Estimating the Spatial Distribution of Precipitation in Iceland Using a Linear Model of Orographic Precipitation

Transcription

1 DECEMBER 2007 C R O C H E T E T A L Estimating the Spatial Distribution of Precipitation in Iceland Using a Linear Model of Orographic Precipitation PHILIPPE CROCHET, TÓMAS JÓHANNESSON, AND TRAUSTI JÓNSSON Icelandic Meteorological Office, Reykjavík, Iceland ODDUR SIGURÐSSON National Hydrological Service, Reykjavík, Iceland HELGI BJÖRNSSON AND FINNUR PÁLSSON Earth Sciences Institute, University of Iceland, Reykjavík, Iceland IDAR BARSTAD Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway (Manuscript received 5 June 2006, in final form 31 January 2007) ABSTRACT A linear model of orographic precipitation that includes airflow dynamics, condensed water advection, and downslope evaporation is adapted for Iceland. The model is driven using coarse-resolution 40-yr reanalysis data from the European Centre for Medium-Range Weather Forecasts (ERA-40) over the period The simulated precipitation is in good agreement with precipitation observations accumulated over various time scales, both in terms of magnitude and distribution. The results suggest that the model captures the main physical processes governing orographic generation of precipitation in the mountains of Iceland. The approach presented in this paper offers a credible method to obtain a detailed estimate of the distribution of precipitation in mountainous terrain for various conditions involving orographic generation of precipitation. It appears to be of great practical value to the hydrologists, glaciologists, meteorologists, and climatologists. 1. Introduction Precipitation is an essential component of the water budget and knowledge of its spatiotemporal distribution at various scales is an important step toward a better understanding and modeling of the hydrological cycle and associated phenomena such as floodings and droughts, landslides and snow avalanches, as well as regional climate and its changes. Traditionally, interpolation methods including various degrees of complexity have been used to estimate area-averaged precipitation or produce gridded datasets from irregularly spaced rain gauge data (see, e.g., Corresponding author address: Philippe Crochet, Icelandic Meteorological Office, Bustadavegur 9, IS-150, Reykjavík, Iceland. philippe@vedur.is Creutin and Obled 1982). However, the theoretical and practical requirements involved with such methods are seldom fulfilled in mountainous terrain where large gradients and nonstationarities induced by the landscape are to be expected. Moreover, sparse rain gauge networks do not offer a representative sampling of the precipitation distribution, making it difficult to identify the covariance function used in the interpolation procedures. To tackle these problems, different strategies have been developed, such as the use of elevation through multivariate geostatistics (Pardo-Iguzquiza 1998; Sharples et al. 2005), regression models that describe in an intuitive manner the effects of topography as well as atmospheric information on orographic precipitation (Basist et al. 1994; Daly et al. 1994; Wotling et al. 2000; Drogue et al. 2002), and the combination of both regression models and an interpolation procedure such as detrended kriging (Phillips et al. 1992; Kieffer DOI: /2007JHM American Meteorological Society

2 1286 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 Weisse and Bois 2001; Kyriakidis et al. 2001; Guan et al. 2005). These methods have mainly been applied to the mapping of climatological precipitation or the statistical characteristics of precipitation. They have the advantage of being relatively simple in their formulation and computationally fast to implement. However, they also strongly rely on the observational coverage in space and time and can fail to provide reliable estimates when the quality of the measurements themselves is poor, for instance, because of wind-induced undercatch, a wellknown problem especially in wintertime when precipitation falls in the form of snow. Correction methods have been proposed and tested (Legates and Willmott 1990; Førland et al. 1996; Goodison et al. 1998; Yang et al. 1999; Førland and Hanssen-Bauer 2000; Rubel and Hantel 1999; Yang and Ohata 2001, Bogdanova et al. 2002; Adam and Lettenmaier 2003) but can only be applied at rain gauge sites where other meteorological parameters such as wind speed and temperature are known as well. Two alternative approaches to geostatistical methods, based on the physical modeling of the mechanisms of orographic precipitation, have received a growing attention over the past decades (see, e.g., Roe 2005 for a review). One of them is provided by the development of sophisticated nonhydrostatic mesoscale numerical models, such as the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model (MM5; Grell et al. 1995) and Meso- NH (Lafore et al. 1998). These models look promising for the detailed estimation of precipitation at spatial scales of a few kilometers and temporal scales of a few hours (see, e.g., Richard et al. 2003; Asencio et al. 2003). Despite their many advantages, computational requirements currently limit their application to relatively small regions and short time periods. Nevertheless, two attempts to simulate precipitation in Iceland with MM5 over several years have recently been made (see Rögnvaldsson et al. 2004; Bromwich et al. 2005). In parallel to this approach, numerous diagnostic models with varying degrees of complexity have also been proposed (see, e.g., Collier 1975; Smith 1979, 2003; Alpert 1986; Alpert and Shafir 1989; Haiden et al. 1990; Barros and Lettenmaier 1993; Sinclair 1994; Pandey et al. 2000; Smith and Barstad 2004; Kunz and Kottmeier 2006a). Within this framework, orographic mechanisms such as airflow dynamics over mountains and cloud physical processes are parameterized with a small set of equations. The resulting models operate at time scales of a few minutes and are not computationally demanding, allowing the estimation (or forecast) of precipitation at fine spatial scales, over long periods of time. Despite the complexity of moist airflow over orography (see, e.g., Rotunno and Ferreti 2001; Medina and Houze 2003; Smith et al. 2003; Galewsky and Sobel 2005), these models have demonstrated downscaling skill in complex terrain and have been proposed to complement rain gauge information in data-sparse regions (Alpert and Shafir 1989) and radar data in unseen regions (Sinclair 1994). The goal of this paper is to apply a model of the quasi-analytic type, namely, the linear theory model of orographic precipitation (hereafter LT model) developed by Smith and Barstad (2004), to estimate the distribution of precipitation in Iceland at a fine horizontal resolution (1 km) and various time scales (day, month, season, year, climatology). The model is driven by 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data of temperature, wind, and precipitation to produce 6- hourly precipitation estimates. The free parameters of the model are adjusted by comparison with precipitation observations at low elevation from a rain gauge network and with precipitation derived from mass balance measurements at high altitude on three large ice caps. The study is organized as follows. A brief model description is given in section 2, and the data and methodology are described in section 3. The simulated precipitation fields are described and interpreted in section 4, and section 5 concludes the paper. 2. Model description The model used in this paper is the linear steadystate theory of orographic precipitation proposed by Smith and Barstad (2004). The reader is referred to this paper and to Smith et al. (2005) and Smith (2006) for a detailed description of the method and to Barstad and Smith (2005) for its evaluation. A brief description is given here. The model treats several central issues regarding orographic generation of precipitation, namely, airflow dynamics and cloud physics and how these processes vary with horizontal topographic scales. The 3D airflow pattern over complex terrain is solved using linear mountain-wave theory, and the resulting precipitation field is found using a linear cloud physics representation including cloud time scales for the formation and fallout of hydrometeors. When an air mass crosses a topographic barrier, condensed water is generated by forced ascent on the windward slopes and converted into falling hydrometeors on a time scale c ; these hydrometeors are advected with the airflow while falling to the ground on a time scale f. On the lee side, cloud water and hydrometeors evaporate. The concept starts by the

