High-resolution limited-area ensemble predictions based on low-resolution targeted singular vectors

Transcription

1 Q. J. R. Meteorol. Soc. (2002), 128, pp High-resolution limited-area ensemble predictions based on low-resolution targeted singular vectors By INGER-LISE FROGNER and TROND IVERSEN University of Oslo, Norway (Received 15 November 2000; revised 22 October 2001) SUMMARY The operational limited-area model, HIRLAM, at the Norwegian Meteorological Institute is used at 0.25 ± latitude/longitude resolution for ensemble weather prediction over Northern Europe and adjacent parts of the North Atlantic Ocean; this system is called LAMEPS. Initial and lateral boundary perturbations are taken from coarse-resolution European Centre for Medium-Range Weather Forecasts global ensemble members based on targeted singular vectors (TEPS). Five winter and ve summer cases in 1997 consisting of 20 ensemble members plus one control forecast are integrated. Two sets of ensembles are generated, one for which both initial and lateral boundary conditions are perturbed, and another with only the initial elds perturbed. The LAMEPS results are compared to those of TEPS using the following measures: r.m.s. ensemble spread of 500 hpa geopotential height; r.m.s. ensemble spread of mean-sea-level pressure; Brier Skill Scores (BSS); Relative Operating Characteristic (ROC) curves; and cost/loss analyses. For forecasts longer than 12 hours, all measures show that perturbing the boundary elds is crucial for the performance of LAMEPS. For the winter cases TEPS has slightly larger ensemble spread than LAMEPS, but this is reversed for the summer cases. Results from BSS, ROC and cost/loss analyses show that LAMEPS performed considerably better than TEPS for precipitation, a result that is promising for forecasting extreme precipitation amounts. We believe this result to be linked to the high predictability of mesoscale ows controlled by complex topography. For two-metre temperature, however, TEPS frequently performed better than LAMEPS. KEYWORDS: Limited-area modelling Mesoscale modelling Numerical weather prediction Probabilistic forecasts 1. INTRODUCTION Since the intrinsic non-periodic properties of atmospheric dynamics were thoroughly described by Lorenz (1963), it has gradually been realised that single deterministic forecasts from best guess initial states do not provide the user with all available information. Generating ensemble forecasts also makes it possible to forecast the probability of an extreme weather event. As long as the error is not saturated initially, and the model performs reasonably, the forecast error will grow with time due to the initial conditions (and model) not being perfect. As the growth rate of errors varies with the actual weather situation, it is necessary to create ensembles every day, and not only estimate the spread from some constant statistical expectation. To forecast extreme events (i.e. rare events, and not necessarily hazardous events) we need the total probability distribution for the actual case. A simple deterministic (or control) forecast is not suf cient. Probabilistic forecasting has only become regular during the last decade or so, and mainly in connection with global prediction models with modest resolution (Buizza et al. 1993; Toth and Kalnay 1993). Due to insuf cient computational power, predictions of full probability distributions are still far from possible. Instead, ensemble prediction systems (EPS) have been developed based on ideas put forward by Lorenz (1965) and Leith (1974). Carefully selected ensemble members that account for uncertainties in initial data are used to quantify the predictability of actual situations. At the European Centre for Medium-Range Weather Forecasts (ECMWF) singular vectors (SVs) that maximise the total perturbation energy over nite time intervals and the extratropical Corresponding author, present af liation: Norwegian Meteorological Institute, PO Box 43, Blindern, N-0313 Oslo, Norway. inger.lise.frogner@met.no c Royal Meteorological Society,

2 1322 I.-L. FROGNER and T. IVERSEN northern hemisphere, are used for computing initial perturbations (Buizza et al. 1993). By maximizing the total energy norm of perturbations in a smaller target area, (Buizza 1994) the system can be designed for a speci c region of interest. Thus, Frogner and Iversen (2001) and Hersbach et al. (2000) generated targeted ensemble prediction systems (TEPS) for parts of Europe. In the target area TEPS account for a larger portion of the entire probability distribution than the operational EPS at ECMWF, with the same number of ensemble members (Frogner and Iversen 2001). The TEPS focus on a limited area, but the resolution of the model is the same as for the ECMWF operational EPS. A mesoscale ensemble prediction system requires that much smaller scales are resolved, rendering global calculations too expensive. As is regularly carried out for deterministic mesoscale forecasts, one option could be to use a limited-area model with ner resolution, and with the global TEPS providing boundary elds at the open lateral boundaries. We call such a system LAMEPS. In a limited-area model initial errors and boundary- eld errors combined with atmospheric instability eventually lead to loss of predictability in the target area. Furthermore, atmospheric models are still not perfect, which also contributes to forecast errors. Lately this has been taken into account at ECMWF by stochastically perturbing the tendencies calculated by the model physics (Buizza et al. 1999). This may be even more important for mesoscale predictions, but in this paper we have used a LAMEPS where only initial and lateral boundary elds are perturbed. Further development of LAMEPS was encouraged by a preliminary feasibility study by Frogner and Iversen (2000). Du et al. (1997) and Stensrud et al. (1999, 2000) also use ensembles for short-range forecasting. A reason for increasing the resolution of the forecast model in the target area is, as for deterministic forecasts, to obtain better descriptions of ground-surface properties and dynamical features responsible for signi cant weather. Moreover, extreme weather events are frequently con ned to areas that are too small to be properly resolved by e.g. the T L 159 resolution used in TEPS, and even large-scale precipitation involves strong mesoscale variability and is strongly in uenced by orography. The simpli ed analysis of Lorenz (1969) gave quite pessimistic prospects for mesoscale predictability. Later tests with full numerical weather prediction (NWP) model systems have revitalized the optimism. A signi cant part of the mesoscale variability is controlled by groundsurface properties (Anthes et al. 1985; Boer, 1994). Thus, slower error-growth rates than predicted by the turbulence model of Lorenz (1969) may occur for some signi cant mesoscale weather systems. Scandinavia is dominated by topography, complex coastlines and seasonally varying sea-ice and snow cover. It is our hope that a mesoscale LAMEPS utilizing global perturbations targeted on northern Europe would enable better forecasts of possible extreme events compared to TEPS or pure deterministic forecasts. So far only ten cases have been studied due to limited computer capacity. The paper is organized in ve sections. In section 2 the set-up for the experiments is described, and in section 3 results are presented. The discussion in section 4 focuses on contrasting results for precipitation and two-metre temperature, as well as sensitivity tests to rule out possibilities for false conclusions. The main conclusions are in section EXPERIMENTAL SET-UP The model used in the experiments is a version of the high-resolution limited-area model, HIRLAM (Källén 1996), which is the current routine model at the Norwegian Meteorological Institute (DNMI). The integration area used covers northern Europe and adjacent parts of the North Atlantic Ocean, see Fig. 1. The model was run with a rotated

