much long-term trend to discern in the wet-day frequency record, in spite of the year-to-year variations. The mean sea-level pressure is a measure of the mass of the atmosphere above. It is not expected to change by very much. We also saw that there was little seasonal variation. For now, we assume that the wet-day frequency just fluctuates on a yearly basis.
The 24-hr precipitation amounts Pr(X>x) = fwe-x/µ Let's look at the second factor: the amounts...
How much does it rain when it rains? µ (mm/day) Let's see how the annual wet-day mean has changed over time. Here black shows observed amounts and red the predicted values. Not quite as high skill score as the wet-day frequency. Not perfect, but there is some degree of predictability.
How much does it rain when it rains? The large-scale conditions associated with the changes in the wet-day mean exhibits a land-sea contrast. But there may also be other conditions affecting the wet-day mean precipitation.
PRELIMINARY RESULTS The question: more heavy rain events? Observations: annual mean µ - Downscaled from 107 CMIP5 GCMs (RCP4.5) We can use the empirical-statistical downscaling model for the wet-day mean to make projections for the future. The example here shows the annual mean wet-day mean downscaled for the entire CMIP5 ensemble. The results suggest a range of ossible outcomes for 2100 rouglhy between 100% and 150%. If the wet-day mean increases by 50%, so will the wetday 95% (~15mm/day 22 mm/day). So we can expect to see more extreme precipitation amounts with a future global warming.
Conclusions Rain is more than just rain... Frequency and magnitude Wet-day mean µ is key Empirical-statistical downscaling land-sea contrast Wet-day mean is sensitive to changing conditions
Thank you for your attention Rasmus.benestad@met.no The R-package 'esd: 'https://www.facebook.com/rclimateanalysis Call: lm(formula = mu ~ t, data = trend) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) -10.021490 2.094946-4.784 4.39e-06 *** t 0.007884 0.001078 7.314 1.97e-11 *** Multiple R-squared: 0.2808,Adjusted R-squared: 0.2755 F-statistic: 53.49 on 1 and 137 DF, p-value: 1.973e-11 Call: lm(formula = fw ~ t, data = trend) Coefficients: (Intercept) -4.251e-03 1.301e-01-0.033 0.974 t 1.507e-04 6.696e-05 2.250 0.026 * Multiple R-squared: 0.03563, Adjusted R-squared: 0.0286 F-statistic: 5.062 on 1 and 137 DF, p-value: 0.02604 Call: lm(formula = n ~ t, data = trend) Coefficients: (Intercept) -23.297569 6.561751-3.551 0.000528 *** t 0.013186 0.003376 3.905 0.000147 *** Multiple R-squared: 0.1002,Adjusted R-squared: 0.09361 F-statistic: 15.25 on 1 and 137 DF, p-value: 0.000147 Call: lm(formula = q95 ~ t, data = trend) Coefficients: (Intercept) -28.316487 9.682669-2.924 0.00404 ** t 0.022081 0.004982 4.432 1.9e-05 *** Multiple R-squared: 0.1254,Adjusted R-squared: 0.119 F-statistic: 19.64 on 1 and 137 DF, p-value: 1.898e-05
Other aspects: duration and intervals
The common source of information ENSEMBLES DMI-HIRHAM5_A1B_ECHAM5_MM_25km-CRU_pr
The common source of information ENSEMBLES DMI-HIRHAM5_A1B_ECHAM5_MM_25km-CRU_pr Monthly totals for Copenhagen