3 DECEMBER 2007 C R O C H E T E T A L postulation of two steady-state advection equations for atmospheric water: U q c S x, y q c x, y c, 1 U q r q c x, y q r x, y, 2 c f where U is the regionally averaged horizontal wind speed with eastward and northward components U and V; c and f are conversion and fallout times; x, y are the Cartesian coordinates; and q c (x, y) and q r (x, y) are vertically integrated cloud water and hydrometeor density, respectively, and have units of kilograms per meters squared. The S(x, y) source term in Eq. (1) is the vertically integrated condensation rate arising from forced ascent: S x, y C w w x, y, z e H w 0 z H w dz. In (3), the air is assumed to be saturated with vapor, C w is an uplift sensitivity factor depending on surface humidity and lapse rate, H w is the thickness of the ambient moist layer, and w(x, y, z) is the terrain-forced vertical air velocity: C w 0, 3 4 H w R T 2, 5 L where 0 is the surface water vapor density, is the environmental lapse rate, and is the average moistadiabatic lapse rate, T is the surface temperature, L is the latent heat of vaporization, and R is the gas constant for vapor. The terrain-forced vertical velocity at ground level is determined from the horizontal wind and the terrain gradient: w x, y, 0 U h x, y. The variations of vertical velocity with altitude are determined using linear mountain-wave theory, which allows the determination of the 3D airflow pattern over complex terrain and represents major improvement over previous versions of the model. It allows us to capture important features of the airflow such as decay of vertical velocity with altitude leading to a reduction in the amount of condensation, lateral airflow around topographic features leading to reduced uplift, and the formation of gravity waves. The effect of vertical stability of the air column is incorporated in the source term. In neutral conditions, vertical velocities at the lower boundary will propagate through the entire moist layer, while in stable conditions, they tend to reduce 6 aloft. In the latter case, the source field is smoothed and reduced. The ratio between transit time, which depends on the mountain width and wind speed, and cloud delay times controls the amount and distribution of precipitation. A narrow ridge or long s will advect generated cloud water from the windward side [where S(x, y) 0] to the lee, where it may become evaporated before it is converted into hydrometeors, and no rain results. Conversely, wide ridges or short values tend to favor precipitation on the windward side because cloud water has time for conversion into hydrometeors and fall out as precipitation [last term in Eq. (2)]. By transformation into Fourier space and algebraic manipulation of Eqs. (1) (3), we obtain an expression for the Fourier transform of the distribution of precipitation rate [Pˆ (k, l)]: Ŝ k, l Pˆ k, l 1 i c 1 i f, where Ŝ(k, l) is the Fourier transform of the source term defined in (3); k and l are the horizontal components of the wavenumber, i 1; and Uk Vl is the intrinsic frequency. The source term S(x, y) may be evaluated as Ŝ k, l C wi ĥ k, l 1 imh w, where ĥ(k, l) represents the Fourier transform of the terrain and m is the vertical wavenumber controlling the depth and tilt of the forced air ascent: m N 2 m k 2 l 2, 9 where N m is the moist Brunt Väisälä frequency. The combination of (7) and (8) results in a single equation representing the LT model: C w i ĥ k, l Pˆ k, l 1 imh w 1 i c 1 i f. 10 We see from (10) that the terrain is the only gridded variable used, and that precipitation intensity and spatial pattern depend on (i) orographic features, (ii) surface temperature, (iii) wind, (iv) stability, (v) moist layer thickness and (vi) cloud delay times. The first term in the denominator of (10) describes how the source term is modified by airflow dynamics, and the second and third terms describe advection during conversion of condensed water and fallout of hydrometeors, respectively. The negative sign in the first term