3 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1323 Figure 1. The different areas used. The area marked a is the HIRLAM integration area; b is the target area in the TEPS-runs; c is the big veri cation area; and d is the veri cation area called Norway. spherical grid with grid resolution ± (all such measures in this paper are latitude by longitude), equivalent to about 28 km between grid points, and 31 levels in the vertical. At the lateral boundaries information is transferred through the use of boundary relaxation (KÊallberg and Gibson 1977). For perturbing the initial and boundary data we used members of the TEPS described in Frogner and Iversen (2001) that focus on this part of the world (Fig. 1). The operational ECMWF models for ensemble predictions were used for TEPS: singular vectors were calculated with resolution T42 and 31 levels (T42L31) and with an optimization time interval of 48 hours. The ensemble members were generated with T L 159L31 (the suf x L stands for Linear Gaussian grid) integrated up to day ten. Four sets of LAMEPS were constructed, each consisting of ten cases with 20 ensemble members plus one control run. Two of the sets (PB-long and NP-long) directly used interpolated TEPS members as initial conditions. The other two (PB-short and NPshort) used separate HIRLAM analyses to integrate the LAMEPS control forecasts, and the difference between TEPS members and the TEPS control as initial perturbations. At the lateral boundaries the PB (perturbed boundary) sets used the same TEPS ensemble members as used for initial conditions. The NP (no perturbed boundary) sets used the TEPS control throughout, i.e. they are run without perturbations of boundary elds.

4 1324 I.-L. FROGNER and T. IVERSEN TABLE 1. SET-UP FOR THE FOUR DIFFERENT TYPES OF LAMEPS EXPERIMENTS Identi cation Initial conditions Boundary conditions Forecast length (h) PB-long TEPS ensemble TEPS ensemble 240 member member NP-long TEPS ensemble TEPS control 240 member PB-short HIRLAM analysis C TEPS ensemble member 60 TEPS perturbation NP-short HIRLAM analysis C TEPS control 60 TEPS perturbation See text for explanation of acronyms. The four sets are summarized in Table 1. In the long runs HIRLAM is used as a pure interpretation tool similar to the technique used for downscaling climate model scenarios. The short runs employ HIRLAM as a true prognostic tool for LAMEPS. The TEPS resolution is approximately ±. For economy of data transfer, data taken out for use in LAMEPS were only of 1.5 ± 1.0 ± resolution. The data were then interpolated to the HIRLAM grid, including an unavoidable interpolation in the vertical. The levels in the two models were not the same, partly due to the different resolution of the topography. All four LAMEPS sets were integrated for ve winter and ve summer cases in The long runs were integrated for 1, 5, 10, 15, and 20 February and for 1, 4, 8, 11 and 15 June; the short runs were integrated for the same days, except that 15 February was replaced by 17 February (due to missing data). For the winter cases boundary data were updated every sixth hour. The original plan was to use the same frequency for the summer cases, but data from TEPS were unintentionally taken out only every 12th hour, hence the boundary data for LAMEPS were updated only twice diurnally. The winter period was very active in the North-Atlantic region (Frogner and Iversen 2001), with cyclones moving from the west over Scandinavia. The summer period started with a ridge in the central North Atlantic Ocean and later the area was dominated by a cyclone that moved slowly northwards. (a) 3. RESULTS Results from the runs started from HIRLAM analyses (short runs) (i) Spread of geopotential height and mean-sea-level pressure. An ensemble prediction system should describe as much as possible of the probability distribution for state development caused by initial-state uncertainty. This is important in order to detect rare, and possibly extreme, weather events. The spread of the ensemble members around the control run in a particular case is a measure of this. As a measure of spread, we use: v s D s i D 1 IX IX q s i D h.e nd p d / I 2 i i D 1 IX u t 1 NX DX.e ind p id / I N D 2 ; id1 id1 id1 nd1 dd1 (1) where N D 20 is the number of ensemble members; I is the number of points inside the veri cation area; D is the number of cases (days); e ind is the parameter value for ensemble prognosis member number n, in grid-point number i, for case d; and p id is

