Statistical downscaling of daily precipitation over Greece

Transcription

1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. : () Published online June 7 in Wiley InterScience ( DOI:./joc.557 Statistical downscaling of daily precipitation over Greece Ioannis Kioutsioukis, a * Dimitrios Melas a and Prodromos Zanis b a Laboratory of Atmospheric Physics, Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece b Department of Meteorology-Climatology, School of Geology, Aristotle University of Thessaloniki, Thessaloniki, Greece ABSTRACT: The capability of a multi-site non-homogeneous hidden Markov model (NHMM) to downscale winter daily precipitation over Greece is explored for the period 97. The input variables were selected from NCEP Reanalysis Data following an optimization procedure and include the precipitation rate as predictor. The most parsimonious NHMM identified five weather states. Successively, the forecast skill of the model was tested against sequentially withdrawn data. The NHMM reproduced successfully both the station-scale statistics like the occurrence and amount of precipitation as well as the spatial pattern of precipitation such as the correlations between stations and the Log-Odds ratios. Also, the temporal correlation in the data at most of the rain gauges was successfully captured at seasonal timescales. Finally, the model was capable of reproducing extreme precipitation events. It modelled successfully the dry spells as well as most of the indices corresponding to very wet events, including the maximum 5-day precipitation amount, the number of extreme precipitation events and their corresponding fraction of the total precipitation amount, better to the stations where the very wet events are not associated with local scale features that could not be captured by the large-scale predictors. The weakest reproduced indices correspond to the mean wet day precipitation and the 9th percentile of precipitation on wet days where the model captured their magnitude but not their interannual variability. Copyright 7 Royal Meteorological Society KEY WORDS daily precipitation; statistical downscaling; Greece; non-homogeneous hidden markov model; multi-site rainfall Received 9 September ; Revised 9 March 7; Accepted 6 April 7. Introduction The concern about climate change along with its possible associated global warming has contributed to the development of sophisticated General Circulation Models (GCMs) over the last decade. Those models simulate large-scale atmospheric processes reasonably well with a typical resolution of.5.5 degrees. At smaller scales, however, there are important climatological processes such as precipitation where GCMs fail systematically to reproduce the observed precipitation statistics at the spatial and temporal scale required for regional climate impact studies. In particular, GCMs tend to overestimate the frequency of daily precipitation and underestimate its intensity. The modelling of the sub-grid variability (downscaling) is achieved through either computationally demanding regional climate models (i.e. based on a deterministic approach) or statistical models (i.e. relate the feature of interest to known predictors based on a statistical optimization approach). Statistical downscaling (SD) techniques model precipitation amounts conditional on the values of a set of synoptic atmospheric variables. Thus, at the core of statistical prediction is the selection of the appropriate atmospheric * Correspondence to: Ioannis Kioutsioukis, Aristotle University of Thessaloniki, Physics Department, Laboratory of Atmospheric Physics, PO Box 9, Thessaloniki 5, Greece. iannos@gmail.com; kioutio@auth.gr predictors that reflect the real physical processes. The various SD techniques can be classified into three broad categories (Wilby et al., ): Weather Classification Schemes (e.g. analogue method, non-homogeneous hidden Markov models(nhmm)) cluster the observation vector into a finite number of discrete weather states, which are defined either a priori from synoptic patterns or through an objective optimization scheme (e.g. cluster analysis), Regression models (e.g. multiple regression, canonical correlation analysis, artificial neural networks) and Weather Generators (e.g. stochastic models, Markov chains) replicate the (local) statistical characteristics of climate variables. Recent studies have compared the skill of different SD techniques in several dissimilar sites (e.g., Wilby et al., 99; Zorita and von Storch, 999; Haylock et al., ). However, the intercomparison, within the different studies, does not clearly favour a specific methodology. The hidden Markov model (HMM) (Rabiner and Juang, 96) is an SD model that assumes the existence of weather states. Its main difference with other proposed weather state models lies in the way how states are determined. HMM identifies states from the precipitation data and not from apriori determined synoptic patterns (where precipitation does not affect the state definition). A HMM represents a stochastic process, in which the Copyright 7 Royal Meteorological Society