4 1288 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 gives an upstream shift to the precipitation pattern while the positive sign in the other two terms generates a downstream shift. All these terms tend to decrease the precipitation amount. The transfer function (10) is sensitive to scale. For given conditions, the efficiency with which precipitation is generated when an air mass crosses a topographic barrier increases with the spatial scale of the barrier. This is a consequence of the increased ability of the induced vertical motion to penetrate into the moist layer and to convert condensed water into hydrometeors. An inverse fast Fourier transform may then be used to compute the precipitation field, P, in x, y space: P x, y max Pˆ k, l e i kx ly dk dl P,0. 11 Here P represents the background or nonorographic precipitation caused by synoptic-scale uplift. The effect of leeside evaporation is simulated in (11) by truncation of negative precipitation values that may be generated by the model in descent regions. A practical advantage of the LT model is its ability to encapsulate the major processes governing orographic generation of precipitation in a relative simple and compact formulation. Furthermore, the limited number of input parameters necessary to apply it, namely, P, U, V, T, N m, c, and f, makes it very fast to implement and to run even with high horizontal resolutions and over long time periods. The main model limitations are the simplification of the vertical structure of the atmosphere through the use of vertical integration and a linearization of the fluid and cloud dynamics, and an assumption of a horizontally uniform background flow and atmospheric properties. Thus, the temperature, wind vectors, static stability, and cloud delay times are assumed constant in space. Furthermore, the atmosphere is assumed to be saturated so time windows when the model should be applied have to be chosen based on some properties of the background flow and will be further discussed below. Also, nonlinear effects such as flow blockings are not captured by the model. Furthermore, the model is not suitable to unstable atmospheric conditions. 3. Data and methodology a. ERA-40 data The input meteorological data to the LT model in this study namely, the background precipitation, ground temperature, and wind vectors have been derived from ECMWF ERA-40 (T159 L60) reanalyses (Uppala et al. 2005) covering the period September 1957 to August As precipitation is not a part of the diagnostic variables that are reanalyzed in ERA-40, the background precipitation was extracted from the ERA-40 prediction runs that are started at 0000 and 1200 UTC each day from the reanalyzed state of the atmosphere. To reduce spinup effects, the initial 12 h of each prediction run were discarded and a sequence of 12-hourly accumulated precipitation fields was generated from the interval h after the start of each run. The Icelandic ERA-40 topography is depicted as a broad bell shape only a few hundred meters high while several mountains actually exceed 1500 m. The reanalyzed data of temperature, wind, and humidity were extracted every 6 h at sigma-pressure level 53 (corresponding to 949 hpa for a mean sea level pressure of 1013 hpa). Figure 1 presents vertically integrated water vapor flux for the period in the direction of the wind at 925 hpa at the location 64 N, 21 W. From this, one can see that the largest amounts of water vapor are carried by southwesterly, southerly, and southeasterly winds. The dominance of these directions will lead to prevailing conditions for orographic generation of precipitation in mountainous regions in the southern part of Iceland. b. Rain gauge data For the comparisons with the simulations, 40 sites located at low elevation have been selected and classified subjectively into three groups corresponding to their broad topographic environment and exposure to prevailing weather systems: 1) sites located in gentle or open terrain, 2) sites mainly subject to orographic enhancement, and 3) sites mainly located in rain-shadow areas (cf. Fig. 2). The rain gauge network records precipitation over 24-h periods ending at 0900 UTC each day, and consists of gauges of Hellman type equipped with a Nipher-type shield. No attempt has been made so far at the Icelandic Meteorological Office to operationally correct gauge measurement errors such as those due to wind, wetting, and evaporation losses. However, according to Einarsson (1972, 1984), measured values for rain may be up to 25% too low. Sigurðsson (1990) suggested a mean annual correction of 1.28 and 1.8, for rain and snow, respectively, at lowland stations and 1.32 and 2 at highland stations. To deal with these biases, two corrections procedures were tested. The first one was applied by Yang et al. (1999) in Greenland for shielded Hellman gauges and the second was proposed by Førland et al. (1996) for the Nordic gauges. Both methods require information about precipitation phase and wind speed, and the second method requires temperature information as well. Both

5 DECEMBER 2007 C R O C H E T E T A L FIG. 1. Wind rose of the vertically integrated water vapor flux in the direction of the wind at 925 hpa located at 64 N, 21 W from 1990 to The radial distance represents the frequency (%) of the wind direction where the water vapor flux is categorized in three bins (all, larger than 100, and larger than 250 kg m 1 s 1 ). corrections were applied to the daily precipitation measurements. For the few stations measuring only precipitation, the closest wind and temperature measurements were used. The two correction procedures produced rather similar annual correction ratios for liquid precipitation but differed significantly for snow with larger corrections for the second method. The decision was made to use the second correction procedure because the results were found to be more in line with the analysis of Sigurðsson (1990). The correction procedure is as follows: P c k P g P w P e. 12 In (12), P c is the corrected daily precipitation, k is a correction factor due to aerodynamic effects, P g the measured daily precipitation, P W the wetting loss [set to 0.14 mm day 1 for rain, and 0.10 mm day 1 for snow as was done by Yang et al. (1999)], and P e is the evaporation loss (set here to 0). In the original formulation, trace precipitation is set to 0, but Førland and Hanssen-Bauer (2000) suggested that half the wetting plus evaporation losses could be added for the trace events in order to adjust for wetting and evaporation. It was decided for simplicity to set conservatively the trace precipitation ( P t ) to 0.10 mm day 1 for any given trace day (P g 0), as was done by Yang et al. (1999), but in that case, P w was set to 0 and the corrected precipitation was thus calculated as P c k P t. 13 For liquid precipitation, the correction factor (k l )is the same for all Nordic gauges: k l exp ln I W h ln I W h c. 14 In Eq. (14), I is the rain intensity (mm h 1 ), c is a gauge coefficient set here at 0.05, and W h is the daily average wind speed at gauge height; W h is derived from the measured 10-m wind speed using a logarithmic profile [see Eq. (7.2.1) in Goodison et al. 1998, p. 64]:

6 1290 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 FIG. 2. Topography of Iceland (1-km resolution), calibration/validation rain gauge network, and snow stakes. W h W H log h z 0 log H z , 15 where W H is the wind speed measured at the height H above ground (generally 10 m), h is the height (m) of gauge orifice above ground (generally 1.5 m), and z 0 the roughness length, set to 0.01 m from September to May and 0.03 m from June to August. The coefficient is the average vertical angle (degrees) to the top of obstacles around the gauge. As the precipitation amount P g was measured over 24 h, the rain intensity was first estimated by Î P g /24. This value was then multiplied by a scaling coefficient, I 1.72 Î, to account for the fact that it is usually not raining continuously for 24-h periods. The scaling coefficient was estimated by quantile regression (see Koenker and Hallock 2001), between the daily intensity Î and the daily intensity I P g /D derived from hourly measurements available at several automatic rain gauge stations, where D is the rain duration estimated from the hourly measurements. The correction factor (k s ) for solid precipitation is calculated with the following expression: exp 0 1 W h 2 T 3 W h T if 1 W h 7ms 1 and T 12 C k s 1.0 if W h 1ms 1, 16 where T is the temperature ( C); and the coefficients 0, 1, 2, and 3 were calibrated for the various gauges used in the Nordic countries. The values for the i coefficients selected here are, respectively, , , , and Values of W h greater than 7 m s 1 were set to 7 m s 1 when the precipitation type was snow, and values of W 10m greater than 20 m s 1 were set to 20 m s 1 when the precipitation type was rain, implying that the corrected precipitation during high winds must be considered quite uncertain. Temperatures lower than 12 C were set to 12 C.

