Temporal disaggregation of daily temperature and precipitation grid data for Norway
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(2) 990. JOURNAL OF HYDROMETEOROLOGY. applies the conceptual Hydrologiska Byråns Vattenbalansavdeling (HBV) rainfall-runoff model (Bergstr€ om 1995; Beldring 2003) with daily meteorological forecast data as input in 117 catchments distributed throughout Norway. The HBV model consists of three main components, which are subroutines for 1) meteorological corrections, snow accumulation, and snowmelt; 2) subroutines for evaporation and soil moisture estimation; and 3) runoff response and routing subroutines. It can further be divided into subbasins and elevations zones. The hydrological models are calibrated and run using an extensive meteorological gridded dataset providing daily temperature and precipitation data from 1957 to the present for all of Norway at 1 3 1 km2 grid resolution (seNorge grids; see section 2a). For each elevation zone, the mean temperature and precipitation is estimated from the daily seNorge grids and used as input to the model. The daily temporal resolution is dictated by the historical meteorological data. Meteorological forecasts and runoff observations, however, are available at a much finer temporal resolution than daily (e.g., hourly). To benefit from these data in runoff forecasting, it is necessary to recalibrate the hydrological models to a more appropriate temporal resolution. Thus, the existing daily temperature and precipitation grids need to be temporally disaggregated. As a compromise between computational costs and necessary hydrological detail, a temporal resolution of 3 h is assumed to be sufficient. Since the early 1970s, there has been a lot of effort spent on disaggregating weather data, and existing approaches vary in their degree of specialization and complexity (e.g., Valencia and Schaake 1972; Santos and Salas 1992; Cowpertwait et al. 1996; Koutsoyiannis and Onof 2001). The most pragmatic approach is to simply distribute daily weather data to subdaily resolutions by assuming uniform distributions. Such distributions are seldom appropriate, and such an approach does not really address the problems pointed out above. Daily temperature is often disaggregated into subdaily series by using a functional time dependency of air temperature during a day (e.g., Baker et al. 1988). For precipitation, Debele et al. (2007) report that besides uniformly distributing it across the day, several solutions are possible: 1) spatially transferring higher-resolution data from nearby gauges to the area of interest (conditional on a significant spatial correlation), 2) stochastically generating subperiod data, and 3) using a multivariate disaggregation model that combines solutions 1 and 2. Koutsoyiannis (2003) and Koutsoyiannis et al. (2003) provide an overview over the historical development of (rainfall) disaggregation models and illustrate the advantages and weaknesses of several univariate and multivariate stochastic models. In common, all approaches. VOLUME 14. produce synthetic series for subperiods that are possible and likely realizations of the actual series and that are statistically consistent with the higher-level data. A common problem with these methods, however, is that generally none or only a very few (nearby) observations with a subdaily temporal resolution are available. That confines the applicability of these approaches for generating subdaily data on a national scale. Indeed, there are only a few examples reporting on generating or providing subdaily meteorological data with high spatial resolution on the regional or national scale. Notable examples are W€ uest et al. (2010), who combine rain gauges and weather radars to produce disaggregated 2 3 2 km2 gridded precipitation data with hourly resolution for Switzerland, and the precipitation simulator NiedSim (short for Niederschlag-Simulator), which provides highresolution precipitation data for any desired point in all of southwest Germany based on the methodology presented in B ardossy (1998). The approach put forward in this study differs somewhat from those described above. In addition to the extensive meteorological seNorge grids with a daily temporal resolution, a hindcast series (1957–2010) with gridded temperature and precipitation data on an hourly temporal resolution is available for northern Europe (see section 2b). The spatial resolution of this hindcast series is, however, an order of magnitude larger (;10 3 10 km2) than for the seNorge grids. For the recalibration of the hydrological models, it is desirable to obtain a higher temporal resolution while at the same time maintaining the spatial resolution of the seNorge grids (1 3 1 km2). That is why we have developed a simple approach to temporally disaggregate the daily seNorge temperature and precipitation grids into 3-hourly resolution by consulting the temporal patterns of the gridded hindcast series. This paper presents and evaluates the proposed disaggregation approach.. 