On correcting precipitation as simulated by the regional climate model COSMO-CLM with daily rain gauge observations
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Precipitation amounts simulated by the regional climate model COSMO-CLM are compared with observations from rain gauges at German precipitation stations for the period 1960–2000. The model overestimates precipitation by about 26 %. This bias is accompanied with a shift of the frequency distribution of rain intensities. The model overestimation varies regionally. A correction function is derived which adjusts rain intensities at every model grid point to the observations.
KeywordsRain Rate Model Bias Precipitation Trend Model Precipitation Rain Gauge Station
Climate change is a global phenomenon, and its impact is usually studied with help of global circulation models (GCMs). The coarse spatial resolution of GCMs, however, makes it difficult to assess regional impacts. Thus, regional climate models (RCMs) are used to transfer GCM output to limited areas with higher spatial resolution by so-called dynamical downscaling (Von Storch et al. 2000; Murphy 1999). Downscaling results for Europe are available, e.g. from the regional climate model COSMO-CLM (Rockel et al. 2008). Like GCM runs, also RCM runs need to be validated for past periods for which observations are available, e.g. Jacob et al. (2001), Petrik et al. (2011) prior to their application for climate projections. In this study, we analyze the simulated precipitation from the so-called Consortial Runs (Hollweg et al. 2008) executed with COSMO-CLM, which provide the physical data base for several studies in the framework of the research program Klimazwei of the German Federal Ministry for Education and Research to support climate protection and adaptation (Bardt et al. 2009).
The amount of precipitation including its temporal and spatial distribution ranks among the most important climate parameters (Rutgersson et al. 2001). However, similar to weather prediction, simulated precipitation is also one of the most uncertain predictants. Feldmann et al. (2008) showed deficiencies of precipitation simulated by COSMO-CLM for south-western Germany. More critical with respect to expected precipitation changes is, however, eastern Germany, where already today annual precipitation falls below 500 mm in some regions. Further reductions would confront especially agriculture with considerable problems. In this study, we evaluate precipitation simulated with COSMO-CLM for Germany and derive a correction function, which corrects COSMO-CLM-predicted precipitation for future scenario runs.
Dobler and Ahrens (2008) corrected the COSMO-CLM precipitation bias by a two-step approach suggested by Schmidli et al. (2006). In a first step, the simulated rain day frequency is adjusted to the observed frequency, by selecting the appropriate rain day threshold for the model, while the observational threshold is set to 1 mm. In the second step, the rain day intensity minus the respective threshold is considered. These reduced intensities are corrected by a scaling factor in such a way that the rain amounts in model and observations are equal after the correction. For the second step, Dobler and Ahrens proposed an alternative approach. Here, the reduced intensities are fitted to a gamma distribution. The different scale and shape parameters for model and observations define the conversion from uncorrected to corrected model rain. Both of the two-step versions ensures that two features of the corrected model rain are guaranteed: the number of rainy days and the total amount of rain are equal to that found in the observations.
In this study, we propose an even stricter approach to bring the distribution of the model in line with that of the observations. We apply the method of quantile matching, using the cumulative frequencies of the two data sets. This is a mapping method first inspired by Panowski and Brier (1968), which sorts the two distributions and connects the data pairs of each two corresponding rank numbers to each other. We assume temporal constancy of the mapping function as any possible change of the function due to global warming is detectable only by future observations.
2.1 Data sets
We analyze the modelled precipitation of the Consortial Runs as provided by the model and data group at the Max Planck Institute for Meteorology in Hamburg (Hollweg et al. 2008). The Consortial Runs are generated by the regional climate model COSMO-CLM (Rockel et al. 2008), which is based on the weather forecast model COSMO of Deutscher Wetterdienst (DWD) (Steppeler et al. 2003). The COSMO-CLM Consortial Runs have a horizontal resolution of 0.165° corresponding to about 18 km, and are nested one-way in the global climate prediction model ECHAM5 which has a resolution of about 1.8° (Roeckner et al. 2006). ECHAM5 runs of the current climate are available from 1860 on (see e.g. http://cera-www.dkrz.de/WDCC/ui/Entry.jsp?acronym=EH5-T63L31_OM-GR1.5L40_20C_1_6H) using the observed greenhouse gas forcings. Different future greenhouse gas and aerosol scenarios are taken from IPCC AR4 for simulating the future climate until the year 2100 (IPCC 2007).