7 DECEMBER 2007 C R O C H E T E T A L FIG. 3. (a) Statistical characteristics (mean, 10, 50, and 90 percentiles) of the ratio between corrected and measured monthly accumulated precipitation. The sample size for each month is indicated at the top of the figure. (b) Mean ratio between corrected and measured yearly accumulated precipitation as rain, mixed type, and snow. A total of 40 stations is used in these estimations. The correction factor k m for mixed precipitation is defined as k m 0.5k l 0.5k s. 17 Figure 3a presents the statistics of the ratio between corrected and measured monthly accumulated precipitation. Figure 3b presents the average ratios between the corrected and measured yearly accumulated precipitation for each phase (rain, mixed, and snow) separately. c. Glaciological data An extensive dataset of glacier mass balance observations in Iceland has been established in a collaboration between several Icelandic research institutes. The measurements have been carried out since 1988 on the Hofsjökull ice cap, since 1991 and 1992 on Vatnajökull, depending on location, and since 1997 on Langjökull (Sigurðsson et al. 2004; Björnsson et al. 1998, 2002). These data provide a unique opportunity to verify the precipitation simulations at high elevations in mountainous regions where very little other information about the magnitude or distribution of precipitation is available. The measurements were made twice a year, usually sometime between mid-september and mid- October in the autumn, and between mid-april and mid-may in spring. The mass balance measurements have been interpreted with mass balance modeling (Jóhannesson et al. 1995, 2006) to yield estimates of the ablation of snow and ice and of the part of the precipitation that falls as rain on the glacier. This makes it possible to estimate the total precipitation over the winter season and in some cases over the summer season also from the measured mass balance at stake locations. The glaciological precipitation estimates do not suffer from wind-loss problems to the same degree as precipitation data from meteorological stations, although other problems, such as those due to snow drift, need to be considered. To simplify the comparisons between the simulations and these observations and give them some consistency, the precipitation values were averaged over the number of days defining the measurement period. The simulated precipitation was accumulated over a fixed 7-month period (October April) and averaged over the corresponding number of days. The comparisons were made on these averaged values. d. Methodology The study domain was a 521 km 361 km rectangle covering the whole of Iceland, with a grid spacing of 1 km (Fig. 2), derived from a 500-m digital terrain model (DTM; obtained from the Icelandic Meteorological Office, National Land Survey of Iceland, Science Institute, University of Iceland, and National Energy Authority in 2004). The LT model was run at this horizontal resolution with a time step of 6 h, using the ERA-40 reanalyses data. The decision to use 1-km grid spacing allows one to obtain a high level of precision while keeping the processing time reasonable and the size of the generated precipitation files manageable. A resolution of 1 km was also used by Smith and Barstad (2004) who also argued that there is no need to smooth the terrain. This is because of the high-frequency filtering that is built into the model dynamics [see Eq. (10)]. The average temperature and wind vectors were cal-

8 1292 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 culated over the domain. The use of low-level wind to estimate the incoming airflow is in line with other studies. Hill et al. (1981) showed that the orographic enhancement of precipitation depends both on low-level wind and on background precipitation and used a wind speed at 600 m, just above the coastal friction layer in their study. Alpert (1986) used a wind inflow at the height of 1000 m, and Alpert and Shafir (1989) used wind vectors derived for the hPa layer. Sinclair (1994) used the mean of the winds from two ECMWF levels (850 and 1000 hpa) to calculate the low-level flow in his modeling study. The 12-h background precipitation was estimated at each grid point by bilinear interpolation, and a cutoff threshold of 0.3 mm (12 h) 1 was applied to limit the observed systematic overestimation of the frequency of occurrence of precipitation (FOP) by ERA-40 (see Crochet 2007). This threshold was found to provide relatively unbiased estimates of the monthly FOP at sites mainly located in gentle terrain and orographicenhanced regions, and a marked reduction of the systematic overestimation observed at sites located mainly in rain-shadow areas. To some extent, the value of this threshold may also be related to the interpolation procedure itself that may tend to exaggerate the spatial extent of the precipitation field between the wet and dry grid points. Since the model was run on a 6-h time step, the 6-h background precipitation was simply derived by dividing the 12-h background precipitation by 2. As the development of the equations in the LT model assumes that the air is saturated, the average relative humidity (RH) was calculated over a subset of the domain located upstream of the estimated incoming airflow, and the LT model was run only when this estimated RH was 90%. In doing so, the model was run 54% of the time. An RH threshold of 80% at 850 hpa was used in the orographic precipitation modeling study of Sinclair (1994). To further ensure that the model is only applied when the air is saturated, the background precipitation was also used as a mask to define the wet regions for application of the LT model. This procedure implicitly assumes that the spatiotemporal distribution of precipitation in Iceland is mainly controlled by large-scale weather systems and topographically induced modifications that take place within their structure. In situations where RH was 90%, the background precipitation alone was used, if any. 4. Results a. Calibration of model parameters The period was used to infer the most suitable values for the free parameters of the model ( c and f and moist stability frequency N m ). The dense data over the three ice caps allow the capture of the precipitation maxima and the identification of precipitation gradients along the different upstream and downstream slopes, and assist in the optimization of the parameters for best overall fit. The 40 rain gauges presented in Fig. 2 were used as a complementary source of information. Several statistical criteria were used together with a visual assessment, using scatterplots and maps, to study the realism of the modeled spatial precipitation distribution and the reproduced minima and maxima. The best overall results were obtained with c f 1200 s and N m s 1. These values are intended to be representative of the average conditions prevailing during the study period. Shorter or N m values produced in general too much windward precipitation and not enough precipitation on the lee sides of mountains. Longer or N m resulted in too low precipitation on the windward side and too much spillover. This average parameterization is in line with earlier results of Barstad and Smith (2005). However, these values may also be dependent on the temporal resolution of the ERA-40 precipitation data used in the present study that most likely overestimate the real FOP (see, e.g., Morrissey et al. 1994). These parameter values were then kept constant for the entire simulation period b. Horizontal resolution The question of the appropriate horizontal resolution in orographic precipitation modeling has been addressed in several studies. Sinclair (1994) found that km resolution was optimal for his diagnostic model, and at smaller grid spacings model shortcomings were such that the use of a mesoscale model was probably necessary to obtain more realistic airflow dynamics. At the same time, his results pointed to a decrease of maximum simulated precipitation with decreasing model resolution. Kunz and Kottmeier (2006b) observed that areal rainfall was underestimated at 10- and 5-km resolution and used a 2.5-km grid spacing with a diagnostic model also based on linear theory of hydrostatic flow, but no attempt was made to test finer resolutions. Sharples et al. (2005) argued that the fluid properties of the atmosphere lead to a loss of information about the actual terrain in a diffusive manner as the height above the terrain increases. They found that a resolution of 5 10 km was optimal for elevation-dependent interpolation of monthly precipitation in complex terrain. Guan et al. (2005) have found an optimal resolution ranging from 3 to 9 km but mostly 5 km for their sophisticated ASOADek mapping method.

