Future extreme precipitation assessment in Western Norway – using a linear model approach

Future extreme precipitation assessment in Western Norway – using a linear model approach G. N. Caroletti and I. Barstad Bjerknes Centre for Climate Research, Bergen, Allegata 55, 5007 Bergen, Norway Geophysical Institute, University of Bergen, Allegata 70, 5007 Bergen, Norway Received: 24 November 2009 – Accepted: 26 November 2009 – Published: 18 December 2009 Correspondence to: G. N. Caroletti (giulio.caroletti@bjerknes.uib.no) Published by Copernicus Publications on behalf of the European Geosciences Union.


Introduction
Precipitation strongly influences human life, and poses great difficulty for the scientist: precipitation results from a chain of different physical processes and varies on spatial and temporal scales.Orographic Precipitation (OP) is of particular interest, as mountain regions occupy about one-fifth of the Earth's surface, are home to one-tenth of the global population and directly affect about half of the world's population (Messerli and Ives, 1997;Becker and Bugmann, 1999).OP is the most important source of fresh water for human communities and for the environment.However, extreme OP events are often the cause of mudslides, avalanches, flash floods, dam breaks, etc. (Roe, 2005).
Precipitation is one of the most difficult meteorological parameters to predict.First and most importantly, precipitation processes are parameterized in even the most complex models.In areas of complex orography, the model resolution needed to properly resolve all important precipitation processes is on the order of kilometers or even less (Smith, 1979).
Although the thermodynamic mechanism of orographic precipitation (e.g., adiabatic cooling and condensation with the uplift of air parcels) is known in its general aspects (Smith, 1979;Roe, 2005), complex topography still makes it difficult for numerical models to accurately reproduce observations (e.g., Bousquet and Smull, 2001;Georgis et al., 2003;Rotunno and Ferretti, 2003;Smith, 2003).
The challenge of matching simulated and observed precipitation is especially acute for General Circulation Models (GCMs).GCM simulations, which provide results on coarse grids of 250-300 km resolution, are not able to account for the observed horizontal variability on smaller scales without great computational investment.The 2007 IPCC Report provides future climate change assessment for precipitation on a global scale through GCMs.

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Full tical downscaling is performed by finding one or more statistical relationships between large scale and finer scale variables (e.g., regression analysis), and then estimating the true local distributions through these relationships.Dynamical downscaling refines large scale information by using physically based models to produce fine-scale information.
Several investigations compared dynamical and statistical downscaling methods for daily precipitation (Wilby et al., 1998;Murphy, 1999;Wilby et al., 2000), showing comparable performance for the two.A comparison between statistical and dynamical methods in regions of complex topography has been carried out in the Alps (Schmidli et al., 2007).Statistical methods have been shown to underestimate interannual variability over the Alps, while the better dynamical models achieve significantly higher skills in winter.Haylock et al. (2006) and Salath é Jr. ( 2005) suggest the utility of including as many models as possible when developing local climate-change projections.
The most common approach to dynamical downscaling is to use RCMs (Giorgi and Mearns, 1999;Wang et al., 2004).RCMs are high-resolution models run over a limited domain.RCMs typically use relatively low-resolution output from GCMs as boundary conditions.Other approaches involve uniformly high-resolution atmospheric GCMs (Coppola and Giorgi, 2005) and stretched grid models (Deque et al., 1995;Barstad et al., 2008); the latter method simulates the globe with a spatial resolution that varies horizontally to allow for a higher resolution around the area of interest.
The goal of this paper is to use a simpler approach, called the Linear Model (LM from now on; Smith and Barstad, 2004).LM has low computational demands that can be useful for dynamically downscaling simulated precipitation from many climate model runs.
In LM, cloud physics and airflow dynamics are described with a simple set of equations.LM has been successfully used both in idealized (Barstad et al., 2007) and realistic (Crochet et al., 2007) problems predicting orography-induced precipitation: incoming moisture is forced upslope by orography; condensation and drift of cloudhydrometeors results in precipitation.LM has also been used to simulate extreme Introduction