We evaluate the present day COSMO-CLM simulations for the past 41 years (1960–2000). The three existing independent model realizations of the present day climate with COSMO-CLM (so-called C20 runs) were generated by nesting COSMO-CLM in three global model runs started at three arbitrary years taken from a 500 years control run. In Sect. 3.6, we will shortly discuss the precipitation changes as expected by climate projections following the moderate future scenario A1B (IPCC 2000).
The present day model output is compared to daily precipitation measurements from rain gauge stations operated by the DWD (Behrend et al. 2010). About 5,000 precipitation stations were recording during the period 1960–2000, which assures that on average each COSMO model grid box of 18 km width is sampled by several observing stations. This high-density precipitation data set has been used by many authors as a reference for the evaluation of model results and reanalysis output of precipitation (e.g. Zolina et al. 2004, 2008; Bachner et al. 2008; Ebell et. al. 2008). Following these authors, we abstain from any wind correction of the gauge estimates. We will show, however, that the observed model bias of 26 % is much larger than measurement errors, which would lead to corrections of only a few percent for most precipitation rates (Nespor and Sevruk 1998; Richter 1995). For very small precipitation rates corrections could amount to 10 % and above, but contribute only marginally to the daily precipitation amounts considered here. Thus, a possible, but relatively small, underestimation by the rain gauges must be kept in mind.
Hollweg et al. (2008) already reported an annual wet bias of the CLM-C20 for Germany of 153 mm, which corresponds to about 20 % of the total annual precipitation amount. They compared the Consortial CLM-C20 runs to so-called reference CLM runs, which are driven by reanalysis data and therefore closer to the true climate. These reference runs themselves have a wet bias compared to observations of in average 48 mm. Thus, both biases add up to about 25 %, which is consistent with our findings. We should mention, however, that Hollweg et al. (2008) consider the latter bias as insignificant because the observational data sets used in their study differ mutually by 85 mm.
2.2 Data processing
Precipitation measurements are known to suffer from deficiencies especially at very low rain rates (Nespor and Sevruk 1998). In these cases, evaporation and wind loss make it difficult to distinguish between dry and wet days. This becomes critical, if climate indices, as e.g. the maximum number of consecutive dry days (CDD), are considered. This parameter depends strongly on the ability to resolve especially the low rain rates. To avoid such problems, Peterson et al. (2001) recommended the usage of a precipitation threshold of 1 mm/day, which has been adopted by many authors, e.g. (Klein Tank and Können 2003; Zolina et al. 2010). However, the present study considers the rain rate itself and no indices based on it, so that a specifically increased threshold for dry days is not necessary here. Instead, the observational threshold of 0.1 mm/day is applied to both observed and model data to distinguish dry from rainy days.
In this study, we compare daily rain amounts observed by rain gauges with modelled precipitation. Due to their different spatial resolutions, the two data sets are not readily comparable. Model data are grid averages, whereas rain gauge measurements are point estimates, which do contain more variability. The surplus of variance of the observational data corresponds to the mean spatial variability within the model grid boxes. This scale problem can be overcome using the additivity of variance, as discussed e.g. by Lindau (2003) and Lindau and Ruprecht (2000). Concerning precipitation this scale problem is discussed in detail by Ruiz-Villanueva et al. (2012). They found extreme high maxima in individual point observations not reflected in radar measurements, which similar to model results are estimates of area averages. Thus, prior to the comparison of both data sets we average all observations within the boundaries of the model grid areas and compute daily precipitation sums from the model output.
3 Methods and results
The resulting number of comparable data pairs is of the order of 107 (about 103 grid boxes cover Germany; 40 years contain about 104 days). Our aim is to convert every model value in such a way that the corrected data reflects the same statistical properties as they are found in the observations. This goal can be achieved by quantile matching, which sorts both data sets in ascending order with respect to precipitation amount and derives a suitable projection. The sorting, which is performed separately for both data sets, assigns a rank number to each individual daily grid box value. By comparing only the resulting ranks, the original model-measurement pairs are disconnected. Instead, precipitation amounts with same rank numbers in both data sets are connected. Since several million data pairs are related to each other, the transfer function is quite smooth and requires no further intermediate step, e.g. by fitting analytical functions.