5 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1325 the value for the control prognosis in point number i for case d. Note that s 2 i D ¾ 2 e.i/ C ¾ 2 p.i/ 2½ a.i/¾ e.i/¾ p.i/; (2) where ¾ e;p.i/ D p h..e n ; p/ d c d / 2 i i, ½ a.i/ D h.e nd c d /.p nd c d /i i =¾ e.i/¾ p.i/, and c di are climatological elds for the dates d. If ensemble members decorrelate beyond the predictability limit, the si 2 tends to twice the variance relative to climatology. To the extent that ensemble members share similar systematic deviations from climatology, the asymptotic value will be smaller than this. Due to only very few cases (D/ the calculated s i is of limited signi cance beyond the actual cases. We have not estimated the quantities in Eq. (2) directly, since suitable estimates of the mesoscale climatology were not available. In Fig. 2 maps of s i for 500 hpa geopotential height (Z500) for the D D 5 winter days are presented for the short runs and for TEPS. PB and TEPS are quite similar, although PB is less smooth than TEPS, as expected. Structural similarities between NP and the two other systems are less clear, and the values are also generally much smaller for NP. For the given choice of integration domain for LAMEPS, perturbing the open lateral boundary conditions is already far more important than the initial conditions after hours into the forecasts. This is con rmed from Fig. 3, which shows the spread averaged over the veri cation area called Norway (the smaller area in Fig. 1). Except for the rst 12 hours (winter) TEPS has a slightly larger spread than PB, which is con rmed for the individual days (not shown). The spread for NP starts to decline after 24 hours (winter) when the initial perturbations leave the veri cation area and the unperturbed boundary elds suppress any further spread. Du and Tracton (1999) also show the importance of perturbing the boundary conditions. The maps of s i for the ve summer days (MSLP; not shown) show the same results. Averaged over veri cation area Norway (Fig. 3) we see a generally smaller spread than for the winter days. Again the spread for PB and TEPS are comparable and much larger than for NP, but in this case the spread for PB is slightly larger for all forecast times. This is, however, not seen for all individual cases. In contrast to the winter cases, the spread for NP does not start to decline during a forecast period of 60 h. For the case of 15 June, NP even has comparable spreads to PB and TEPS throughout. In summer the propagation of disturbance energy is considerably slower than in winter, and initial perturbations are more completely contained inside the integration domain than in winter. The results for spread measured by the r.m.s. of mean-sea-level pressure (MSLP; not shown) are similar to those of Z500. Figure 4 shows the r.m.s. difference between PB and NP for Z500 over the veri cation area Norway. The values are already considerable after the rst forecast day, emphasizing the importance of perturbing lateral boundary conditions. Figure 4 also shows information added by HIRLAM as measured by the area-averaged r.m.s. difference between PB and TEPS for Z500. For time t D 0 the number measures the difference between the HIRLAM analyses and ECMWF analyses. Using a different analysis has a marked effect. Also Fig. 4 shows that after about 24 h (winter) and 36 h (summer), the r.m.s. difference between PB and NP is larger than between PB and TEPS. After this the boundary conditions dominate the results in the veri cation area. Propagating mesoscale dynamics may still have in uence to the extent that HIRLAM may breed such systems over the distance from the in ux boundaries. Furthermore, mesoscale features related to topography and ground-surface contrasts may also be important (e.g. Machenhauer et al. 1998).

6 1326 I.-L. FROGNER and T. IVERSEN Figure 2. Maps of spread for 500 hpa geopotential height (contour interval 5 m) for the ve winter cases and 20 ensemble-members. The top row shows maps for forecast time C12 h, C36 h and C60 h for PB-short, the second and third rows are similar but for NP-short and TEPS, respectively. See text for further details.

7 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1327 Figure 3. Spread for 500 hpa geopotential height for veri cation area Norway. The thin lines are for the ve winter cases and the thick lines are for the ve summer cases. Solid lines are TEPS, dashed lines are PB-short and chain-dashed lines are NP-short. See text for further details. Figure 4. The root-mean-square (r.m.s.) difference between PB-short and NP-short for 500 hpa geopotential height for veri cation area Norway (thin lines), and between PB-short and TEPS (thick lines). The solid lines are for the ve winter cases and the dashed lines for the ve summer cases. See text for further details.