2. Data a. SeNorge grids For mainland Norway, daily gridded temperature and precipitation data from 1957 to present at 1 3 1 km2 grid resolution are available and are provided to the public by the Norwegian Meteorological Institute (met.no) on www.senorge.no (Engeset et al. 2004). These grids are derived by the interpolation of observed daily mean temperature and accumulated precipitation over the interval 0600–0600 UTC. The temperature grids are interpolated by applying a residual kriging approach with around 150 observations (Tveito et al. 2005). Topography and geographic locations are used as deterministic components to. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(3) JUNE 2013. VORMOOR AND SKAUGEN. consider large-scale climate trends, that is, the dependency of temperature on altitude and continentality (Tveito and Førland 1999). The resulting ‘‘detrended’’ temperature data more closely fulfill the assumptions of stationarity and isotrophy that are required for geostatistical analyses (Tveito et al. 2005). Ordinary kriging is then used to model the residuals as a stochastic field (e.g., Isaaks and Srivastava 1989). The spatial interpolation of precipitation is carried out by applying triangular irregular networks (TINs) with terrain adjustment using about 630 observations from staffed measurement stations (Tveito et al. 2005). Triangles are built between three points, which are then transformed to a regular 1 3 1 km2 precipitation grid. Based on the altitude of the observation stations, another TIN is created and the difference in elevation for a grid cell between this TIN and the digital elevation model is used to correct the interpolated precipitation with respect to altitude. Referring to Førland (1979), a 10% increase in precipitation for every 100-m increase in altitude is assumed for elevations below 1000 m MSL (5% per 100 m above 1000 m MSL). Observed precipitation is further corrected for the state of precipitation (liquid versus solid) determined by the interpolated temperature data from the procedure described above, and for systematic wind losses considering a simple model introduced by Førland et al. (1996). Cross validation for the temperature and precipitation grids was performed for a 3.5-yr time period (Mohr and Tveito 2008). Correlation coefficients between estimated and observed 24-h mean temperature and accumulated precipitation are r 5 0.95 and r 5 0.88, respectively. The mean absolute errors are reported to be 0.958C for temperature and 1.5 mm for precipitation. Temperature estimates agree best during summer, when a considerable mixing within the atmospheric boundary layer is present. Precipitation estimates agree best during winter, when large-scale precipitation patterns dominate over convective precipitation.. b. High-resolution hindcast series Gridded temperature and precipitation hindcasts with hourly temporal resolution and 0.18 grid spacing are available for the time period between September 1957 and December 2010. These hindcast series have been generated by the dynamical downscaling of two global atmospheric analyses to a regional domain: 1) the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) global atmospheric reanalysis (Uppala et al. 2005) for September 1957 to August 2002 and 2) operational atmospheric analyses from the ECMWF for September 2002 to December 2010 (Haakenstad et al. 2012). For the dynamical. 991. downscaling, a hydrostatic numerical weather prediction model, the High-Resolution Limited-Area Model (HIRLAM) version 6.4.2 (Und en et al. 2002) is used. Validated against observed data, HIRLAM results do not depend strongly on the forcing data that are used (Haakenstad et al. 2012). The HIRLAM domain is a rotated spherical grid, resolved by 248 3 400 grid points with 0.18 (;10 3 10 km2) horizontal grid spacing, and it covers the regions of northern Europe including Iceland, the British Isles and the Scandinavian Peninsula, the North Sea, the Norwegian Sea, and the Barents Sea (Reistad et al. 2011). Vertically, the model is resolved by 40 hybrid levels and driven by the operational atmospheric reanalyses (ERA and ECMWF) at the boundaries with temperature, wind, specific humidity, and cloud water in all 40 levels plus surface pressure. The dynamic timing interval of the model is 4 min. Every 6 h, a 9-hourly forecast is simulated and background fields for several variables are obtained for every hour. As the first 3 h are influenced by the initialization of the model, only the data from the last 6 h of each forecast are used. In this way, a historical weather data series with an hourly temporal resolution is extracted from the achieved HIRLAM model runs. Detailed specifications on the functionality of the HIRLAM model can be found in Und en et al. (2002). There are only a very few publications about the quality of the HIRLAM temperature and precipitation (hindcast) data. Regarding