2 6 I. KIOUTSIOUKIS ET AL. observed process (e.g. multi-site precipitation) is conditional on an underlying hidden process (the weather states). Transition probabilities from one weather state to the next are fixed and conditioned only on the current state. Alternatively, the NHMM, introduced by Hughes and Guttorp (99), has variable transition probabilities that are conditioned by atmospheric predictors. Recently, NHMMs have shown their capability to reproduce daily precipitation probabilities, spatial patterns in precipitation occurrence, wet and dry spell length statistics and the probability distributions of precipitation amounts at multiple sites in both temperate mid-latitude regions (Pacific north-west USA and south-western Australia) (Bellone et al., ; Charles et al., ; Mehrotra et al., ) as well as tropical regions (Robertson et al., ) with observed precipitation probabilities reaching even %. The Eastern Mediterranean is an area of relatively high predictability for seasonal precipitation (e.g. Eshel and Farrell, ; Haylock and Goodness, ; Kioutsioukis et al., ). In this work, we explore the predictability for individual point locations. In particular, we investigate the ability of NHMMs to generate accurate rainfall occurrences and intensities at a network of stations distributed over Greece (seasonal precipitation probabilities in the region do not exceed.) and which is characterized by a highly non-homogeneous domain where precipitation is generated by several mechanisms including fronts, localized convective systems and coastal circulation systems. The objectives of this work are to: downscale with NHMM the winter precipitation (JFM) over Greece during the period 97 by using atmospheric predictors from the NCEP/NCAR Reanalysis data, including precipitation rate (Widmann et al., ; Schmidli et al., ). cross-validate the skill of the method for an independent period in reducing the deviation between the large-scale precipitation and the station-scale precipitation. evaluate the performance of the approach in handling extreme events through the use of selected climatic indices.. Methodology.. Modelling approach A brief description of the NHMM dynamics is given below. Further details are found in Kirshner (); Kirshner and Smyth (). The NHMM assumes the existence of a finite number (K) of weather states (S,S,...,S K ) which progress according to a temporally non-homogeneous Markov chain. Let S t be the discrete weather state at time t (one of S,S,...,S K ), T be the total length of the time series and S :T = (S,...,S T ) be the sequence of weather states corresponding to the precipitation time series R :T = (R,...,R T ). The transition probabilities for the Markov chain are assumed to be a function of a multivariate predictor input time series X :T corresponding to measured atmospheric variables. Precipitation occurrences at a network of stations are assumed to follow an auto-logistic model, given a weather state, while precipitation amounts are assumed to be conditionally independent between stations within weather states (i.e. spatial dependence is captured implicitly via the state variable). The temporal evolution of the precipitation field modelled through NHMM rests on the following conditional probabilities assumptions: P(R t S :t,r :t,x :t ) = P(R t S t ) P(S t S :t,x :t ) = P(S t S t,x t ) (a) (b) Equation (a) states that the precipitation field on day t(r t ) depends only on the weather state of day t(s t ) and thus it assumes R t being independent from the past weather states, precipitation values and atmospheric variables. Equation (b) states that the weather state on day t (S t ) depends only on the weather state on the previous day and the values of the atmospheric variables on day t. The adopted parameterization of the transition probabilities is given by the following logistic regression: P(S t = i S t = j,x t = x) = exp ( σ ji + ρ i x) K exp ( σ R,ρ R D () σ jk + ρ k x) k= In Equation () K is the number of weather states. The functional form of Equation () can be shown to be equivalent to the one defined in Hughes et al. (999) and Bellone et al. (), i.e. it is the product of a baseline transition matrix with a positive function of atmospheric predictors. More details about the kind of model on Equation () are provided in Robertson et al. (). Daily precipitation amounts at each station are parameterized as a combination of a delta function (dry days modelling) and an exponential function (wet days modelling) and which is represented as follows: P (R t = r S t = i) = M P ( Rt m = r S t = i ) m= P(Rt m = r S t = i) { π = ( ) im : Rt m θ π im λim exp ( λ im Rt m ) : Rt m >θ () In Equation () M is the number of auxiliary atmospheric variables. Finally, the parameter estimates (σ, ρ, π, λ) are obtained by maximizing the likelihood via the Expectation-Maximization (EM) algorithm (Dempster et al., 977). Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