8 1328 I.-L. FROGNER and T. IVERSEN (ii) Event-speci c veri cation. A rationale behind the use of limited-area mesoscale models such as HIRLAM is the expectation of improved predictions directly related to (extreme) weather-events. We have used veri cation measures well suited to probabilistic forecasts. The Brier Skill Score (BSS; Brier 1950; Stanski et al. 1989) measures the quality of the forecast of speci c events within a range from 1 to 1, where BSS D 1 is a perfect forecast, BSS D 0 indicates no improvement over the standard forecast (e.g. climatology), and BSS < 0 when the standard forecast is the better. Relative Operating Characteristic (ROC) curves (Mason 1982), and the areas under the curves are, like the BSS, designed to test forecasts of speci c events. A hit rate (H D the number of correct forecasts of the event divided by the number of times the event occurred) and a false alarm rate (F D the number of times the event was incorrectly forecast divided by the number of times the event was not observed) are compared. The ROC curve is plotted as a diagram with F along the abscissa and H along the ordinate. Deterministic forecasts of the event will be veri ed as a point in the diagram. The closer the point is to the upper-left corner (H D 1, F D 0), the better the forecast. For ensemble forecasts one may require a number of ensemble members to predict an event before considering it to have been forecast. By varying this threshold, the ensemble predictions may be represented as a curve, a ROC curve. Here the data are binned into classes according to the number of ensemble members that predict the event in each case, thus giving 21 different thresholds for making the ROC curve. A perfect forecast is represented by a curve along the ordinate axis up to the upper-left corner, then parallel with the abscissa axis to the upper-right corner. The area under the ROC curve is an overall measure of the quality of the ensemble forecast of events. An area of one is perfect, whilst 0.5 is useless since false alarms are as frequent as hits. The cost/loss analysis (Katz and Murphy 1997; Richardson 2000) is associated with decision-making problems that take into account the economic bene t a user could obtain by using a forecast (instead of climatology for example) when deciding whether or not to take preventive action against a possible hazardous weather event. A speci c user must estimate the ratio between his costs incurred for taking preventive actions and the loss he will suffer if the event occurs without any action having been taken. The economic value is calculated using hit rates and false-alarm rates, and a value of one indicates a perfect forecast. For an EPS the value can be presented in a diagram with the cost/loss ratio along the abscissa. Users that have a positive cost/loss ratio will bene t from the EPS. (iii) Precipitation. Veri cation of forecasts of precipitation against synoptic observations is not straightforward. This is due to the very different scales of observations and the forecasts. Ghelli and Lalaurette (2000) proposed to dispense with this problem by socalled super-observations constructed to be representative of precipitation grid squares. Here all precipitation stations in Norway inside the small veri cation area (Fig. 1) were aggregated into precipitation super-observations representative of our ± grid. Total precipitation (large scale and convective) from TEPS and LAMEPS were compared to this using BSS, ROC curves and cost/loss analyses. Unfortunately, the precipitation observations are only taken at 0600 UTC, leaving us with only one time-interval for verifying the short runs: C18 to C42 hours accumulated precipitation. Unfortunately, since the summer period only had output from TEPS every 12 hours (0000 and 1200 UTC), it was impossible to verify these. In Figs. 5(a) and (b) the comparison for TEPS and PB-short for a threshold of more than 20 mm day 1 is shown. For both measures LAMEPS is much better than TEPS. This is the case for most events, except for moderate events between 1 15 mm day 1

9 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1329 Figure 5. (a) and (c) ROC curves and (b) and (d) cost/loss analyses for more than 20 mm 24 h 1 total precipitation and 30 mm 24 h 1 total precipitation, respectively, for forecast time 1.75 days, computed for the veri cation area Norway and all ve winter cases. Solid lines are results for TEPS, dashed for PB-short. In (a) and (c) NTOT is the number of points the event is tested for; NOCC is the number of times the event occurred in the sample; and P CLI is the climatological frequency. See text for further details. for which there is no general conclusion from the cost/loss analysis. The improvement of LAMEPS over TEPS increases as the event becomes rarer (e.g. heavy rainfall), and in Figs. 5(c) and (d) the results for events with more than 30 mm day 1 are convincing. Although the number of occurrences is small (74) and may lead to the measures being unstable, it is worth noting that for LAMEPS the false-alarm rate is practically zero and the hit rate is close to unity. In Fig. 6 the area under the ROC curves and the BSS are shown; LAMEPS is better than TEPS for both measures and for all thresholds, except BSS for 30 mm day 1. To get some idea of HIRLAM s in uence on the precipitation intensities, we have also considered probabilities of different precipitation intensities. The probability is

10 1330 I.-L. FROGNER and T. IVERSEN Figure 6. BSS and area under ROC curves as a function of precipitation intensity events (0.3, 1.0, 2.5, 5.0, 7.5, 10.0, 15.0, 20.0, 25.0 and 30.0 mm 24 h 1 ). Thin lines are area under ROC curves and heavy lines are BSS. LAMEPS results are for PB-short. See text for further details. Figure 7. Probability of large-scale precipitation (LSP) for TEPS (solid lines) and PB-short (dashed lines) for different thresholds ( no rain is less than 0.01 mm 12 h 1 ), computed for veri cation area Norway and the ve summer cases. See text for further details.

11 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1331 Figure 8. (a) Area under ROC curves, (b) Brier Skill Scores, (c) ROC curves, and (d) cost/loss analyses for TEPS (solid lines), PB-short (dashed lines) and NP-short (chain-dashed lines) for 2 m temperature colder than 6.0 K compared to climatology, computed for the veri cation area Norway and for all ve winter cases. In (c) NTOT is the number of points the event is tested for; NOCC is the number of times the event occurred in the sample; and P CLI is the climatological frequency. See text for further details. de ned as: p D 1 I D N IX DX id1 dd1 nd1 NX f idn ; (3) where f idn D 1 for occurrence and zero otherwise. This measure does not take observations into account, it is purely based on the forecasts. Large-scale precipitation (LSP) in TEPS and PB are compared: in Fig. 7 probabilities for ve precipitation events are compared for the summer cases. PB has a higher probability of no rain than TEPS, for little to moderate precipitation TEPS has a larger probability. For moderate precipitation the probabilities are about the same for PB and TEPS, whilst for heavy precipitation events PB has a larger probability than TEPS. These results are desired for a limited-area model with better representation of topography and dynamical structures than TEPS. For example, when precipitation is forecast in southern Norway, the coarser TEPS model tends to spread the precipitation more on both sides of the mountains than HIRLAM. Similarly, precipitation produced in frontal regions with embedded mesoscale structures is expected to be better resolved in HIRLAM. In summary, this gives rise to the higher