temperature, Bremnes and Homleid (2007) report that HIRLAM reproduces diurnal variations as good as other operational numerical weather prediction models used by the national meteorological office in Norway. Temperature errors vary depending on season: they tend to be larger during winter than in summer because of the model’s limitation in describing small-scale processes associated with land surface cooling, especially in winter. On a daily average, however, the errors are very low. During the night, the errors are relatively larger than during daytime (M. Køltzow 2013, met.no, personal communication). Regionally, temperature is modeled better along the coast than in inland Norway. Regarding precipitation, there is no indication about the diurnal performance of HIRLAM because of a lack of hourly observation data.. 3. Method: The disaggregation approach The temporal patterns of the HIRLAM hindcasts are used to disaggregate the daily seNorge data for temperature and precipitation into 3-hourly values for September 1957 to December 2010. The HIRLAM hindcast grids are. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(4) 992. JOURNAL OF HYDROMETEOROLOGY. spatially downscaled and geospatially adjusted to the domain of the seNorge grids, which cover 1195 3 1550 km2 (1 852 250 km2) with the southwest corner at UTM 33N 75000 6450000, where UTM is the Universal Transverse Mercator coordinate system. As a result the HIRLAM ;10 3 10 km2 resolved grids are spatially downscaled to a 1 3 1 km2 grid resolution with the 10 3 10 grid cells given equal values. In this process the spherical geographic coordinates of HIRLAM are converted to the UTM coordinate system, which leads to the fact that the downscaled HIRLAM grid cells are not identically overlapping with the seNorge cells. Therefore, a nearest-neighbor classification (for the center of the cells) is performed to identify the HIRLAM grid cells that are located closest to the particular seNorge grid cells and that are used for the temporal disaggregation of the particular seNorge grid cells. Daily mean temperature is then disaggregated into 3-hourly values by adding the difference between a daily seNorge grid and a daily HIRLAM grid to a 3-hourly HIRLAM grid as shown in Eq. (1): 3. å THIRLAM1h. TseNorge3h 5 i51. 0. 3. 1. 24. å THIRLAM1h C. B B 1 BTseNorge24h 2 i51 @. 24. C C. A. (1). The daily HIRLAM grids are represented by the mean of 24-hourly summed values for a certain day (t) corresponding to the 0600 (t 2 1) to 0600 (t) UTC seNorge day (t refers to the date associated with the recorded seNorge value). A total of eight 3-hourly HIRLAM grids are calculated for the previous day (t 2 1) at the intervals 0600–0900, 0900–1200, 1200–1500, 1500–1800, 1800–2100, and 2100–2400 UTC and for the current day (t) at the intervals 0000–0300 and 0300–0600 UTC. The deviation between daily seNorge and daily HIRLAM temperature is thus added to each of the eight 3-hourly HIRLAM temperature grids, which give eight grids for temperature per 24 hours with 1 3 1 km2 spatial and 3-hourly temporal resolutions. Note that the difference between daily seNorge and HIRLAM temperature is assumed to be constant for all time intervals in a given day. Daily accumulated precipitation is disaggregated into 3-hourly precipitation by using the temporal distribution derived from the HIRLAM series as illustrated in Eq. (2):. VOLUME 14. 0. 3. 1. B å PHIRLAM1h C C Bi51 C. PseNorge3h 5 PseNorge24h 3 B C B 24 A @ å PHIRLAM1h. (2). i51. Eight fractions of 3-hourly precipitation per 24 hours are generated by dividing the sum of 3-hourly precipitation (same intervals as for temperature) to the accumulated daily precipitation from the hourly HIRLAM hindcast series. Each grid with 3-hourly fractions for precipitation is then multiplied with the daily seNorge precipitation grid for the corresponding 24 h. This results in eight grids per day providing precipitation with a 1 3 1 km2 spatial and a 3-hourly temporal resolution. In the case that a grid cell in the HIRLAM hindcast is showing no daily precipitation, the fractions are set to 0.125, which means that daily precipitation in the corresponding seNorge grid cell is distributed uniformly over the eight 3-h time intervals. By applying these two simple schemes, the daily meteorological seNorge data are disaggregated into 3-hourly resolution for approximately 53 years, while respecting the observed daily means as derived from the seNorge series and the spatiotemporal correlation of the HIRLAM hindcast series. In principle, these approaches can also be adjusted for a disaggregation down to hourly values (the limit is given by the temporal resolution of the HIRLAM hindcast series).. 