3 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE 6 FLORINA SERRAI KAVALA ALEXANDROUPOLIS 9 KOZANI IOANNINA LARISSA KERKIRA NEA ANCHIALOS PREVEZA LAMIA AGRINION KEFALLINIA PATRAI ELEFSINA ARAXOS ATHENS ANDRAVIDA TRIPOLIS LIMNOS MITILINI CHIOS SAMOS 7 KALAMATA KOS KYTHIRA RHODES RETHYMNON IRAKLION IERAPETRA KARPATHOS Figure. The network of stations distributed over the study domain. The Dotted Line refers to the NCEP grid (Gauss) for precipitation (.9 lat.9 lon) while the Continuous Line refers to the NCEP grid for the other meteorological variables (.5 lat.5 lon). This figure is available in colour online at Data... Predictant Precipitation amounts were recorded at stations covering Greece (Figure ). No data was missing for the study period 97. The threshold θ in Equation has been set to mm.... Predictors Thirty-five gridded (E 7.5E, N.5N) atmospheric variables provided by NCEP (Table I) were considered as potential candidates for precipitation predictors. The selection approach and the representation of the variables in a summary form (principal modes of weighted averages across the domain) are based on the singular value decomposition (SVD) technique (von Storch and Zwiers, 999; Bellone et al., ). Briefly, the correlation matrix C, where the element c ij gives the correlation between the precipitation at station i and the NCEP atmospheric variable Y at node j, is decomposed using the SVD method: C (NxG) = U (NxN) S (NxG) V (GxG) () In Equation (), N and G refer respectively to the number of rain gauges () and grid nodes (6). The columns of the unitary matrix U are called left singular vectors and form an orthonormal basis of C N. Similarly, the columns of the unitary matrix V are called right singular vectors and form an orthonormal basis of C G. Table I. The examined atmospheric input variables from ncep. NCEP INPUTS LEVEL Precipitation rate Surface Temperature (surface) Surface Sea level pressure Surface Geopotential height, 5, 7, 5, Relative humidity, 5, 7, 5, Specific humidity, 5, 7, 5, Temperature (air), 5, 7, 5 E-W wind, 5, 7, 5,, S-N wind, 5, 7, 5,, Precipitable water Surface The diagonal matrix S has the same dimension as C, with non-negative diagonal elements in decreasingordercalled singular values. The new summary variable is constructed by multiplying the atmospheric variable Y with the ith column of V : Y SVD = Y (T xg) V (Gx) (5) and explains the s i / k s k of the correlation between Y and the observed precipitation. T is the total length of the time series... Setup of NHMM Simulations The total number of auxiliary atmospheric variables along with the number of hidden states used in the NHMM Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

4 6 I. KIOUTSIOUKIS ET AL. model is estimated on the basis of the Bayes Information Criterion (BIC): BIC = L + p log(t ) (6) where L is the log-likelihood, T the total length of the time series (7 records) and p the number of model parameters. The following steps are undertaken to identify the optimum NHMM order and the best atmospheric predictors:. Determine the model order by minimizing BIC on a HMM for precipitation occurrence. Compare results of the model selected after optimization with models of lower order and identify the most parsimonious.. Select the input variables that minimize BIC on a NHMM for precipitation occurrence; reconfirm the results in terms of model order. Finally, the precipitation amounts are simulated through a NHMM with the hidden states identified in step () and by using the summary variables identified in step () as auxiliary variables.. Results for downscaled scenarios.. Estimation of NHMM Parameters Table II shows a subset of the results obtained from fitting the NHMM model to the observed precipitation data using as predictors the three NCEP atmospheric variables: the large-scale precipitation field, the geopotential height at 5 hpa and the relative humidity at 7 mb (skill scores of all input variables are given in Table III). BIC decreases rapidly with N increasing from to 5 and reaches the minimum at N = 5 before increasing slowly for N>5. Similarly, the log-likelihood increases sharply with N increasing from to 5, then increases slowly until reaching the maximum at N = and start decreasing for