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Interactive Discussion precipitation events (Smith and Barstad, 2004;Barstad et al., 2007).LM has the additional benefit of being able to rigorously separate the simulated cause of changes in OP.
This study focused on Western Norway, a region of steep orography characterized by heavy precipitation on its windward side.The precipitation is the result of strong winds on the upwind side of the mountains, due to the high frequency of extra-tropical cyclones that impact the area (Andersen, 1973(Andersen, , 1975;;Barstad, 2002).Precipitation in Western Norway is dominated by forced uplift and not thermally driven convection, so the LM's structural inability to account for convection is not a so severe problem.
The precipitation simulations in this paper will result from the dynamical downscaling of data from 12 IPCC A1B scenario model simulations (IPCC Report, 2007).The A1B scenario is chosen because it represents a moderate emission scenario.Section 2 describes Smith and Barstad's Linear Model.Section 3 explains the methods used to downscale Western Norway's orographic precipitation and to compare future periods with the control scenario from the recent past.Section 4 explains the downscaled results, with a focus on the change in the number of OP events and the change in magnitude of extreme OP events.Section 5 explains how to apply the results to station data for assessing future precipitation; and by making use of LM's transparency it investigates the reasons for the change in OP extremes.Section 6 provides a summary of results.

The linear model
LM makes use of a simple system of equations to describe the advection of condensed water by a mean wind.Smith and Barstad (2004) start by considering a distributed source of condensed water S(x,y) arising from forced ascent (Fig. 1).The source is the sum of a background rate of cloud water generation and local variations created Fourier space are denoted by the simbol "ˆ"): assuming saturated conditions (see Table 1 for the explanation of the symbols used).By following Smith's (2003a) steady-state advection equations describing the vertically integrated cloud water density q c (x,y) and hydro-meteor density q s (x,y) and applying simple algebra, an expression for the Fourier transform of the precipitation distribution P is obtained: which is dependent on the source S (x,y) and considers time delays (the conversion and fall-out terms τ c and τ f ).
Combining (1) and (2) gives a "transfer function" relating the Fourier transform of the terrain ĥ and the precipitation field P : whose denominator's factors represent airflow dynamics (first term), cloud delays and advection (second and third terms).
The precipitation distribution is then obtained by an inverse Fourier transform P (x,y) = P (k,l )e i (kx+l y) d kdl . (4) The A1B scenario provides daily data for mean horizontal wind (U,V ) and mean moist stability frequency N m .These are constant values for the whole domain, and are updated daily.
In short, the Linear Model describes the effect of orography and mean wind on precipitation, and with some complexity the effect of temperature, humidity, moist stability, conversion and fallout times of hydrometeors.Introduction