4. Results and discussion The presented disaggregation approaches for temperature and precipitation are validated by comparing the disaggregated data with 3-hourly observed data from five meteorological observation stations for the time period 2000–05. The disaggregated data used for validation are extracted from the nearest grid cell to the observation stations. The stations are Blindern (Oslo), Lillehammer, Trondheim, Tromsø, and Furuneset (see Fig. 1). These five stations represent the climatic variability in Norway well, with a wet maritime climate on the west coast (Furuneset and Tromsø), an intermediate climate at some distance from the coast (Blindern and Trondheim), and a dry inland climate (Lillehammer). It is important to mention that these stations are automatic stations with hourly recordings that are not used for the generation of the daily seNorge grids. In addition to comparing with observed data, the seNorge disaggregated data (seNorge DA) are evaluated against 1) daily seNorge data simply split into eight parts (in the following seNorge 24/3 h) and 2) 3-hourly. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(5) JUNE 2013. VORMOOR AND SKAUGEN. 993. a. Temperature. FIG. 1. Map of mainland Norway indicating the topography and the location of the five validation stations.. HIRLAM data. The seNorge 24/3-h data are represented by eight equal fractions of the daily total for precipitation and eight identical replications of the daily mean for temperature. Pearson correlation coefficients (r), mean absolute errors (MAE), and root-mean-squared errors (RMSE) are used to indicate the accuracy of the disaggregated temperature and precipitation data. Note that for temperature, we compare deviations from the monthly means. By this, we exclude the effect of the annual cycles, which may lead to an overestimation of the correlation. For precipitation the seasonal dependency is much less than for temperature, and accuracy estimation with monthly anomalies turned out to be similar to those obtained with raw observation data. That is why we use the latter for the accuracy estimation for precipitation. In addition, empirical cumulative distribution functions (CDFs) are estimated for precipitation with occurrence probabilities lower than 20%. This is done to evaluate the accuracy of intense rainfall, which is the major driving force for the generation of floods in small catchments and therefore of particular interest and a major motivation for this study.. Table 1 shows the statistical measures r, MAE, and RMSE indicating the performance of the disaggregation model for temperature. Relatively high correlations (r 5 0.77–0.93) are found for all temperature series, including seNorge 24/3 h and HIRLAM. However, the correlation between seNorge DA (r 5 0.89–0.93) and observed series are consistently higher than the correlations between observations and seNorge 24/3 h (r 5 0.76–0.86) and HIRLAM (r 5 0.77–0.91), respectively. The error estimates in Table 1 show that the seNorge DA series consistently have the lowest errors (both MAEs and RMSEs) for each of the five stations. The difference between seNorge DA, seNorge 24/3 h, and HIRLAM is largest for Blindern and Lillehammer, both characterized by significant annual amplitudes in temperature. At these two stations the errors of the seNorge DA are up to 40% smaller than the errors of seNorge 24/3-h and HIRLAM data, respectively. Also at Trondheim, Tromsø, and Furuneset, the errors for the seNorge DA are considerably smaller (about 20%–30%) in comparison with the other two series. The largest errors are found for Lillehammer, which is characterized by the highest degree of continentality of all the five stations. This is line with the regional performance of HIRLAM, that is, that temperature is modeled best along the coast rather than in inland Norway. Consequently, the absolute errors are supposed to be smaller at the coast, but the benefit of the disaggregation is highest for the inland areas, which is due to the implicit bias correction of HIRLAM temperature by the regionalized observed daily data of seNorge [see Eq. (1)]. Table 1 also shows the difference in median and mean values of the three series with regard to observed values. All three series tend to slightly overestimate temperature, but none of the series emerge as unique in showing consistently the smallest differences. Figure 2 shows scatterplots that compare the deviation from the monthly means of the three generated temperature series with those of the observed series for the five validation stations. The shapes of the scatter of the points show the high level of accuracy for the seNorge DA temperature data. Here, for all the stations the majority of the points are closely located along the perfect-fit diagonal line. For the seNorge 24/3-h series the scatter of the points around the diagonal line is a little higher than for both the seNorge DA and the HIRLAM series. The fit of the HIRLAM series to the diagonal line is better compared to seNorge 24/3 h but often a little weaker compared to the seNorge DA series. In addition, some bias is seen for the HIRLAM series. At Blindern and Lillehammer the majority of the. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(6) 994. JOURNAL OF HYDROMETEOROLOGY. VOLUME 14. TABLE 1. Statistical measures (r, MAE, and RMSE) and differences in median and mean for the three temperature series (i.e., deviations from the monthly means) at the five validation stations. Bold numbers signify the most accurate series. Station Blindern. Furuneset. Lillehammer. Trondheim. Tromsø. Series. r. MAE. RMSE. DT median. DT mean. seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM. 0.93 0.76 0.89 0.89 0.81 0.77 0.93 0.77 0.87 0.92 0.82 0.91 0.92 0.86 0.90. 1.05 1.98 1.62 1.16 1.47 1.61 1.28 2.17 1.82 1.34 1.90 1.35 1.17 1,46 1,54. 1.44 2.66 2.15 1.57 1.95 2.13 1.77 2.89 2.30 1.77 2.48 1.77 1,53 1,89 1,91. 0.1 0.0 0.9 0.4 0.43 0.0 0.2 0.2 0.9 0.7 0.6 0.2 0.7 0.6 1.2. 0.2 0.1 1.1 0.3 0.3 20.2 0.3 0.3 0.9 0.8 0.7 0.3 0.6 0.6 1.2. points are located slightly below the diagonal line, which means that HIRLAM tends to overestimate temperature at these locations (see also the last two columns in Table 1). At Furuneset, HIRLAM tends to underestimate low temperatures and overestimate high temperatures, which is probably a consequence of a misrepresentation of the station’s proximity to the sea because of the coarse spatial resolution of the model. Temperature in a HIRLAM grid cell depends on its most dominant land cover type (water, ice, bedrock, low vegetation, or wood). Furuneset is physically located on a peninsula in the North Sea. The HIRLAM grid cell that covers Furuneset, however, is probably characterized by dominating bedrock and low vegetation cover, which would lead to an overestimation of continentality. The tendency to underestimate low temperatures and overestimate high temperatures may also be consistent to a known tendency of HIRLAM to underestimate cloud cover. This tendency is higher during daytime than during the night (M. Køltzow 2013, met.no, personal communication). In summary, the seNorge DA temperature data are found to be very accurate compared to observed data. Although the differences in the correlation coefficients are rather small, the error estimates and the scatterplots show that the seNorge DA data are superior compared to both the other two series. This implies, for a recalibration of the hydrological models at a higher temporal resolution, the seNorge DA temperature data are preferable when compared to seNorge 24/3-h data and the HIRLAM hindcast data.. b. Precipitation In Table 2, the statistical measures r, MAE, and RMSE illustrate the performance of the disaggregation model for precipitation. Generally, the correlation coefficients. are lower than for temperature. This is probably because of the more continuous nature (both temporally and spatially) of temperature compared to precipitation. The highest correlations are found for Trondheim with correlation coefficients between r 5 0.62 and r 5 0.51. Almost no correlation is found for the precipitation series at Furuneset, which is located at the Norwegian west coast (r 5 0.08 and r 5 0.05). At this location (see Fig. 1), precipitation can be very intense and variable because of the coastal and complex terrain, which will induce orographic effects varying with the wind direction. However, the correlations between the seNorge DA data and observed data are, also for this station, higher than for the other series. The error estimates for precipitation show a similar pattern as seen for the temperature series, but it is not as distinct since none of the series is consistently better when compared to the others. For three out of the five stations (Blindern, Lillehammer, and Tromsø), however, both the MAE and RMSE are smallest for the seNorge DA. At Trondheim, seNorge DA shows the smallest MAE, while seNorge 24/3 h shows the smallest RMSE. Only for Furuneset does the HIRLAM series provide the smallest errors. Another measure that is presented in Table 2 is the accuracy of the precipitation series in estimating 3-hourly intervals without any precipitation (zeroMatch). Here, for all stations the seNorge DA precipitation series show the best score for correctly predicting the time intervals with zero precipitation (i.e., the probability of dry days), while the poorest scores are found for HIRLAM. The best scores for seNorge DA are found for Blindern and Tromsø with 72.5% and 55.4% correctly predicted intervals. The poorest match for seNorge DA is found for Furuneset with only 38.5% correctly. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(7) JUNE 2013. VORMOOR AND SKAUGEN. 995. FIG. 2. Scatterplots comparing the deviation from monthly means of observed data and modeled temperature series from seNorge DA, seNorge 24/3 h, and HIRLAM hindcast data for the five validation stations and the period 2000–05.. predicted time intervals. All series tend to underestimate the amount of time intervals with zero precipitation, that is, they predicted precipitation when no precipitation occurred. For seNorge 24/3 h this is expected since daily precipitation is uniformly distributed over all subdaily intervals. Thus, precipitation is also allocated to intervals when no precipitation is measured.. The HIRLAM hindcast series overestimates intervals with precipitation because of a well-known tendency of simulating a constant small amount of precipitation (Skaugen 2002). However, although the intervals with precipitation are overestimated, it does not necessarily imply an overestimation of the accumulated precipitation (see. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(8) 996. JOURNAL OF HYDROMETEOROLOGY. VOLUME 14. TABLE 2. Statistical measures (r, MAE, and RMSE), the percentage of correctly predicted time intervals with zero precipitation (ZeroMatch), and the deviation of accumulated precipitation compared to observations for the three precipitation series at the five validation stations. Number of time intervals with zero precipitation: Blindern, 6771; Furuneset, 6167; Lillehammer, 6842; Trondheim, 12 633; and Tromsø, 7835. Bold numbers signify the most accurate series. Station Blindern. Furuneset. Lillehammer. Trondheim. Tromsø. Series. r. MAE. RMSE. ZeroMatch. Deviation of åPobs. seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM seNorge DA seNorge 24/3 h HIRLAM. 0.55 0.38 0.42 0.08 0.05 0.06 0.48 0.32 0.38 0.62 0.52 0.51 0.44 0.39 0.36. 0.29 0.68 0.66 1.43 1.38 1.23 0.38 0.44 0.44 0.30 0.35 0.35 0.38 0.43 0.45. 1.05 1.16 1.17 3.71 3.41 3.40 1.16 1.30 1.22 0.79 0.76 0.83 1.56 1.57 1.62. 72.5% 64.2% 43.2% 38.5% 29.2% 31.8% 54.2% 44.6% 29.6% 54.5% 38.3% 45.6% 55.4% 47.3% 34.6%. 214.1% 214.1% 210.7% 26.9% 26.9% 240.1% 213.7% 213.7% 13.1% 130.0% 130.0% 138.1% 18.6% 18.6% 69.2%. Table 2, last column). At Blindern and Furuneset, the accumulated precipitation for both the seNorge and HIRLAM series is less than the observed accumulated precipitation. At Trondheim and Tromsø accumulated precipitation is overestimated by all the series. At Lillehammer, both seNorge series underestimate accumulated precipitation by 13.7%, whereas HIRLAM overestimates only by a small degree (3.1%). This is the smallest deviation from observed precipitation values in the entire comparison and may well be within the measurement uncertainty. Another outstanding disagreement between the seNorge and HIRLAM series is seen at Furuneset. Here, the seNorge series are quite close to the observations (26.9%), whereas HIRLAM underestimates by 40.1%, which is the highest deviation from observed precipitation in the comparison. This large deviation is due to the coarse resolution of HIRLAM and its limitation in representing the complex coastline of Norway. Consistently high deviations for all series are found for Trondheim (HIRLAM 138.1%; seNorge 130%). The consistently lowest deviation for all series is found for Tromsø (HIRLAM 19.2%; seNorge 18.6%). What is really compared here are the differences in precipitation and temperature between the seNorge grids derived from manually observed stations and adjusted to a topography averaged over 1 3 1 km2 and the closely located automatic weather stations. Differences in elevation and exposure between the grid cell and the locations of the automatic stations may account for some of the differences shown in Table 2. Since the designated use of the seNorge DA series is to recalibrate the hydrological models at a finer temporal resolution, which makes them suitable for simulating. extreme events of short durations, it is important to evaluate the accuracy of heavy rainfall with small occurrence probabilities. Therefore, for all of the precipitation series at each validation station, empirical CDFs are calculated for precipitation with occurrence probabilities ,20% (i.e., cumulative densities above 0.8). These are compared with the empirical CDFs of observed values. The plots with the CDFs for all stations and series are shown in Fig. 3. Figure 3 shows that the empirical CDFs for seNorge DA tend to be closest to those of the observed data for three of the five stations (Lillehammer, Furuneset, and Tromsø). Visual inspection shows almost perfect matches between the empirical CDFs of the seNorge DA data and observed values at the stations Furuneset and Tromsø. The difference between seNorge DA and HIRLAM at Lillehammer is quite small. The poorest match is generally found for the empirical CDF of seNorge 24/3 h, which is expected because of the uniform distribution of daily rainfall over all the time intervals. However, a similarly poor match is also found for the HIRLAM series at Furuneset. At Blindern and Trondheim seNorge DA and HIRLAM perform almost equally well. A slight tendency of underestimating extreme precipitation is seen for HIRLAM at all stations and for seNorge DA at Blindern and Lillehammer. From the different measures, which have been used to evaluate the different precipitation series, seNorge DA appears as the best method for generating temporally fine resolution data. However, this recommendation is not as straightforward as for temperature. Although the seNorge DA data have the highest correlation with the observed precipitation, the claim for superiority is not. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(9) JUNE 2013. VORMOOR AND SKAUGEN. 997. FIG. 3. Empirical cumulative distribution functions for observed, seNorge DA, seNorge 24/3 h, and HIRLAM precipitation data for the validation period 2000–05 at the five validation stations.. supported by all the error measures. The skill in predicting time intervals without precipitation is clearly highest for the seNorge DA data, which is an important feature, for example, if the presence of precipitation is used as an index of cloudiness in energy balance modeling of snowmelt or evapotranspiration. When considering the empirical CDFs of the modeled precipitation series, it is shown that the accuracy in extreme precipitation is best simulated by the seNorge DA data for three out of the five stations. This is a very important skill and very promising with respect to the simulation of floods from short-duration intense precipitation. A final point is that the spatial resolution of the disaggregated seNorge grids is a magnitude higher than the spatial. resolution of the HIRLAM hindcast. This implies that the spatial variability in precipitation due to topographical variability is better resolved by the seNorge DA series. In summary, an overall assessment of the evaluation measures described and discussed above suggests that the seNorge DA series comes out best. The skill in simulating extreme precipitation is considered to be especially important. One critical remark, however, that refers to both disaggregated temperature and precipitation series is that we know only a very little about the accuracy of the HIRLAM hindcast in representing the diurnal cycle. Possible errors in timing of HIRLAM may be transferred to the disaggregated data that will also influence. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
(10) 998. JOURNAL OF HYDROMETEOROLOGY. the hydrological simulations. However, on a 3-hourly resolution, small errors in the representation of diurnal cycle will not affect the disaggregation. Information on this kind of error will be possible to assess when the data have been used for hydrological simulations.. 5. Conclusions and outlook This paper presents a simple and, we believe, novel approach for the temporal disaggregation of temperature and precipitation grid data on the national scale. By consulting the temporal patterns of a HIRLAM hindcast series for Northern Europe with an hourly temporal and ;10 3 10 km2 spatial resolution, existing daily meteorological 1 3 1 km2 grids for all of Norway were disaggregated into 3-hourly values for the period September 1957 to December 2010. The validation of this approach shows that the disaggregated 3-hourly dataset is very accurate compared to observed values for temperature. With regards to precipitation the evaluation of the seNorge DA series compared to the seNorge 24/3 h and HIRLAM series also suggest that the seNorge DA series should be the favored choice as input in high temporal resolution rainfall-runoff models, although the distinction between the series was not as clear as for temperature. By applying the presented disaggregation approaches we further narrow the gap in temporal resolution between historical and forecasted meteorological data. In this way, it will be possible for the flood forecasting service in Norway to make much better use of the temporally detailed meteorological forecasts. It is important to note, however, that the overall precision of the hydrological forecasts will not necessarily improve, but it will be possible to help in forecasting critical events of short duration and small spatial scales that would go unnoticed using a daily resolution. In addition, a historical national gridded dataset of 3-hourly temporal resolution and 1 3 1 km2 spatial resolution opens up possibilities for more detailed study and modeling of, for example, snowmelt, evapotranspiration, and extreme values. The 3-hourly resolution data can also be consulted for the statistical downscaling of climate change control and scenarios series needed in impact modeling. The approach described in this paper is not confined only to Norwegian conditions, but can, in principle, be applied anywhere. Moreover, the approach is not only limited to the disaggregation of gridded data but can also be applied for disaggregating daily data from meteorological observation stations. The proposed method for disaggregation takes the best features from the observed grid, such as a small bias and high spatial resolution, and combines them with the. VOLUME 14. best features of the HIRLAM atmospheric model, that is, a physically based description of the meteorological processes and high temporal resolution. Acknowledgments. We thank the Norwegian Meteorological Institute (met.no) for providing the HIRLAM hindcast data. We are grateful to Hilde Haakenstand and Morton Køltzow from met.no for