9 DECEMBER 2007 C R O C H E T E T A L FIG. 4. Simulated precipitation accumulated for the winter 2001/02. Various small-scale features are simulated, reflecting the orographic generation of precipitation in the different mountainous regions of Iceland and rather dry conditions inland and in isolated valleys. These optimal resolutions do not imply that actual precipitation does not exhibit variations at smaller scales. They are partly related to model shortcomings and also to the separation distance between the rain gauges used to judge the model skill. The gauge distribution is often not dense enough to properly describe the spatial variability of precipitation in complex terrain. Barstad and Smith (2005) have argued that the classic statistical tests have the tendency to punish detailed estimates more than smooth ones. Daly et al. (1994) argued that the best digital elevation model (DEM) resolution is rather a function of data density than of the actual scale of orographic effects and that the temporal resolution of the data is also a factor to consider. Their choice to use a 5-min DEM in their Precipitation-elevation Regressions on Independent Slopes Model (PRISM) was partly driven by this practical consideration. However, they also found observational evidence indicating that a DEM with no more than 2-km grid spacing might be needed to resolve some observed orographic features and they did not exclude this possibility in a future development of their model. For statistical models, the use of smoothed or averaged topographic information is also a way to encapsulate and model broader scales of orographic effects. It is also worth mentioning that some of these statistical modeling studies use a high grid spacing under 2-km resolution in the final mapping process even though model parameters are averaged over a few square kilometers in the regression equations (see, e.g., Kyriakidis et al. 2001; Drogue et al. 2002). To briefly investigate the effect of the horizontal resolution on the quality of the simulations, several model runs were performed with a smoothed 1-km orography averaged over 5 km 5kmand8km 8 km windows, using the optimal parameterization defined previously. The results did not indicate any improvement in the model skill with increasing smoothing. The scatterplots between simulations and glaciological data sometimes appeared to become more scattered and/or the simulated precipitation more biased with these orographies, suggesting that meteorological processes taking place at scales shorter than 5 km are reflected in the glaciological data and are resolved by the LT model. These results are also consistent with those from Kunz and Kottmeier (2006b). A 1-km horizontal resolution was therefore used in this study without any further smoothing.

10 1294 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 FIG. 5. Mean winter precipitation (mm day 1 ) on three ice caps. Comparison (all years and all snow stakes) between (a) (c) LT model simulations and observed winter mass balance for each glacier averaged over the number of days in each period and (d) (f) ERA-40 simulations and observed winter mass balance for each glacier averaged over the number of days in each period: (a), (d) Hofsjökull, (b), (e) Langjökull, and (c), (f) Vatnajökull. The solid (dashed) lines are the regression (1:1) lines. c. Comparison between simulated winter precipitation and glaciological data As an example, Fig. 4 presents simulated precipitation for the winter 2001/02. Figure 5 presents a comparison for all data from each glacier and Table 1 shows the statistics over the entire period. There is a good overall agreement between observations and LT model simulations over the three ice caps, especially over Hofsjökull and Langjökull, where the simulations display remarkable skill. The results indicate that the LT model captures the main physical processes taking place in the mountainous areas of Iceland quite well, and that the chosen parameterization is suitable outside the calibra-