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Downscaling GCMs
General Circulation Models (GCMs) have typically too coarse a grid to adequately resolve terrain responsible for orographic precipitation.The LM approach can be used to dynamically downscale GCM data.Variables and parameters used for input to the LM are shown in Table 2.
21 models performed A1B scenario testing, for a total of 41 model runs (Table A1).Not all of them were available due to incomplete data sets or other inconsistencies that could affect the plausibility of our final results.Those which had missing data were dismissed, along with those showing unreasonable predictions for Western Norway temperature (annual average temperature between −40 • C and 0 • C).Our selection are based on 12 simulations from 10 GCMs (Table 3).Conversion and fallout times have been set to 1000 s.Typical conversion times are between 200 s and 2000 s (Smith, 2003); longer residence times within clouds result in a delay of the precipitation.The time delays τ=1000 s values are not expected to be exact, but generally summarize the combined effect of many cloud physics processes (Barstad and Smith, 2005), and have been used in LM for studies at the regional scale (Smith, 2006;Crochet et al., 2007).Longer time delays typically result in more precipitation being advected past regions of steep topography, increased precipitation on the lee side of the topography and lower precipitation intensity overall.Conversely, shorter time delays result in more intense rain shifted upwind (Smith and Barstad, 2004;Barstad et al., 2007).
The Linear Model's grid corresponds to the Digital Elevation Model (DEM) GTOPO30 topography grid (US Navy, 2003), and has a resolution of 30 .At a latitude of 60 • , this corresponds to an average grid spacing of about 450 m×900 m, sufficient to resolve important scales affecting orographic precipitation.
Our main concern are extreme OP events, so the only days considered are those with a relative humidity above or equal to 85%.Lower relative humidities result in relatively weak to no OP (Barstad et al., 2007).In addition, only days with wind direction between Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion 180 • and 300 • (westerly winds) were considered, since they are the only ones to give significant OP (Barstad, 2002).Precipitation intensity is calculated in mm/day.There are several possible ways of defining an extreme event.One alternative is to use the tails of a climatological distribution, through the use of quantiles (Jones, 2000;Cooley, 2005).A second alternative ("peak-over-threshold" method) is to consider as extreme any result exceeding a certain threshold value (Cooley, 2005).An advantage of using the percentile method when performing model-comparison is that it is a relative method that can be used for all model runs and thus provides consistency.
In this paper, the 99th percentile of the distribution is used to define an extreme OP event.Different models use different parameterizations and we do not know a priori which ones are most appropriate for a future situation.Thus, looking at the absolute values could be misleading (Klein Tank and Konnen, 2003).We compare instead the extreme OP intensities of future periods to the control period data within a particular simulation.If simulations from different models agree on a relative increase, then it is more likely to be a consequence of the scenario and not to result from individual model variability.
The model domain is between 57 • 30 and 64 • 20 N and 4 • and 10 • 40 E.This includes all of southern Norway.In this area we have selected the 74 grid points nearest to weather stations that were active and measured precipitation during all of the control period 1971-2000.The stations are all located in Western Norway.
Figure 3 shows an increase in the relative number of days with orographic precipitation in future periods relative to the control period.All model runs show an increase in OP days in the future periods, although not all agree on whether there will be more days with OP in the first or in the second future period.Introduction

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In order to evaluate the relative change in the extreme OP intensity from the control period to the future periods, we normalize the absolute 20-years 99th percentile of every model to its own control period 30-years 99th percentile.
The result of this procedure for both future periods is shown in Fig. 4. All models show an increase in the intensity of Orographic Precipitation extremes.The mean ensemble result shows a strong +10% and +16% increase in extreme OP in the 2046-2065 and 2081-2100 intervals, with associated standard deviations of 6% and 11%, respectively.
A time evolution of the ensemble mean 99th percentile of OP is plotted in Fig. 5, with the standard deviation taken into account.Even with the most conservative prediction, we still see an increase in the intensity of the extreme events at the station.
To see if there is a change in pattern as the moist air proceeds into the fjords and mountains, we look at four sections, perpendicular to the coast, two along-fjord (Sognefjord in Sogn-og-Fjordane county and Hardangerfjorden in Hordaland county) and two along-wind cross-sections (one in Hordaland from the city of Bergen to the city of Voss, and the other over the districts of Flora and Gloppen in Sogn-og-Fjordane).The four cross-sections allow us to witness the effect on precipitation of the ascension of the air along its most favorable path (Fig. 6).All show a strong increase in OP extremes in future periods towards the control scenario.There is also an increase in OP extremes from the 2046-2065 period to the 2081-2100 period.
The largest increase in OP intensity happens on the coast, but these stations also exhibit the least significant increases in absolute values, as seen from Table 4 (which shows these only for the first cross-section -Flora-Gloppen).The trend is evident also when grouping all 74 stations on account of their proximity to the coast and elevation in coastal stations, fjord stations, inland/valley stations and mountain stations (Table 5 and Fig. 7 5 Further applications