N>. Hence in terms of BIC and L, the most parsimonious choice of model order is for N = 5... State Description Following the results illustrated in Section., a NHMM with five states using three atmospheric variables in summary form (large-scale precipitation field, geopotential Table II. Comparison of several NHMMs using the three input variables: precipitation rate (NCEP), Geopotential Height (5 hpa) and Relative Humidity (7 mb). Number of States BIC L Table III. Skill scores of the summary variables. CC is the mean absolute Pearson correlation among all the stations between the summary variable and the observed precipitation and CV the percentage of correlation explained by the first summary variable. NCEP Variable CC CV Precipitation rate..9 Surface temperature.9. Sea level pressure.6.9 Geopotential height hpa..9 Geopotential height 5 hpa..97 Geopotential height 7 hpa..99 Geopotential Height 5 hpa.7.99 Geopotential height hpa..99 Relative humidity hpa..9 Relative humidity 5 hpa..9 Relative humidity 7 hpa..95 Relative humidity 5 hpa..97 Relative humidity hpa.6.9 Specific humidity hpa..9 Specific humidity 5 hpa..97 Specific humidity 7 hpa.. Specific humidity 5 hpa..55 Specific humidity hpa..9 Air hemperature hpa.. Air hemperature 5 hpa.. Air hemperature 7 hpa.. Air hemperature 5 hpa.. E-W wind hpa..7 E-W wind 5 hpa..69 E-W wind 7 hpa.7.7 E-W wind 5 hpa.5.7 E-W wind hpa..6 E-W wind hpa.7.5 S-N wind hpa.. S-N wind 5 hpa.7.9 S-N wind 7 hpa.7.95 S-N wind 5 hpa..95 S-N wind hpa.9.9 S-N wind hpa..9 Precipitable water..96 height at 5 hpa, relative humidity at 7 mb) was then fit to the precipitation amounts. State (Figure ) corresponds to the dry days representing approximately half of the days for the examined period (9%, see Table IV). On the contrary, State has a high probability of precipitation all over the region with a mean precipitation of over mm; precipitation amounts are higher in the areas of the north-west and south-east and lower in the middle area. State is highly persistent followedbystate(tablev)whilestatesand5have equally high transition probabilities towards other states like state (wet) towards state (dry) or state 5 (wet) towards state (very wet). States and 5 look very similar as both refer to rainfall in the continental part but originate from different synoptic situations as shown in Figure. Additionally, State 5 acts as precursor to State (very wet) and State as precursor to State (dry). Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

5 6 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE (a) HS = HS = HS = HS = HS = 5 (b) HS = HS = HS =.5 HS = HS = 5 Figure. (a) Precipitation Probabilities corresponding to the five weather states identified by the NHMM including the first summary variable for geopotential height at 5 hpa and relative humidity at 7 mb (b) As in Figure (a) but for precipitation amounts. This figure is available in colour online at Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

6 6 I. KIOUTSIOUKIS ET AL. Table IV. Rainfall statistics for the identified weather states. Weather state State frequency (No days) State frequency (%) Precipitation probability (%) Mean Wet day precipitation (mm) Table V. Transition probabilities. From/To Finally, State is mainly associated with maritime rainfall. Also, the identified states are realistically discrete in meteorological terms. Figure (a) illustrates the principal field of geopotential height (GH) at 5 hpa (average field over the days classified into a particular state) associated with each state through the Viterbi algorithm (Rabiner and Juang, 96). State (dry) corresponds to the maximum GH and state (wet) to the minimum over the area. Similarly, State (dry) corresponds to the minimum relative humidity (RH) (Figure (b)) and maximum sea level pressure (SLP) (Figure (c)). In addition, State points to the days with prevailing anticyclonic synoptic conditions (Figure (c)) with very high RH (Figure (b)). The SLP, although it was not selected as a predictor, represents the true forcing factor and hence its contours (Figure (c)) are displayed in order to show that the NHMM in its present configuration reflects the real physical processes without being overparameterized. In meteorological notation, the weather states (Table IV) and their transitions (Table V) can be summarized as follows: State 5 corresponds to westerly flow at 5 hpa associated with a latitudinal pressure gradient. Also, it is linked to a surface low pressure system over Italy. State can be considered as a continuation of State 5 with the low pressure system moving eastwards and extending over Greece. This is observed both at GH (at 5 hpa) and at SLP. State can also be considered as further development of State with the low pressure shifting further (a) 5 HS = HS = HS = HS = 5 5 HS = Figure. (a) Contour of the geopotential height at 5 hpa for each weather state identified by the NHMM (b) As in Figure (a) but for the relative humidity at 7 mb (c) As in Figure (a) but for the sea level pressure. This figure is available in colour online at Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