One model run (C20-1) is used for the derivation of the transfer function and a second run (C20-2) is used for verification. Both runs describe only the past climate, thus it is cannot be guaranteed that the derived conversion function also applies for the future. In using the derived transfer function for future runs, we hypothesize that our transfer function does not change significantly in time.
In Sect. 3.1, we derive the 26 % model wet bias. In Sect. 3.2, a general correction function is derived by mapping the daily grid averages of the model to those of the observations. Using this general correction, monthly biases remain, but we show in Sect. 3.3 that these biases are random, because the standard deviation of the monthly biases is in the same range as the root mean square (RMS) difference between two independent model runs. When in Sect. 3.4, the same methodology is applied spatially, i.e. to grid box averages instead of monthly averages, the biases of two independent model runs are highly correlated, which calls for a separate correction of each grid box. In the final Sects. 3.5 and 3.6, we discuss the change of precipitation as given by model scenarios for the coming decades and compare trends in the past of both model results and observations.
3.1 The model bias
Fraction of rain-free days for individual rain stations (row 1) and after averaging within the model grid cells as obtained for an increasing minimum number of stations; also, the model results are changing slightly, as for higher minimum numbers some grid boxes are no longer taken into account
At least 1 stations
At least 2 stations
At least 3 stations
At least 4 stations
While the overall model wet bias is 26 %, the regional bias over large parts of eastern Germany is even 50 % (Fig. 1b). We hypothesize is that this bias will project also to future scenarios. Strong regional biases also occur at the Black Forest with an overestimation of the rain at the windward side and opposite effects at the lee side of the mountains. Schwitalla et al. (2008) discuss these orographically induced errors and show that they can be largely reduced by enhancing the spatial resolution of the model. Another possibility to reduce the orographically induced bias would be to use the prognostic precipitation, which is newly implemented into COSMO (Seifert and Beheng 2006a, b).
3.2 The general transfer function for precipitation
3.3 Monthly means
Mean and standard deviation that is generated by the monthly precipitation bias of two COSMO-CLM runs; in the last row, it is not the annual cycle of the bias, but the root mean square (RMS) difference between the two runs, which is considered
Std dev (mm/day)
3.4 Spatial means and individual grid box correction
When we apply the correction function to the independent second model realization (C20-2) a bias of 2.96 mm/a remains from the original bias of 188 mm/day and the error of an individual pixel is 23.78 mm/a (Fig. 8b). This error is mainly induced by the model uncertainty itself, because its spatial structure does not differ in a statistical sense from the pattern given in Fig. 6, where the difference between the two runs is shown. The last pattern is characterized by a mean bias of 4.6 mm/a and a standard deviation 21.9 mm/a. If differences between two model runs are considered to be unavoidable model uncertainties, an error of 21.9 mm/a for individual grid boxes and an overall error of 4.6 mm/a for the entire domain is expected. The characteristics for Fig. 8b are with 2.9 and 23.8 mm/a comparable. Since they are in the same range as the expected model errors, we conclude that the scatter shown in Fig. 8b is due to the model uncertainty.
3.5 Future precipitation changes
3.6 Precipitation trends
COSMO-CLM when driven with the C20 global runs of the current climate overestimates precipitation as compared to observations from German precipitation stations. In this study, we derived a transfer function for the modelled precipitation based on the method of cumulative frequencies, which transforms the frequency distribution of the model into that observed at the rain gauges. Seasonal variations of the model bias are shown to be random; thus, a specific monthly correction is not required. In contrast, spatial variations of the model bias are significant. Consequently, our transfer function is derived separately for every model grid box. The overall effect of the correction reduces the modelled precipitation by 26 %. Owing to this large bias, the absolute values of modelled rain from COSMO-CLM are useful only after correction. In particular, uncorrected precipitation amounts from the model scenarios would be much higher than presently observed, even if the model would not produce any significant trend. Precipitation changes predicted for the next decades are, however, within the range of the model uncertainty.
The correction function presented here is assumed to be independent of time; thus, the trends found in the two independent model realizations of the past arise in both, the corrected and the uncorrected data. Surprisingly, the concordant trends do not occur in the observations for the period 1960–2000. We can conclude that statistically significant precipitation trends may well occur also for stable climates, even if they do not happen in reality.
This work has been performed within the project LandCaRe 2020 of the research program klimazwei supported by the Bundesministerium für Bildung und Forschung BMBF (01 LS 05107).
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
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