Assessment
Station observations, provided by the Norwegian Meteorological Institute, can be used as a basis for assessing future precipitation changes.We apply the average relative increase in downscaled OP extremes to the station data to generate an estimate of the future absolute intensities of extreme OP.The 99th percentile of 1971-2000 OP extremes for the Flora-Gloppen section are shown in Table 8.Applying the relative increase for each individual station from the LM (Table 6) results in the 2046-2065 and 2081-2100 estimates shown ("local" method).
For instance, for Gjengedal the 30 years observed 99%-ile of OP is 66.7 mm/day.
The model indicates an increase in Gjengedal OP extreme intensities for the 2046-2065 time period of about 10%, with an associated standard deviation of 4%.Thus, the absolute value for 2046-2065 is 73 mm/day, with a standard deviation of 3 mm/day.An alternative method to retrieve absolute values of future precipitation is to use the relative increase depending on the "geographic setting".In this method, the mean relative increase in extreme OP for all the stations from the group is applied to all stations.This method could provide more reliable data, especially where the precision of our model data is suspect.In situations of high quality output from the downscaled LM, less accurate forecasts could result compared to the "local" method because local variabilities will be smoothed away in the averaging process.Moreover, the mean result will be biased depending on the distribution of available weather stations.The increase and associated standard deviations for the four geographical groups are shown in Table 7. Applying these relative increases to the observed data of the Flora -Gloppen section, we get the results shown in the "geographic setting" columns of Table 8.
We see that there is some difference in the results of the two methods; if we take for instance Grøndalen, for 2046-2065 we see that the value is 94±6 for the first method and 90±5 for the "geographic setting" method.A definitive statement on which method is preferred cannot be provided without a further study of local meteorology.Introduction

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Influx analysis
LM can also be used to understand the mechanisms behind downscaled changes in OP extremes.
In order to do this, we calculate the influx of moist air into the region, where U is the horizontal wind magnitude; Lγ is the water vapor scale height.
Furthermore, e S (T ) is the saturation vapor pressure, T ref is the temperature at the ground, R v =461 J kg −1 K −1 is the gas constant for vapor, L=2,5×10 6 J kg −1 is the latent heat and γ is the environmental lapse rate (Smith and Barstad, 2004).
There is a linear relationship between the moist air influx and the precipitation in LM (cf.transfer function (3)); the rest of the OP extreme change is connected to the wind direction at a given station.Figure 8 shows the results of an assessment of the cause of 2046-2065 extreme OP intensities change at the Bergen sample station.Ten simulations out of twelve show a positive sign to the change from moisture influx, and eight out of twelve show a positive sign to the change from wind direction.
The Linear Model offers the possibility to break down the moisture influx to its components.Smith and Barstad (2003) show that the moisture influx (F ) depends on density ρ S (T ), H w (N,T ) and wind speed U: If we write H=H w × ρ S ref , the increase in influx will be: In this way, using the properties of partial differences, we get: We can thus rewrite Eq. ( 6) using Eq. ( 7): In Eq. ( 8) we can compute separately the influence of wind magnitude from the sum of temperature and stability influences on the influx (Fig. 9).A residual, spurious term emerges from the approximations used, but it is shown to be small.The effect of temperature and stability can now be assessed separately, to see how they contribute to the change in moisture influx.Figure 10 shows that the change in moisture influx is driven primarily by temperature changes in most models.
The combined result of these assessments for Bergen in 2046-2065 (Table 9 and Fig. 11) suggests that temperature is the dominant factor behind increases in OP extreme intensities.All models agree on a temperature increase from the control period to the future period.The dominant role of temperature changes in driving extreme OP increases is our most important and robust result.
Wind speed and direction are important factors to understand a single model, but there is a large model-to-model uncertainty in the importance of both, as evidenced by the high values for standard deviation in Table 9.
Wind direction has an important impact on precipitation.Westerly winds tend to produce more precipitation over the whole region because of the large-scale influence of topography.Local, small-scale topography can partly block moisture influx coming from some directions.For instance, at the Bergen station, LM shows an increase in OP when the wind direction is comprised between 272 simulations could be that the positive and negative contributions from the models will cancel out and emphasize even more the importance of temperature.Stability gives only a negligible contribution.

Discussion
Several studies (Trenberth et al., 2003;Allan and Soden, 2008;Liu et al., 2009) have attributed the widespread increase of heavy precipitation to global warming.Trenberth et al. (2003) noted that the increase in surface temperature is stronger at higher latitudes.However, the atmospheric general circulation tends to move the moisture from polar regions towards lower latitudes, so there is need for studies addressing whether the increasing moisture would be within reach of extratropical storms that impact the high-latitude regions -a necessary condition for these regions' warming to have an impact on high-latitude precipitation.Zhang et al. (2007) used observations and GCM simulations to determine whether there was an anthropogenic-warming induced change in precipitation in the 1925-1999 time period.The study, which addressed precipitation over the whole planet, showed an increase in precipitation both in the observations and in the models for Norway, suggesting that these conditions might already have happened during the last century's warming.
Our study addresses Trenberth's concerns in that it shows an increase of OP occurrences at high latitudes, and indicates that temperature change is responsible for about 50% of the future increase in extreme OP values.Temperature changes are more robust than changes to the winds.Due to the uncertainties in wind changes, it is difficult to establish how important they might be in future scenarios.Using wind values from an RCM or downscaling the IPCC wind values could address this problem.Introduction