discussions and comments on the performance of HIRLAM. Axel Bronstert and two anonymous reviewers are thanked for their valuable comments that helped to improve the manuscript. REFERENCES Baker, J. M., D. C. Reicosky, and D. G. Baker, 1988: Estimating the time dependence of air temperature using daily maxima and minima: A comparison of three methods. J. Atmos. Oceanic Technol., 5, 736–742. Bardossy, A., 1998: Generating precipitation time series using simulated annealing. Water Resour. Res., 34, 1737–1744. Beldring, S., 2003: Estimation of parameters in a distributed precipitation-runoff model for Norway. Hydrol. Earth Syst. Sci., 7, 304–316. Bergstr€ om, S., 1995: The HBV model. Computer Models of Watershed Hydrology. V. P. Singh, Ed., Water Resources Publications, 443–476. Bl€ oschl, G., and M. Sivapalan, 1995: Scale issues in hydrological modelling: A review. Hydrol. Processes, 9, 251–290. Bremnes, J. B., and M. Homleid, 2007: Verification of operational numerical weather prediction models March to May 2007. Met.no Note 04/2007, 62 pp. [Available online at http://met. no/Forskning/Publikasjoner/Publikasjoner_2007/filestore/ 04_2007.pdf.] Bronstert, A., and A. Bardossy, 2003: Uncertainty of runoff modelling at the hillslope scale due to temporal variations of rainfall intensity. Phys. Chem. Earth, 28B, 283–288. Cowpertwait, P. S. P., P. E. O’Connell, A. V. Metcalfe, and J. A. Mawdsley, 1996: Stochasting point process modelling of rainfall. II. Regionalisation and disaggregation. J. Hydrol., 175, 47–65. Debele, B., R. Srinivasan, and J. Y. Parlange, 2007: Accuracy evaluation of weather data generation and disaggregation methods at finer timescales. Adv. Water Resour., 30, 1286–1300. Engeset, R., O. E. Tveito, E. Alfnes, Z. Mengistu, H.-C. Udnæs, K. Isaksen, and E. J. Førland, 2004: Snow map system for Norway. Proc. 23rd Nordic Hydrological Conf., Tallinn, Estonia, Nordic Association for Hydrology, 112–121. Førland, E. J., 1979: Nedbørens høydeavhengighet (Precipitation and topography, in Norwegian with English summary). Klima, 1, 3–24. ——, and Coauthors, 1996: Manual for operational correction of Nordic precipitation data. DNMI Rep. 24/96, DNMI, Oslo, Norway, 66 pp. Haakenstad, H., M. Reistad, J. E. Haugen, and Ø. Breivik, 2012: Update the NORA10 hindcast achieve for 2011 and a study of polar low cases with the WRF model. Met.no Rep. 17/2012, 69 pp. Isaaks, E. H., and R. M. Srivastava, 1989: An Introduction to Applied Geostatistics. Oxford University Press, 592 pp.. 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(11) JUNE 2013. VORMOOR AND SKAUGEN. Koutsoyiannis, D., 2003: Rainfall disaggregation methods: Theory and applications. Proc. Workshop on Statistical and Mathematical Methods for Hydrological Analysis, Rome, Italy, University of Rome, 1–23. [Available online at http://itia.ntua. gr/getfile/570/1/documents/2003RainDisag.pdf.] ——, and C. Onof, 2001: Rainfall disaggregation using adjusting procedures on a Poisson cluster model. J. Hydrol., 246, 109–122. ——, ——, and H. S. Wheater, 2003: Multivariate rainfall disaggregation at a fine timescale. Water Resour. Res., 39, 1173, doi:10.1029/2002WR001600. Mohr, M., and O. E. Tveito, 2008: Daily temperature and precipitation maps with 1 km resolution derived from Norwegian weather observations. Preprints, 17th Conf. on Applied Climatology, Whistler, BC, Canada, Amer. Meteor. Soc., 6.3. [Available online at https://ams.confex.com/ams/pdfpapers/ 141069.pdf.] Reistad, M., Ø. Breivik, H. Haakenstad, O. J. Aarnes, B. R. Furevik, and J.-R. Bidlot, 2011: A high-resolution hindcast of wind and waves for the North Sea, the Norwegian Sea, and the Barents Sea. J. Geophys. Res., 116, C05019, doi:10.1029/2010JC006402. Santos, E. G., and J. D. Salas, 1992: Stepwise disaggregation scheme for synthetic hydrology. J. Hydraul. Eng., 118, 765–784.. 999. Skaugen, T., 2002: A spatial disaggregation procedure for precipitation. Hydrol. Sci. J., 47, 943–956. Tveito, O. E., and E. J. Førland, 1999: Mapping temperatures in Norway applying terrain information, geostatistics and GIS. Nor. Geogr. Tidsskr., 53, 202–212. ——, I. Bjørdal, A. O. Skjelvåg, and B. Aune, 2005: A GIS-based agro-ecological decision system based on gridded climatology. Meteor. Appl., 12, 57–68. Unden, P., and Coauthors, 2002: HIRLAM-5 scientific documentation. HIRLAM-5 Project, SMHI, Norrk€ oping, Sweden, 144 pp. Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 2961–3012. Valencia, D., and J. C. Schaake, 1972: A disaggregation model for time series analysis and synthesis. Rep. 149, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Cambridge, MA, 190 pp. W€ uest, M., C. Frei, A. Altenhoff, M. Hagen, M. Litschi, and C. Sch€ar, 2010: A gridded hourly precipitation dataset for Switzerland using rain-gauge analysis and radar-based disaggregation. Int. J. Climatol., 30, 1764–1775.. Brought to you by NVE | Unauthenticated | Downloaded 06/15/21 07:43 AM UTC.
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