12 1332 I.-L. FROGNER and T. IVERSEN Figure 9. As Fig. 8 but for 2 m temperature greater than 4.0 K compared to climatology, and for all ve summer cases. probability both of heavy and of no precipitation in HIRLAM than in the TEPS-model. For the winter period the results are similar, with the exception that the precipitation intensities are a bit higher before LAMEPS overtakes TEPS. (iv) Two-metre temperature. The sets are veri ed against synoptic observations of 2 m temperature, and the winter and summer days are veri ed separately. The climatological frequency needed in the calculation of BSS and the cost/loss analysis is based on the sample (the observations for all time steps within the sets). The comparison of TEPS, PB-short and NP-short for a threshold of 6.0 K compared to climatology for the ve winter days is shown in Fig. 8. In Fig. 8(a) the area under the ROC curve shows that for most of the forecast time PB is better than TEPS. NP is comparable to PB for the early forecast times only. The improvement of PB over TEPS is not con rmed by BSS (Fig. 8(b)), TEPS have higher values than PB throughout. The ROC curve at forecast time 2.5 days (Fig. 8(c)), clearly shows that PB is better according to this measure. For the cost/loss ratio, Fig. 8(d), we see a marked improvement for PB over the two others. Users with any value of the cost/loss ratio would bene t most by using PB, but the bene t over TEPS is larger for small ratios.

13 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1333 Figure 10. Spread for 500 hpa geopotential height for the veri cation area Norway for the ve winter cases. The solid line is TEPS, the dashed line is PB-long and the chain-dashed line is NP-long. See text for further details. For smaller anomalies than 6 K, TEPS is generally better than PB and NP for all four measures (not shown). For more extreme deviations from climatology PB is generally the better system, although for BSS there is no general conclusion. Thus, the rarer the event, the better PB detects it compared to TEPS. For the summer days the picture is different. Here TEPS generally performs better throughout, however, with a tendency for PB to approach TEPS as deviation from climatology increases. Unfortunately, the number of cases is too small to get stable results for extreme anomalies. For some large, negative thresholds PB is better than TEPS according to cost/loss analysis for small cost/loss ratios. In Fig. 9 an example for the summer days is presented: the threshold is 4 K higher than climatology, and there is no doubt that TEPS is the better for all four measures. A cold bias in the HIRLAM forecasts may account for some of the mixed results for temperature. At the time of these experiments there was an underestimation of cloud cover from the HIRLAM model, a problem that increased with increasing resolution. Due to the close relationship with the 2 m temperature, this caused a negative bias at inland stations in the winter (Homleid and Ødegaard 2000). Such a cold bias could lead to a positive effect of LAMEPS for negative thresholds, and a negative effect of LAMEPS for positive thresholds. (b) Results from the runs started without HIRLAM analyses (long runs) The HIRLAM runs started directly from the TEPS members without using mesoscale analyses, are run up to day ten. As seen from the short runs, the boundary conditions are dominant over the initial conditions after about 2 days. From these long runs we can investigate what happens after the initial perturbations have ceased to have any

14 1334 I.-L. FROGNER and T. IVERSEN Figure 11. The r.m.s. difference between PB-long and PB-short for 500 hpa geopotential height for veri cation area Norway. See text for further details. in uence, i.e. between approximately days two and ten. The spread for the ve winter days for the Norway area is in Fig. 10. Again we have the same conclusion as for the short runs: TEPS gives a slightly larger spread than PB; but here we can see that the spread for TEPS and PB continue to follow each other closely all through the 10 days, and that the spread continues to increase up to day ten. Frogner and Iversen (2001) showed that the increase in the latter part of the period is nonlinear. The importance of perturbing the boundary conditions in LAMEPS is even greater in this case. From maps of s i for the three systems (not shown), TEPS and PB are similar for all ten forecast days, while NP bears little resemblance to the other two beyond the rst day or two. The r.m.s. difference between PB-long and PB-short shown in Fig. 11 measures the effect of using a separate mesoscale analysis. The effect is largest for the winter days and increases slightly with forecast time. For t D 0 the values in Fig. 11 and Fig. 4 (thick lines) should ideally be the same, however, the unavoidable interpolation introduces differences. These interpolation errors will be discussed in the next section. 4. DISCUSSION The overall comparison between LAMEPS and TEPS, the way they are set up in our experiments, does not permit straightforward conclusions. For precipitation LAMEPS is no doubt much better for the ve winter days investigated and, judging from the frequency of different precipitation intensities, it is probable that LAMEPS is also better for the summer cases. For the 2 m temperature the results are far from convincingly in favour of LAMEPS, and for some measures TEPS is clearly better. Also the difference in spread for geopotential heights and MSLP is not as originally expected.