11 DECEMBER 2007 C R O C H E T E T A L TABLE 1. Comparisons of LT model (ERA-40) simulations and measured winter accumulated precipitation on three ice caps, averaged over the number of accumulated days. Positive error values indicate higher simulated precipitation relative to measurements. Statistics/period Vatnajökull Langjökull Hofsjökull R (0.06) 0.4 (0.21) 0.78 (0.07) Slope 0.68 (1.2) 0.95 (2.5) 0.99 (1.26) Intercept 3.7 (3.8) 1.14 ( 0.06) 0.23 (3.19) (mm) Mean relative 16.3 ( 48.5) 1.3 ( 53.7) 3.4 ( 42.8) error (%) Median relative 17.9 ( 51.1) 4.9 ( 60.7) 1.32 ( 51.4) error (%) RMSE (mm) 2.7 (5.4) 2.9 (6.4) 1.52 (5.21) Mean error 1.5 ( 4.5) 0.7 ( 5.4) 0.15 ( 4.19) (mm) Median error (mm) 1.5 ( 4.1) 0.3 ( 5.5) 0.14 ( 3.96) tion period. The location of the precipitation maximum is usually well identified and coincides with the observations. A comparison with the ERA-40 simulations alone helps to appreciate the gain in accuracy provided by the LT model over mountainous terrain. The study of each individual winter (not shown) revealed some variability in the quality of the simulations, with either slight overestimation or underestimation, but the patterns are usually well depicted. This variability in the quality of the simulations in space and time results from different causes. Most importantly, it is the result of the natural variability of the stability frequency and cloud delay times, whose values have been fixed in the model runs. The column-averaged values may change depending on the height of the melting layer and the phase of the hydrometeors. The sensitivity of the simulated precipitation to uncertainty in parameter values, such as condensation and fallout times, background precipitation, wind-direction, and stability frequency has been documented in Barstad and Smith (2005) with synthesized and real data. Rotunno and Ferreti (2001) and Galewsky and Sobel (2005) have shown that the horizontal gradient of moisture and the latent heat release that accompanies condensation control the distribution of static stability and therefore airflow dynamics. Also, the quality of the input meteorological information may sometimes be questionable or with such a horizontal variability that average values are not always suitable. Finally, the validity of the model itself may sometimes be questionable and some physical processes that are not captured by the model may degrade the quality of the simulations. 1) HOFSJÖKULL The measurements started in 1988 and the spatial coverage of this ice cap has been relatively homogeneous since The maximum measured and simulated precipitation usually occur close to the top of this ice cap. This peak value is in general slightly underestimated by the LT model. The precipitation distribution along the three snow-stake lines indicates a quasi-linear increase in precipitation with elevation. With some exceptions, it is observed that this precipitation gradient is quite similar on the different sides of the ice cap. However, there is a difference in the precipitation amount produced on the different sides, more or less marked in the different years because the directions of the incoming precipitation systems have different frequencies in different years. The slope receiving the largest precipitation amounts most likely faces the direction of the prevailing precipitation systems. The southeasterly (SE) and southwesterly (SW) flows most often dominate. The model usually simulates the spatial distribution of precipitation well, both on the windward and lee sides of the bell-shaped ice cap. These results also indicate indirectly that the quality of the simulated ERA- 40 wind direction is probably good. Snow drift also affects some of the lowest stakes and corrupts the validation. Figure 6 presents as an example the results for the winter 2001/02. 2) LANGJÖKULL The measurements started in 1997 and have had a similar spatial coverage from year to year. Apart from the first winter where the largest amounts are strongly underestimated by the simulations, the quality of the simulations is quite good. The maximum measured precipitation is usually located slightly south of the top of this glacier. Here too, it appears that the vertical precipitation gradient displays a rather similar behavior on the different sides of the ice cap. The magnitude and pattern of the precipitation depend also on the prevailing wind directions, and the SW and SE flanks receive the largest precipitation amounts. Snow drift appears to affect the observations at one specific stake located at the foothill of the glacier near the southern margin. Figure 7 presents the results for the winter 2001/02. 3) VATNAJÖKULL The measurements started in 1992 and the spatial coverage has varied considerably over the years. The precipitation gradient is similar on different parts of the ice cap, although somewhat more variability is observed than on the other two ice caps. The overall quality of the simulation is usually good, but not as good as

12 1296 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 FIG. 6. Validation of the LT model simulations accumulated over the winter 2001/02 for Hofsjökull and averaged over the number of days in the period. (a) Observations vs LT model simulation; the solid (dashed) lines are the regression (1:1) lines. (b) Geographical location of snow stakes. (c) Elevation vs simulated precipitation. (d) Elevation vs observed precipitation. For this winter, the simulation is realistic. Above 1100 m, the precipitation is distributed anisotropically along the different slopes, indicating that the prevailing winds were oriented between SE and SW. Snow drift probably affected the observations at the three lowest stakes on the northern slope and the two lowest stakes on the SE slope. on the other two ice caps. Some systematic discrepancies affect specific regions of this large ice cap. There is a tendency for an overestimation of precipitation in the vicinity of Öræfajökull, the highest peak in the southern part of the glacier, where the slopes are locally very steep. Flow splitting might be the cause of an overestimation on and near sharp peaks. The LT model will not produce a reduced precipitation on single peaks due to splitting. On the other hand, a systematic underestimation of the precipitation is usually found on the lower parts of the northern and northeasterly (NE) slopes, which are located most of the time on the lee side of the synoptic wind field. This result could arise from different reasons. At the lowest stakes, snow drift might take place. At higher altitudes, spillover might occur more and/or more often than simulated over this large glacier. This result also indicates that the LT model may not simulate windward and leeside precipitation equally well, even though this problem was not observed on the other two glaciers. The trajectory of an air parcel on the lee side can be rather complex (Smith et al. 2003). Vatnajökull is the largest glacier in Iceland (8100 km 2 ). The complex topography of Vatnajökull together with the vicinity of a mountain range along the SE coast of Iceland makes it more difficult to simulate the precipitation there than on the other two glaciers whose shape is relatively simple. Finally, yet another reason for this underestimation might be that mesoscale precipitation systems might have been produced over this large glacier during periods assumed dry at the synoptic scale, in our procedure. Figure 8 presents the results for the winter 1995/96, for which the observations have the best spatial coverage. d. Comparison between simulated monthly precipitation and rain gauge data Comparison at individual rain gauges shows that the LT model can locally produce realistic estimates. Fig-