7 65 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE HS = 6 7 (b) 5 HS = HS = HS = HS = HS = (c) 5 5.e+5 HS = 5 HS = HS =.5e+5.6e HS =5 Figure. (Continued). Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

8 66 I. KIOUTSIOUKIS ET AL. (a) Nearest NCEP gridpoint Station Data (b) Nearest NCEP gridpoint 6 6 Station Data Figure. quantities against the Reanalysis Data (nearest NCEP grid point): (a) precipitation probabilities (left) (b) mean wet day precipitation (mm) (right). This figure is available in colour online at (a) (b) (c).9 (d) Figure 5. quantities against those modelled by NHMM: (a) precipitation probabilities, (b) mean wet day precipitation (mm), (c) Spearman correlations between all stations pairs, (d) Log-Odds ratios. This figure is available in colour online at eastward over eastern Greece and Turkey. Due to this further eastward shift, higher precipitation amounts are noticed in the eastern parts of Greece. State also evolves from State with a further eastward shift and weakening of the low pressure system whilst anticyclonic conditions prevail over Greece. Due to the anticyclonic conditions, the lowest amounts of precipitation (driest conditions) and the lowest RH values are recorded. From a transport perspective it is presumable that advection of cold and dry air from the North occurs in this state. This flow pattern looks very similar to the etesian winds pattern in summer time. State is associated with the transport of air masses from NW over Greece. State can be a further development of State and also a precursor state of State... Simulated Precipitation Amounts... Hindcast As stated in the introduction, GCMs tend to overestimate the frequency and underestimate the intensity of wet day precipitation. This is clearly shown in Figure where observed precipitation occurrence and amounts are plotted against the nearest-neighbourhood NCEP grid point. The NHMM improves substantially the picture after downscaling the GCM output (Figure 5(a), (b)). The quality of the fit, i.e. how well the NHMM reproduced the spatial pattern of the precipitation, is examined through the Spearman correlation between all the station pairs (Figure 5(c)) and the Log-Odds ratios (Figure 5(d)). The Log-odds ratio for stations i and j varies in between and +. A Log-Odds ratio with a large value either positive or negative indicates, respectively, a strong positive or a strong negative association whereas a value Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

9 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE 67 5 ALEXANDROUPOLIS 5 NEA ANCHIALOS AGRINION 5 5 ANDRAVIDA 5 5 KEFALLINIA 5 ARAXOS 5 ATHENS 5 ELEFSINA 5 IRAKLION 5 5 IERAPETRA 5 5 KAVALA 5 5 KOZANI 5 5 KERKIRA 5 5 IOANNINA 5 LARISSA LIMNOS 5 5 LAMIA 5 KALAMATA KOS KYTHIRA 5 5 KARPATHOS 5 SERRAI FLORINA PREVEZA 5 MITILINI 5 PATRAI CHIOS TRIPOLIS 5 SAMOS 5 RHODES 5 Figure 6. Quantile Quantile plots of observed versus modelled amounts at stations. This figure is available in colour online at (a) (b) Figure 7. (a) Interannual variability of seasonal precipitation occurrence estimated through the Pearson correlation between observed (station data) and modelled (NHMM) time series of the Seasonal Number of Wet Days. The correlation ranges for filled circles, crossed circles and open circles are..,.7. and.6.7, respectively. Stars denote correlations below.6 (b) As in Figure 7(a), but for the root mean square error (RMSE). The RMSE ranges for filled circles, crossed circles and open circles are 5 7 (days), 7 9 (days) and 9 (days), respectively. Stars denote RMSE above days. This figure is available in colour online at close to reflects a weak association: ( ) log odds ratio N N = log N N (7) In Equation (7), the term N ij represents the number of days where precipitation occurs at () both stations i and j (N ), () none of the stations (N ), () station i only (N ) and () station j only (N ). The rank correlations and the log-odds ratios were well reproduced apart from a small fraction of points. Further investigation revealed that the majority of those points are not related to particular stations but are associated with the unexplained local spatial correlation not captured by the hypothesis of conditional spatial independence, given the weather state. The suitability of the exponential function for fitting the precipitation data distribution is evaluated through quantile quantile plots of the observed precipitation versus the predicted precipitation (Figure 6). It appears that the fit varies from station to station. The best fit is found at the wettest sites (e.g. Ioannina, Preveza) and the islands whereas the worst fit is produced at those Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