15 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1335 The few cases tested certainly set limits as far as the possibility of generalizing the results is concerned. Nevertheless, the results for precipitation are very convincing. There is a basic difference between the physical processes accounting for precipitation and 2 m temperature in areas dominated by complex topography such as in Norway. Under stable conditions, small-scale topographical features will cause vertical motion throughout the troposphere through inertia gravity waves. Such waves may partly enhance and partly suppress large-scale precipitation, and the model-description of these dynamics should gradually improve with increases in horizontal resolution. Furthermore, unstable circulations may also arise as humid air-masses are lifted, and even if the induced motion still needs to be parametrized with 28 km resolution, the improved shape and height of mountains should trigger these processes more correctly in space and time. Anthes et al. (1985) and Boer (1994) revealed the considerable predictability of mesoscale atmospheric ows connected with topography. Improved predictability in weather conditions connected with topography seems to be the main cause of the improved results reported in this paper, one could therefore expect that much simpler methods of a statistical nature could yield the same improvements over TEPS. For example, one could apply MOS (Model Output Statistics) or Kalman lter techniques on the EPS or TEPS runs. Two recent studies by Bremnes (2000, 2001) do not show any systematic improvements from the use of MOS over Norway, such as we obtained for LAMEPS. In addition, MOS requires a long time series to compute the statistics and the Kalman lter technique is not very applicable as we do not have consecutive days. A simple bias correction could probably not selectively improve the hit-rate statistics as is seen for the LAMEPS. Regarding these issues, and the results of Bremnes, we have not compared the LAMEPS results with MOS or Kalman lter techniques. For the prediction of air temperature close to the ground, the gradual improvement with increased resolution is less clear. This parameter is more related to very local features and their in uence on the surface boundary layer. In Norway, even a 28 km grid resolution is far from resolving narrow valleys and contrasting ground surface properties that in uence the air temperature close to the ground. In addition, most synoptic stations in these regions are located in the bottom of valleys, and could be strongly in uenced by inversions, especially in the winter. The veri cation could be made more scalerepresentative by aggregating super-observations also for 2 m temperature, but this is less straightforward than for precipitation. Another possibility could be the use of MOS or Kalman ltering of the data from the ensemble members. Since for the short runs the reference state is the HIRLAM analysis, the TEPS perturbations may not correspond to the HIRLAM error structures. This could mean that the instabilities in the initial conditions are not well prescribed. However, as the boundary conditions are dominant over the initial conditions by about 24 hours, it is mainly instabilities before this time that may suffer. The spread of the ensemble members around the control should be as small as possible, but re ect the uncertainty in the present situation and the initial conditions. At present spread is often underestimated, and one would expect the measure of spread presented in Eqs. (1) and (2) to increase as new sources of variability are included in a model system. This was not obtained here for the few cases run. This may be partly due to HIRLAM being less able to transfer energy into growing perturbations than the ECMWF model, leading to smaller variance relative to climatology. Another possibility is that there are larger systematic errors or deviations from climatology in HIRLAM, so that the anomaly correlation tends to zero more slowly. The latter may well be the reason due to the small number of cases; however, we have not been able to verify this.

16 1336 I.-L. FROGNER and T. IVERSEN (a) Can practical limitations of the LAMEPS set-up cause false conclusions? There are ample possibilities that practical constraints of the LAMEPS might cause unphysical results. The amount of data needed for initial and boundary conditions had to be kept reasonable to handle. Two systems with different grid types and resolutions require interpolations in order to use data from one as input for the other, as well as when comparing the output. Such interpolation could give rise to important errors in the results. In all the results presented so far the veri cation of LAMEPS and TEPS are done in a grid of ±. This means that there is no interpolation of the TEPS elds, except for the resolution enhancement when taking out elds in a ner Gaussian grid from the spectral coef cients. For the HIRLAM elds, errors may arise when elds are bi-linearly interpolated to the TEPS ± grid from the rotated spherical grid. We have checked to what extent this could inadvertently ruin some of the added information generated by HIRLAM. Results from TEPS in approximately the original resolution ( ± ) are rst interpolated to the HIRLAM grid, and then back to the ± grid. This is the same way that the HIRLAM elds were interpolated for veri cation, hence TEPS results should have no advantage in this test. A comparison between the two approaches (not shown) gives almost identical results in terms of the veri cation measures. The test is not complete, since the HIRLAM elds include information on smaller scales than the TEPS elds. We nd it unlikely, however, that the interpolation from the HIRLAM grid to the TEPS ± grid gives rise to important errors, since this interpolation does not involve any coarser resolution than the original grid. For the ROC, BSS and cost/loss measures model results are compared to observations, hence interpolation to observation points is unavoidable. We conclude that the horizontal interpolation of model output from HIRLAM to the TEPS grid for veri cation does not introduce errors that selectively favour TEPS over LAMEPS. A potentially more serious interpolation error could come from constructing the initial and boundary elds. TEPS data used as input to LAMEPS have a resolution of ±, which is much coarser than the ± in the HIRLAM model. Even if the perturbations are constructed from singular vectors calculated with an even coarser model, there is still a chance that HIRLAM is not perturbed with the best possible TEPS elds. The choice of resolution was purely practical and related to data transportation and storage. To investigate this, the spread for the winter days for TEPS Z500 extracted in ± resolution is compared to the spread for TEPS Z500 extracted in resolution ±. The TEPS eld with ± resolution is, for the purpose of this test, interpolated to the HIRLAM grid and then interpolated back to the TEPS grid with resolution ±, in the same way as the LAMEPS results. The veri cation results of the two approaches are very similar (not shown), and in fact the coarse TEPS has a slightly larger spread than the ner TEPS. Hence, the coarse TEPS data do not suppress the growth of the LAMEPS perturbations. Figure 12(a) shows the r.m.s. difference between the TEPS perturbations in the ± grid, and TEPS perturbations in the ± grid. By comparison with Fig. 3, we conclude that the error is not crucial for excitation of instabilities in HIRLAM, as the values are small compared to Fig. 3 (also the case for the long HIRLAM runs). Figure 12(b) shows that the r.m.s. differences between the ensemble members themselves are almost constant ( m). The perturbations have, therefore, smaller relative interpolation errors than the elds themselves. In Fig. 13 the r.m.s. difference between PB-long and TEPS ( ± ) is shown. As PB-long starts directly from the TEPS ensemble members themselves, the r.m.s.

17 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1337 Figure 12. (a) The r.m.s. difference between the TEPS perturbations in resolution ± and in resolution ± for the big veri cation area (a TEPS perturbations is the TEPS ensemble member minus the TEPS control run); (b) the same as (a) but for the ensemble members themselves. In each case the solid line is for the ve winter cases and the dashed line for the ve summer cases. See text for further details. Figure 13. The r.m.s. difference between PB-long and TEPS in resolution ± for 500 hpa geopotential height for the veri cation area Norway. The solid line is for the ve winter cases and the dashed line is for the ve summer cases. See text for further details.