13 DECEMBER 2007 C R O C H E T E T A L FIG. 7. As in Fig. 6 but for the winter 2001/02 for Langjökull. The quality of the simulation is not as good on this glacier as on Hofsjökull, perhaps because this glacier has a more complex orography and some of the processes taking place are therefore more difficult to simulate. The simulation slightly overestimates the precipitation amount on the SW and western parts. The SE and northern parts, on the other hand, are well simulated. ure 9 presents a validation for each group of stations and a comparison with raw ERA-40 results. Table 2 presents the statistics. The results illustrate the capacity of the LT model to simulate precipitation distribution at a local scale by dynamical downscaling of synopticscale ERA-40 precipitation. The study of the model performance for each month made it possible to identify some intermonthly and interannual variability in the quality of the accumulated precipitation fields, in the same manner as already observed in the validation based on data from the ice caps. An example is given in Fig. 10 for the summer e. Simulation of individual storms The ability of the LT model to simulate daily precipitation fields was assessed through case studies for the period , using all available measurements from the rain gauge network. The analysis revealed that the model performed well in a large number of cases, but poor estimates sometimes arose, presumably caused by the same reasons as mentioned in the previous sections. Discrepancies between estimates of 24-h precipitation ending at 1200 UTC and 24-h gauge precipitation ending at 0900 UTC may also affect the validity of the comparisons, especially when the precipitation field is intermittent and/or moves rapidly with time. A point comparison between model output and station data may also introduce some problems of data representivity, especially when the wind velocity and the horizontal drift of hydrometeors are important. The inspection of a large number of cases indicated that the largest source of discrepancy was a wrong identification of the wet and dry regions, leading sometimes to large errors on the windward side of the mountains. In properly identified precipitation areas, systematic overestimation or underestimation was sometimes observed. This is probably related to errors in the cloud time delays, stability frequency, and large-scale wind field. In a large number of the studied cases, where the model performed well, it was observed that the spatial extent of the ERA-40 precipitation field was too large

14 1298 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 FIG. 8. As in Fig. 6 but for the winter 1995/96 for Vatnajökull. This winter was well simulated, except on the NE corner where a marked underestimation is seen. in the descent region, downstream of the main mountain barriers. The LT model dries this leeside precipitation when the ERA-40 precipitation is lower in absolute value than the modeled negative leeside precipitation [Eq. (11)]. To illustrate this effect, Fig. 11 shows simulated precipitation for two days in 1992 and 2000, one with northerly winds (U 3.3ms 1, V 12.4 m s 1, T K) and the other one with southerly winds (U 0.9ms 1, V 10.4 m s 1, T K). In both cases, a clear intensification of the precipitation on the windward side of mountains near the coast is simulated, together with a marked precipitation shadow on the lee side illustrating well the lee drying in the descent region due to the evaporation of hydrometeors and condensed water. Figure 12 presents a comparison of the two simulated precipitation fields against the rain gauge network, and illustrates clearly the ability of the LT model to downscale the ERA-40 precipitation and simulate the pattern and magnitude of daily precipitation when the parameterization is right and the large-scale meteorological situation is realistic. To illustrate what to expect from the model performances on a day-to-day operational situation, Fig. 13 presents a validation for a sequence of events taken in chronological order and for which more than 50% of the rain gauge network received precipitation. Finally, Table 3 presents the statistics of the probability of detection (POD) and false alarm rate (FAR) over the entire period and confirms that the LT model reduces the FAR, but at the expense of a reduction of the POD. f. Statistical characteristics of daily precipitation The statistical characteristics of daily precipitation were estimated each year and for each month over the period , at each of the 40 stations given in Fig. 2, namely, the FOP, the mean and several quantiles (Q p ) of precipitation rate greater than or equal to 0.1 mm day 1, which correspond to the nonexceedence probability p (p 25%, 50%, 75%, 90%). Figure 14 presents the scatterplots considering all stations together, and Table 4 summarizes the results. Table 5 gives the same statistics calculated with ERA-40 for comparison. The quantiles are usually unbiased, except sometimes at the lowest probabilities where a systematic overestimation is evident and for the Q 90 value that is

15 DECEMBER 2007 C R O C H E T E T A L FIG. 9. Validation of monthly accumulated precipitation at meteorological stations over the period Observations vs LT model simulations in (a) gentle terrain, (b) rain-shadow areas, (c) orographically enhanced terrain. Observations vs ERA-40 in (d) gentle terrain, (e) rain-shadow areas, and (f) orographically enhanced terrain. The solid (dashed) lines are regression (1:1) lines. underestimated at some sites. At some stations, a systematic overestimation (underestimation) of all the quantiles is observed. The scatter is also more or less pronounced depending on the sites. The systematic overestimation of FOP by ERA-40 at sites mainly located in rain-shadow areas was successfully eliminated or strongly reduced after dynamical downscaling with the LT model. This FOP reduction is to a large extent due to the lee drying of the excess ERA-40 background precipitation. At some sites, however, mainly located in orographically enhanced regions along the south coast, a slight systematic overestimation of FOP with ERA-40 was not completely removed after dynamical downscaling with the LT model, indicating that at these locations the slight excess of FOP was driven either by a wrong identifica-

16 1300 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 TABLE 2. Comparisons of LT model (ERA-40) simulations and gauge-corrected monthly accumulated precipitation for the period Positive error values indicate higher simulated precipitation relative to gauge-corrected measurements. Statistics Gentle Shadow Enhancement R (0.64) 0.49 (0.44) 0.59 (0.43) Slope 0.71 (1.08) 0.89 (0.92) 0.90 (1.5) Intercept 27.6 (8.5) 10.0 ( 7.7) 13 (14.6) (mm) Mean relative 17.3 ( 3.4) 24.0 (67.4) 22.2 ( 22.4) error (%) Median relative 7.6 ( 11.6) 1.5 (35.7) 9.8 ( 32.1) error (%) RMSE (mm) 51.2 (44.4) 39 (43) 72.9 (109.1) Mean error 6.4 ( 15.9) 2.9 (13.9) 2.1 ( 63.4) (mm) Median error (mm) 6.2 ( 10.1) 0.66 (17.9) 10.5 ( 39.3) tion of the wet and dry regions by ERA-40 in the windward regions or not enough drying by the LT model when these regions were in the lee side. This wrong identification may also indicate that a fixed cutoff threshold of 0.3 mm (12 h) 1 may not be optimal all over Iceland. Finally, the largest systematic overestimation (underestimation) of monthly accumulated precipitation (cf. Fig. 9) at some sites was mainly the result of an overestimation (underestimation) of the mean precipitation rate rather than the remaining slight bias in FOP. g. Precipitation climatology The 30-yr averaged monthly and annual precipitation fields were derived for the two standard periods and Figure 15 presents the 30-yr averaged annual precipitation for the period The pattern is similar to the simulated precipitation in 2001/02 in Fig. 4 and is characterized by a decrease of precipitation with latitude modulated by the orographic generation of precipitation in the different mountainous regions corresponding to the dominating SE to SW flows. The pattern is smoother than the underlying topography (Fig. 2). The area-averaged values are 1830 and 1740 mm yr 1 for the periods and , respectively. Table 6 presents statistics for the mini- FIG. 10. Validation of monthly accumulated LT model simulations at meteorological stations for the summer (a) June, (b) July, (c) August, and (d) September. The solid (dashed) lines are the regression (1:1) lines.