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Summary
An efficient downscaling method, Smith and Barstad's Linear Model, has been used to physically downscale precipitation from 12 model runs of the IPCC 2007 A1B scenario over Western Norway.The results show an increase in OP occurrence and an increase in the intensity of OP extremes over 74 grid points corresponding to Norwegian weather stations.The increase in intensity is around 10% of the absolute values for the 2046-2065 scenario and around 15% for the 2081-2100 scenario.An an assessment of absolute future changes to extreme OP has been conducted, based on the relative increase of the model results and on weather station observations.The main reason for the increase of precipitation has been investigated for the Bergen meteorological station.The increase in moist air influx contributes to about two thirds of the increase, while the rest depends on the wind direction.By separating out the factors that contribute to moisture influx, results show that temperature increases are the main cause increased influx, and thus extreme Orographic Precipitation, for all models.Temperature accounts for roughly 50% of the increase in magnitude of the extreme OP events.The present paper is meant as an introduction to possible uses of analysis connected to LM downscaling and shows methods that can be applied generally to many different model simulations.Downscaling climate scenarios with LM seems to open up interesting possibilities for insight for both climatologists and weather forecasters.
by terrain-forced uplift.Smith and Barstad propose an upslope model enhanced by considering airflow dynamics that provide a source term in Fourier space (variables in ). Coastal stations reach almost a 20% increase in the 2081-2100 time period when compared to 1971-2000 extreme OP intensities, while all others present similar result ranging around 9% in2046-2065 and 14% in 2081-2100.
• and 269 • , around 255 • , around 231 • , and between 217 • and 203 • .Because of the big uncertainties in the wind values, including more simulations might give a better picture of the wind's role; however, a possible outcome of adding more

Fig. 6 .Fig. 9 .
Fig. 6.Twelve-models relative increase in extreme OP for four sections of Norway's western coast.The stations' locations are shown on the map on the right (see Fig. 2 for the position of this region in the domain's area).The gray shading shows the height a.s.l.along the sections.
ref is the saturation water vapor density at the ground, and

Table 1 .
Some symbols used in the model.

Table 4 .
Mean of extreme OP intensities for twelve model-runs for Flora and Gloppen districts stations, expressed in absolute values (mm/day), including standard deviation.

Table 5 .
Changes in extreme OP intensities by geographic setting, relative to the 1971-2000 control period."Mountain" stations are inland stations located above 400 m a.s.l.

Table 6 .
Flora-Gloppen section.Relative increase of extreme OP intensity to the control scenario as a mean intensity of 12 LM-downscaled model runs.

Table 7 .
Twelve-model runs 99%-ile of orographic precipitation, expressed as an increase relative to the 1971-2000 control period, for all stations divided into four groups depending on their geographic setting, with associated standard deviation.

Table 8 .
Flora-Gloppen section.Extreme OP intensity of station data from Norwegian Meteorological Institute and assessment of future orographic precipitation extremes, obtained via local increase method and geographic setting increase method.

Table 9 .
Percent contributions for the increase in extremes by the factors affecting precipitation.

Table A2 .
Ratio of days with orographic precipitation to total number of days for three time slices, 12 model runs, Bergen-GFI station.
a Increase is in both cases evaluated in respect to the 1971-2000 control period.

Table A3 .
99%-ile of orographic precipitation for 12 model runs, Bergen Florida station.The first and last year of the scenarios have a three years forward running mean, while the second and next-to-last have a four years forward running mean.
a Increase in both cases refers to the 1971-2000 period.

Table A4 .
Mean values for wind magnitude, stability and temperature during extreme OP events, comparing 1971-2000 means with 2046-2065 for every model run and showing the 12-model runs average.