10 6 I. KIOUTSIOUKIS ET AL. (a) (b) Figure. (a) Interannual variability of seasonal precipitation amounts estimated through the Pearson correlation between observed (station data) and modelled (NHMM) time series of the Total Seasonal Precipitation. The correlation ranges for filled circles, crossed circles and open circles are..,.7. and.6.7, respectively. Stars denote correlations below.6 (b) As in Figure (a) but for the root mean square error (RMSE). The RMSE ranges for filled circles, crossed circles and open circles are 6 (mm), 6 9 (mm) and 9 (mm), respectively. Stars denote RMSE above mm. This figure is available in colour online at (a). (b) Figure 9. Quantities against the realizations modelled by the NHMM for the reserved period: (a) precipitation probabilities (left), (b) mean wet day precipitation (mm) (right). This figure is available in colour online at stations having marginally significant correlations with the NCEP precipitation (e.g. Larissa). The results did not improve significantly following the addition of a second exponential term in Equation. Figure 7 shows the interannual variability of the modelled total number of seasonal rain days per station in terms of their Pearson correlation along with the observed rain days. Besides the capability to model the spatial structure of the precipitation field, as seen in the previous paragraphs, the NHMM also captured the temporal structure of the precipitation field. Stations exhibit generally high correlation coefficients at all sites (more than. in the majority of the stations) except at one station (Serres). The root mean square error (RMSE) of the downscaled seasonal rain days is about 7.7 days. A similar conclusion is reached by looking at the interannual variability of the total seasonal precipitation at each station (Figure ). All stations had generally correlation values above.75 with maximum values found at the coastal stations of Kos (.), Samos (.7), Ierapetra (.7) and Iraklion (.7). As in the case of the station of Serres, precipitation amounts were not modelled adequately also in the stations of Larissa and Kozani, which were previously identified through the q q plots. The RMSE of the downscaled seasonal rainfall amounts is. mm.... Forecast The NHMM is tested for its ability in providing accurate downscaling in cases of reserved data, i.e. data, which is not used during the training phase. Figure 9 presents the results for the full period obtained after sequentially withdrawing 6-year blocks each time (i.e. forecast for the years is based on using the 977 dataset for training, forecast for the years is based on using the and 9 datasets for training, etc.). Ten different realizations were generated. The encircled results correspond to the median forecast per station (Figure 9). A comparison with Figure 5 (hindcast) reveals that model predictions are quite robust to the inclusion of hidden data. The same conclusion is reached from the q q plots (Figure ), which are generated from one randomly selected realization. The skill of the NHMM in reproducing the interannual variability of extreme events (heavy precipitation, consecutive dry days) is evaluated through the use of selected precipitation indices (Nicholls, 995; Haylock et al., ) that are grouped into three clusters: statistical distribution of precipitation: pav (average precipitation on all days), poc (number of events > threshold), pint (average precipitation on days > threshold) Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

11 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE 69 ALEXANDROUPOLIS 5 5 NEA ANCHIALOS AGRINION 5 5 ANDRAVIDA 5 5 KEFALLINIA 5 ARAXOS 5 ATHENS 5 ELEFSINA 5 IRAKLION 5 5 IERAPETRA 5 5 KAVALA 5 5 KOZANI 5 5 KERKIRA 5 5 IOANNINA 5 LARISSA LIMNOS 5 5 LAMIA 5 KALAMATA KOS KYTHIRA 5 5 KARPATHOS 5 SERRAI FLORINA PREVEZA 5 MITILINI 5 PATRAI 5 CHIOS 5 5 TRIPOLIS 5 SAMOS 5 RHODES 5 Figure. Quantile Quantile plots of observed versus modelled amounts at stations for the reserved period. This figure is available in colour online at very wet events: pq9 (9th percentile on days > threshold), px5d (maximum precipitation from any five consecutive days), pfl9 (fraction of total precipitation from events > long-term 9th percentile), pnl9 (number of events > long-term 9th percentile) very dry events: pxcdd (maximum number of consecutive five days with < threshold) The Spearman correlation between observed and modelled precipitation indices provides an indirect