18 1338 I.-L. FROGNER and T. IVERSEN Figure 14. The map view of the r.m.s. difference in 500 geopotential height between: (a) PB-long and TEPS in resolution ± for initial time for all winter cases and all ensemble members; (b) the same as (a) but for the r.m.s difference between PB-short and TEPS. See text for further details. difference at t D 0 should be equal to zero without interpolation errors. Initial values are about 5 6 m, hence there are considerable interpolation errors. Figure 14(a) shows a map of PB-long minus TEPS ( ± ) at initial time, averaged for the winter cases and all the ensemble members. The topography is clearly recognizable in this gure. The model levels in the two integrations are not the same because HIRLAM has a better representation of the topography than the coarser TEPS model; vertical interpolation is therefore unavoidable. Furthermore, this interpolation is responsible for most of the error seen in Fig. 13. Introducing a HIRLAM analysis at least partly makes up for this vertical interpolation error, see Fig. 14(b), since the pattern is more uniformly distributed over the whole area. LAMEPS may be disfavoured as a consequence of properties of the veri cation measures themselves. The TEPS elds are smoother, and smooth elds often give better results with veri cation measures that are sensitive to phase errors. We have checked this by smoothing the LAMEPS elds so that they become comparable to the resolution of TEPS elds. By successively applying a Shapiro lter (Shapiro 1970, 1975) 200 times, most of the energy on scales resolved by HIRLAM but not by TEPS, is removed. The r.m.s. difference between PB and PB-200 (PB smoothed 200 times) was calulated (not shown) and the values are under 1.2 m both for the summer and winter days for all forecast times. One may conclude, erroneously, that this shows that HIRLAM has not introduced any new information to the ensembles. Nonlinear interactions can, however, lead to up-scale developments in quasi-two-dimensional turbulence (Fjørtoft 1953). There is also a possibility that the choice of veri cation area in uences the results. We have calculated full veri cations over a larger area, but the conclusions are the same. Targeted perturbations that to a large extent have to pass over the open boundaries of HIRLAM, are not necessarily well suited for LAMEPS. The perturbations used at initial time are frequently small inside the integration area. It is possible that using

19 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1339 northern hemispheric EPS or a combination of TEPS members with varying optimization time intervals would give better results for LAMEPS. In this connection, the issue of interpolation in time between boundary- eld input becomes important. This could disadvantage LAMEPS compared to TEPS, in particular in the summer cases when we had to use 12-hourly updates only, and this could be a source of error that renders the summer cases particularly bad. On the other hand, during summer a smaller part of the perturbations needs to be transferred through the boundaries due to slower energy propagation. For one date (15 June) all initial perturbations were inside the integration area without giving better results than for other dates. In the winter cases with better time resolution the ensemble spread in LAMEPS is smaller than in TEPS, and the BSS for 2 m temperature performed better with TEPS. Finally, the number of cases is not very large, and it is possible that the results are due to chance. There is a marked difference in the results between the winter and summer cases, which indicates that any nal conclusion on the success of LAMEPS cannot be drawn before more experiments are carried out. It should also be mentioned that work by others on LAMEPS has produced optimistic results for precipitation (Marsigli et al. 2001) but using an even smaller sample selected for its extreme precipitation intensities. 5. CONCLUSIONS We have constructed an ensemble prediction system, LAMEPS, with a limitedarea model. We compared it to the targeted ensemble prediction system, TEPS, using r.m.s. spread of the ensemble members, Brier Skill Scores (BSS), Relative Operating Characteristic (ROC) curves and cost/loss analysis. The TEPS system is used as initial and boundary conditions in LAMEPS. Different sets of LAMEPS are made, one with perturbations of both the initial and boundary conditions, and one when only the initial conditions are perturbed and the boundaries kept the same for all ensemble members. Perturbing the boundaries is crucial for the performance of the LAMEPS. After only hours the spread is substantially smaller than when perturbing both initial and boundary elds. We also found that using a mesoscale analysis for the LAMEPS control forecast is crucial for the ensemble prediction. LAMEPS has a much ner resolution than TEPS. The results show that the frequency of intense large-scale precipitation events in LAMEPS is higher than for TEPS. The same is true for non-occurrences of precipitation. For precipitation LAMEPS was a considerable improvement over TEPS for the ve winter cases, especially for the large precipitation events. For 2 m temperature in the winter LAMEPS was best for deviations larger or equal to 6 K from climatology using all measures except BSS. For the summer, TEPS was generally superior to LAMEPS. Measured by r.m.s. of Z500 and MSLP, the spread obtained by LAMEPS and TEPS is not signi cantly different. Physical and potentially false causes for the results were discussed. Except for unavoidable vertical interpolation and possible spurious effects of interpolation of boundary elds in time (not fully tested), none of the limitations of the practical set-up could account for the results. All in all these rst results from a LAMEPS system appear promising, in particular for forecasting extreme precipitation events. In a situation when such events may become more frequent due to global warming, our results may be important for regional weather forecasters. However, clearly more experimentation is needed both to con rm