17 DECEMBER 2007 C R O C H E T E T A L FIG. 11. (a) Simulated daily precipitation on 8 Sep 1992 when the main wind direction on Iceland was from the north and (b) on 13 Sep 2000 when the wind direction was from the south. Locations of weather stations are shown with symbols. Filled (open) symbols denote stations where precipitation was observed (not observed). Triangles (squares) denote stations on the upslope (downslope) side of mountains. This upslope/downslope assessment was made by calculating the vertical velocity w(x, y, z) at ground level. mum and maximum annual values for the period Summary and conclusions A physically based orographic precipitation model has been adapted for Iceland. This model includes 3D airflow dynamics over complex terrain, hydrometeor formation and fallout times, and leeside evaporation. The model was driven using ERA-40 reanalyses data. Gridded estimates of precipitation on a 1-km grid were calculated and then accumulated over various time scales for the period This made it possible FIG. 12. Validation of daily accumulated simulations at meteorological stations on 8 Sep 1992 [(a) upslope and (b) downslope] and 13 Sep 2000 [(c) upslope and (d) downslope]. The solid (dashed) lines are the regression (1:1) lines. The filled (open) symbols are LT model (ERA-40) estimates.

18 1302 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 FIG. 13. Validation of daily accumulated LT model simulations at meteorological stations on several days: (a) 30 Jan 1999, (b) 1 Feb 1999, (c) 2 Feb 1999, (d) 3 Feb 1999, (e) 4 Feb 1999, (f) 10 Feb 1999, (g) 11 Feb 1999, (h) 12 Feb 1999, and (i) 13 Feb The dashed lines are the 1:1 lines. Panels (a), (b), and (h) illustrate cases with credible simulations, although the largest observed values are underestimated. Panels (d), (e), (f), and (g) illustrate cases in which the identification of the position of the precipitation field is poor leading to very poor estimates. Panels (c) and (i) illustrate two cases in which the location of the precipitation field was well identified, but a poor model parameterization, and/or possibly errors in the large-scale synoptic wind field, lead to respectively a slight systematic underestimation and overestimation at most of the sites. to construct the climatology of precipitation for two 30-yr standard periods, with basically the same accuracy for both periods and for the entire domain. The simulated precipitation was found to be in good agreement with what is known about the distribution of precipitation in Iceland from glacier mass-balance measurements and from observations at meteorological stations, suggesting that the LT model represents TABLE 3. Simulated daily precipitation fields: POD and FAR for ERA-40 and LT model simulations for the period Statistics ERA-40 LT model Mean POD (%) Median POD (%) Mean FAR (%) Median FAR (%) 18 14

19 DECEMBER 2007 C R O C H E T E T A L FIG. 14. Comparisons of statistical characteristics of daily LT model simulations and gaugecorrected precipitation calculated at 40 stations, each year for each month over the period : (a) Q25, (b) Q50, (c) mean, (d) Q75, (e) Q90, and (f) FOP. The solid (dashed) line represents the regression (1:1) line. the essential physics and dynamics of orographic generation of precipitation at a fine spatial and temporal scale. The methodology proposed in this paper appears to be suitable for a broad range of settings involving the orographic generation of precipitation and is likely to be of practical value for hydrologists, glaciologists, meteorologists, and climatologists. This model used together with global reanalysis and analysis data available over the past 50 yr offers new possibilities in terms of spatial estimation of precipitation in complex terrain, especially in regions of high latitude and altitude where ground observations are lacking and affected by various biases, making the use of geostatistical methods sometimes impractical. The procedure makes it possible to simulate the distribution of snow accumulation on glaciers in more detail than has usually been done in glacier mass balance studies and

20 1304 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8 TABLE 4. Comparisons of statistical characteristics of daily LT model simulations and gauge-corrected precipitation calculated at 40 stations, each year for each month over the period Positive error values indicate higher simulated precipitation relative to gauge-corrected measurements. TABLE 5. Comparisons of statistical characteristics of daily ERA-40 simulations and gauge-corrected precipitation calculated at 40 stations, each year for each month over the period Positive error values indicate higher precipitation relative to gauge-corrected measurements. Statistics FOP Q 25 Q 50 Mean Q 75 Q 90 Mean error Median error Mean relative error (%) Median relative error (%) RMSE R Statistics FOP Q 25 Q 50 Mean Q 75 Q 90 Mean error Median error Mean relative error (%) Median relative error (%) RMSE R opens new possibilities to model and analyze the evolution of mass balance over the past 50 yr on poorly monitored glaciers in regions with complex topography. In mountainous regions with rain gauge networks of sufficient density and where measurement errors are acceptable or well corrected, the LT model could be used to simulate a first-guess precipitation field and residuals of the observations could be interpolated for local adjustment and further improvement. The statistical properties of simulated daily precipitation were found to be in agreement with observations. Fine-mesh maps of such statistical parameters could be derived by this approach, making it possible to FIG. 15. The 30-yr averaged annual precipitation derived from LT model simulations for the period Thin black curves are 250-m-elevation contours and thick black curves are the outline of the four main Icelandic ice caps.