evaluation of the interannual variability, which is captured by the model (Figure ) in downscaling both station-scale average as well as extreme precipitation events. The indices are calculated independently for the south-east (SE) and the north-west (NW) areas. Here, the results for each withdrawn period are presented separately in order to evaluate the sensitivity of the forecast in terms of the training/testing time window. The threshold has been set equal to the value of the parameter θ, i.e.mm. The indices pav, poc and pxcdd are predicted best by the model and in addition they appear to be quite robust towards the selection of the training period and region. Pnl9 and px5d are generally well reproduced but are more sensitive to the selection of the training window. In addition, they are typically better estimated in the SE region (marine environment) with lower spreading between the stations compared to the NW region (continental area). The fraction of total precipitation due to very wet events, i.e. pfl9, shows high sensitivity to both the time window and the region. This index is represented efficiently only in some stations and in particular, at those stations where the very wet events are not related to local scale features. On the other hand, pint and pq9 were not represented adequately except for some limited cases. This result did not change noticeably by using a non-zero threshold. To summarize, the model predicted adequately the interannual variability of the seasonal number of rain days and their corresponding seasonal precipitation amount, the number of extreme precipitation events and their corresponding fraction of the total precipitation amount, the maximum 5-day precipitation amount and the maximum number of consecutive dry days. On the contrary, in most cases, it failed to reproduce the interannual variability of the mean wet day precipitation and the 9th percentile of precipitation on wet days, despite capturing their magnitude.. Discussion A multi-site statistical model is investigated for its capability in downscaling winter daily precipitation over Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

12 69 I. KIOUTSIOUKIS ET AL. (a) SE NW pav poc pint pq9 px5d pnl9 pfl9 pxcdd pav poc pint pq9 px5d pnl9 pfl9 pxcdd (b) (c) SE NW pav poc pint pq9 px5d pnl9 pfl9 pxcdd pav poc pint pq9 px5d pnl9 pfl9 pxcdd 9 9 SE 9 9 NW pav poc pint pq9 px5d pnl9 pfl9 pxcdd pav poc pint pq9 px5d pnl9 pfl9 pxcdd (d) SE NW pav poc pint pq9 px5d pnl9 pfl9 pxcdd pav poc pint pq9 px5d pnl9 pfl9 pxcdd (e) 995 SE 995 NW pav poc pint pq9 px5d pnl9 pfl9 pxcdd pav poc pint pq9 px5d pnl9 pfl9 pxcdd Figure. Correlations of observed and modelled precipitation indices for south-east (SE) region (left) and north-west (NW) region (right): The validation periods are (a) , (b) 977 9, (c) 9 9, (d) and (e) 995. Results correspond to realisations generated from the model. This figure is available in colour online at Greece. The observed data covers the period from 97 to. Three atmospheric input variables were selected following an optimization procedure from Reanalysis Data. Five weather states were identified with the most parsimonious NHMM. The forecast skill of the model was then tested against data, which was not used for the training period. The NHMM reproduced successfully the station-scale precipitation statistics such as precipitation occurrence and its amounts. The spatial pattern of precipitation was also very well reproduced as can be recognized from the correlations between stations and the Log-Odds ratios. Also temporal correlation in the data was successfully captured at most rain gauges, although better in the SE than NW region. Finally, the downscaling ability of the model was explored for extreme precipitation events through the use of selected indices. The model captured satisfactorily the average precipitation amounts and the very dry events (dry spells) and modelled successfully most of the indices corresponding to very wet events including the maximum 5-day precipitation amount, the number of extreme precipitation events and their corresponding fraction of the total precipitation amount. The weakest reproduced indices correspond to the mean wet day precipitation and the 9th percentile of precipitation on wet days where the model captured their magnitude but not their interannual variability. The presented methodological framework is probabilistic in nature and generates predictions associated with uncertainty bounds. It can be used for studies of climate variability using GCM forecasts as inputs instead of Reanalysis Data. Despite the assumption of time invariance of the predictor predictand relationship here, we have also to assume that the GCM forecasts are reliable. Systematic biases in mean or variance of the GCM predicted field could be adjusted based on comparison with historical observations. However, it is also likely that the GCM predictions for an individual grid point are rather noisy and/or be shifted spatially. These factors suggest there should usually be better information in the large-scale GCM prediction, i.e. the use of summary input variables predicted across the region rather than the individual grid point, following a similar procedure adopted in this work for reanalysis data. Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc

13 STATISTICAL DOWNSCALING OF DAILY PRECIPITATION OVER GREECE 69 The forecasts can be further improved through a modified parameterization scheme that adds spatial structure within the weather types as well as with the inclusion of auxiliary variables that account for local weather types. Acknowledgements Dr I. Kioutsioukis was supported with a Science Grant from the Greek Ministry of Education under the Pythagoras Research EPEAEK- project. The authors wish to thank Dr Lorenzo Van Wijk for the valuable review of the English text and the anonymous reviewers for their significant comments on the earlier version of this article. References Bellone E, Hughes JP, Guttorp P.. A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts. Climate Research 5:. Charles SP, Bates BC, Hughes JP A spatiotemporal model for downscaling precipitation occurrence and amounts. Journal of Geophysical Research D: Atmospheres : Charles SP, Bates BC, Smith IN, Hughes JP.. Statistical downscaling of daily precipitation from observed and modelled atmospheric fields. Hydrological Processes : 7 9. Dempster AP, Laird NM, Rubin DB Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society Series B-Methodological 9:. Eshel G, Farrell B.. Mechanisms of eastern Mediterranean rainfall variability. Journal of the Atmospheric Sciences 57: 9. Haylock M, Goodness C.. Interannual variability of European extreme winter rainfall and links with mean large-scale circulation. International Journal of Climatology : Haylock MR, Cawley GC, Harpham C, Wilby RL, Goodess CM.. Downscaling heavy precipitation over the United Kingdom: a comparison of dynamical and statistical methods and their future scenarios. International Journal of Climatology : 97. Hughes JP, Guttorp P. 99. Incorporating spatial dependence and atmospheric data in a model of precipitation. Journal of Applied Meteorology : Hughes JP, Guttorp P, Charles SP A non-homogeneous hidden Markov model for precipitation occurrence. Journal of the Royal Statistical Society. Series C, (Applied Statistics) : 5. Kioutsioukis I, Rapsomanikis S, Loupa R.. Robust stochastic seasonal precipitation scenarios. International Journal of Climatology : Kirshner S.. Modeling of multivariate time series using hidden Markov models, PhD thesis, University of California, Irvine. Kirshner S, Smyth P.. The MVNHMM Toolbox. University of California: Irvine, CA, Mehrotra R, Sharma A, Cordery I.. Comparison of two approaches for downscaling synoptic atmospheric patterns to multisite precipitation occurrence. Journal of Geophysical Research D: Atmospheres 9: 7. Nicholls N Long-term climate monitoring and extreme events. Climatic Change :. Rabiner LR, Juang BH. 96. An introduction to hidden Markov models. IEEE Transactions on Acoustic Speech Signal Processing : 6. Robertson AW, Kirshner S, Smyth P.. Downscaling of daily rainfall occurrence over Northeast Brazil using a hidden Markov model. Journal of Climate 7: 7. Robertson AW, Kirshner S, Smyth P, Charles SP, Bates BC.. Subseasonal-to-interdecadal variability of the Australian monsoon over North Queensland. Quarterly Journal of the Royal Meteorological Society : Schmidli J, Frei C, Vidale PL.. Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods. International Journal of Climatology : von Storch H, Zwiers F Statistical Analysis in Climate Research. Cambridge University Press: Cambridge. Widmann ML, Bretherton CS, Salathe EP.. Statistical precipitation downscaling over the Northwestern United Statesusing numerically simulated precipitation as a predictor. Journal of Climate 6: Wilby RL, Charles SP, Zorita E, Timbal B, Whetton P, Mearns LO.. Guidelines for Use of Climate Scenarios Developed from Statistical Downscaling Methods, Data Distribution Centre of the Intergovernmental Panel on Climate Change. Wilby RL, Wigley TML, Conway D, Jones PD, Hewitson BC, Main J, Wilks DS. 99. Statistical downscaling of general circulation model output: a comparison of methods. Water Resources Research : 995. Zorita E, von Storch H The analog method as a simple statistical downscaling technique: comparison with more complicated methods. Journal of Climate : 7 9. Copyright 7 Royal Meteorological Society Int. J. Climatol. : () DOI:./joc