20 1340 I.-L. FROGNER and T. IVERSEN these results for precipitation, and also to better understand the lack of improvements for 2 m temperature. We have not discussed the wind forecasts; wind extremes should be better predicted in a high-resolution LAMEPS. ACKNOWLEDGEMENTS We are grateful to ECMWF for letting us use their computer resources for computing the necessary initial and boundary conditions. We are also grateful to the Norwegian Meteorological Institute for letting us use their operational model and making it possible for Inger-Lise Frogner to work there and use the system and computer resources. We are especially grateful to Dr Jan Erik Haugen for help in the technical set-up of the experiments, as well as for useful scienti c comments and discussions. We also wish to thank two anonymous reviewers for valuable comments. This paper is written in connection with I.-L. Frogner s PhD, and she was supported by a 3-year grant from the Norwegian Research Council. Anthes, R. A., Kuo, Y. H., Baumhefner, D. P., Errico, R. M. and Bettge, T. W. REFERENCES 1985 Predictability of mesoscale motions. Issues in atmospheric and oceanic modelling. In Advances in geophysics: Part B, Volume 28. Eds. B. Saltzman and S. Manabe. Academic Press, Orlando, USA Boer, G. J Predictability regimes in atmospheric ow. Mon. Weather Rev., 122, Bremnes, J. B Wind dependent prediction of daily local precipitation. Internal report, The Norwegian Meteorological Institute, PO Box 43, N-0313 Oslo, Norway 2001 Lokale statistiske tilpasninger av ensemble-prognoser for nedbør. Internal report, The Norwegian Meteorological Institute, PO Box 43, N-0313 Oslo, Norway Brier, G. W Veri cation of forecasts expressed in terms of probability. Mon. Weather Rev., 78, 1 3 Buizza, R Localization of optimal perturbations using a projection operator. Q. J. R. Meteorol. Soc., 120, Buizza, R., Tribbia, J., Molteni, F. and Palmer, T. N. Buizza, R., Miller, M. and Palmer, T. N Computation of optimal unstable structures for a numerical weather prediction model. Tellus, 45A, Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc., 125, Du, J. and Tracton, M. S Impact of lateral boundary conditions on regional-model ensemble prediction. CAS/JSC Working Group Numerical Experimentation (WGNE), WMO/TD-No. 942, WMO, Geneva, Switzerland Du, J., Mullen, S. L. and Saunders, F Short-range ensemble forecasting of quantitative precipitation. Mon. Weather Rev., 125, Fjørtoft, R On the changes in the spectral distribution of kinetic energy for two-dimensional, non-divergent ow. Tellus, 5, Frogner, I.-L. and Iversen, T On prediction spread in a limited area with open boundaries. Institute Report Series, No. 116, Department of Geophysics, University of Oslo, Norway 2001 Targeted ensemble prediction for northern Europe and parts of the North Atlantic Ocean. Tellus, 53A, Ghelli, A. and Lalaurette, F Verifying precipitation forecasts using upscaled observations. ECMWF Newsletter No. 87. Available from ECMWF, Shin- eld Park, Reading, Berkshire RG2 9AX, UK Hersbach, H, Mureau, R., Opsteegh, J. D. and Barkmeijer, J A short-to-early medium-range ensemble prediction system for the European area. Mon. Weather Rev., 128, Homleid, M. and Ødegaard, V A study of 2 meter temperature forecasts from NWP models at Norwegian synop stations. Research Report No 112, The Norwegian Meteorological Institute, PO Box 43 Blindern, N-0313 Oslo, Norway

21 HIGH-RESOLUTION ENSEMBLE PREDICTIONS 1341 KÊallberg, P. and Gibson, J Lateral boundary conditions for a limited area version of the ECMWF model. Pp in WGNE Progress Report No. 14. WMO, Geneva, Switzerland Katz, R. W. and Murphy, A. H Economic value of weather and climate forecasts. Cambridge University Press, Cambridge, UK Källén, E. (Ed.) 1996 HIRLAM documentation manual, system 2.5. Available from SMHI, S Norrköping, Sweden Leith, C. E Theoretical skill of Monte Carlo forecasts. Mon. Weather Rev., 102, Lorenz, E. N Deterministic non-periodic ow. J. Atmos. Sci., 20, A study of the predictability of a 28-variable atmospheric model. Tellus, 17, The predictability of a ow which possesses many scales of motion. Tellus, 21, Machenhauer, B., Windelband, M., Botzet, M., Christensen, J. H., Deque, M., Jones, R. G., Ruti, P. M. and Visconti, G. Marsigli, C., Montani, A., Nerozzi, F., Paccagnella, T., Molteni, F. and Buizza, R Validation and analysis of regional present-day climate and climate simulations over Europe. MPI Report No 275. Max- Planck-Institute, Hamburg, Germany 2001 A strategy for high-resolution ensemble prediction. II: Limitedarea experiments in four Alpine ood events. Q. J. R. Meteorol. Soc., 127, Mason, I A model for assessment of weather forecasts. Aust. Meteorol. Mag., 30, Richardson, D. S Skill and economic value of the ECMWF ensemble prediction system. Q. J. R. Meteorol. Soc., 126, Shapiro, R Smoothing, ltering and boundary effects. Rev. Geophys. Space Phys., 8, Linear ltering. Math. Comput., 29, Stansk, H. R., Wilson, L. J. and Burrows, W. R. Stensrud, D. J., Brooks, H. E., Du, J., Tracton, S. and Rogers, E. Stensrud, D. J., Bao, J.-W. and Warner, T. T Survey of common veri cation methods in meteorology. Atmospheric Environment Service Research Dept., Available from Forecast Research Division, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada 1999 Using ensembles for short-range forecasting. Mon. Weather Rev., 127, Using initial conditions and model physics perturbations in shortrange ensemble simulations of mesoscale convective systems. Mon. Weather Rev., 128, Toth, Z. and Kalnay, E Ensemble forecasting at the NMC: The generation of perturbations. Bull. Am. Meteorol. Soc., 74,