Data assimilation approaches such as the ensemble Kalman filter method have become an important technique for paleoclimatological reconstructions and reanalysis. Different sources of information, from proxy records and documentary data to instrumental measurements, were assimilated in previous studies to reconstruct past climate fields. However, precipitation reconstructions are often based on indirect sources (e.g., proxy records). Assimilating precipitation measurements is a challenging task because they have high uncertainties, often represent only a small region, and generally do not follow a Gaussian distribution. In this paper, experiments are conducted to test the possibility of using information about precipitation in climate reconstruction with monthly resolution by assimilating monthly instrumental precipitation amounts or the number of wet days per month, solely or in addition to other climate variables such as temperature and sea-level pressure, into an ensemble of climate model simulations. The skill of all variables (temperature, precipitation, sea-level pressure) improved over the pure model simulations when only monthly precipitation amounts were assimilated. Assimilating the number of wet days resulted in similar or better skill compared to assimilating the precipitation amount. The experiments with different types of instrumental observations being assimilated indicate that precipitation data can be useful, particularly if no other variable is available from a given region. Overall the experiments show promising results because with the assimilation of precipitation information a new data source can be exploited for climate reconstructions. The wet day records can become an especially important data source in future climate reconstructions because many existing records date several centuries back in time and are not limited by the availability of meteorological instruments.
Precipitation is one of the key components of the climate system. Understanding its variability is fundamental due to its impact on the ecosystem and on human society. Instrumental observations are the main data source for studying its spatiotemporal variability. However, instrumental measurements are often insufficient because long time series are rarely available and their spatial distribution is rather sparse, especially further back in time. To examine the decadal variability of precipitation, longer time series are needed. This is often done by analyzing proxy records, documentary data, or model simulations.
Simulations suggest, for instance, that the tropical monsoon regions are characterized by the largest interannual variability of annual precipitation, and the interannual variability exhibits significant changes on the multi-decadal scale
One challenge in global reconstructions is the required observation network density. To test how dense a network for a climate field reconstruction needs to be, pseudo-proxy experiments can be performed. A set of such experiments was conducted by
Thanks to the introduction of new techniques in the field of paleoclimatology, nowadays spatially complete and physically consistent reconstruction can be derived. Paleoclimate data assimilation provides a framework in which observational data and model simulations are optimally combined to obtain global, three-dimensional climate fields. Using the data assimilation approach is advantageous because by assimilating only one type of climatic variable (e.g., temperature), we can gain information from other climatic fields present in the model simulation based on their covariances between the observed and unobserved variables. Monthly instrumental temperature and sea-level pressure data, documentary temperature data, and tree-ring proxy records have been successfully used with the ensemble Kalman fitting (EKF) method to reconstruct past climate fields
In this paper, monthly precipitation information in the form of precipitation amounts or the number of days with precipitation in each month (wet days) is assimilated with the EKF method
This paper is structured as follows: in Sect. 2 an overview of the EKF techniques is given and the model simulation and the observations are introduced. Section 3 describes the experimental framework and the skill metrics used for evaluation. In Sect. 4 the results are presented, and they are discussed in Sect. 5. We conclude how monthly precipitation information can be assimilated best in Sect. 6.
To reconstruct climate fields by assimilating monthly precipitation amounts and the number of wet days per month, the ensemble Kalman fitting (EKF) data assimilation technique was used (described in detail in
The EKF is implemented serially; that is, observations are assimilated one by one, which makes the assimilation process computationally more efficient. The localization of
The Chemical Climate Change over the past 400 years (CCC400) model simulations serve as the model background. They were produced with the ECHAM4.5 model
The location of precipitation observations
Precipitation observation data are obtained from the Global Historical Climatology Network – Daily database
The daily precipitation sums were converted to monthly totals. For the conversion of daily precipitation sums into the number of wet days, a threshold of 1 mm was used (i. e., days with precipitation
Rain gauge measurements are subject to systematic, random, and representativity errors
To estimate the representativity error, we analyzed all GHCN-Daily station data over the contiguous United States and adjacent territories (lat:
The distribution of the representativity error of precipitation
The representativity error was estimated using the following procedure for both precipitation amounts and wet days: (1) an average value for all months between 1961 and 1990 was calculated at each single grid box from the stations located within one grid box according to the resolution of the CCC400 model simulation. (2) The spatially averaged monthly time series of each grid box were subtracted from all station series within the grid box. (3) The standard deviation of the resulting series was calculated. (4) The median value of the standard deviation was taken as the representativity error.
Figure
An important feature of our assimilation process is that only anomalies are assimilated. Both model and observation data are transformed into anomalies using a moving 70-year time window around the current year (this window is shorter at the edges of the available period, from which the anomalies are calculated). Working with anomalies alleviates the problem of model biases
If more than one station is available within the same grid box, then the average of the observation anomalies was assimilated. As in previous studies
When data for 6 months are combined together in
Summary of experiments and their setups.
A set of experiments was conducted, which are summarized in Table
Finally, an additional experiment was conducted to reconstruct a severe drought event in Europe in order to demonstrate the potential of assimilating precipitation data. Six available stations from GHCN-Daily were used to reconstruct the extreme drought year of 1842
In order to evaluate the skill of the sensitivity experiments, two commonly used skill metrics – correlation and the root mean squared error skill score (RMSESS) – are calculated over the 1950–2004 time period. The CRU TS3.10 dataset
Summer season correlation differences of precipitation
Assimilating monthly precipitation amount data (exp_R) led to improved precipitation skill compared to the existing correlation between the CCC400 model simulation ensemble mean and the reference dataset. The monthly correlation differences of precipitation show clear improvement (winter: Fig. S1 in the Supplement, summer: Fig. S2). The correlation differences between the analysis and the model simulation are almost always positive in the case of temperature and sea-level pressure in all months (Figs. S1, S2). In terms of RMSESS values, during boreal winter the monthly precipitation fields show reduced skill in the high northern latitudes and in Siberia (Fig. S1). The skill of the precipitation reconstruction gradually decreases from October to March over Siberia (Fig. S1). The negative RMSESS values remain present in April and to a lesser extent in May over northern North America and Siberia, while the RMSESS values are mainly positive throughout June and September in the Northern Hemisphere (Fig. S2). The precipitation reconstruction has mixed skill over Australia. Mostly negative RMSESS values characterize the northern and northwestern regions, while positive skill is seen in the southern and eastern parts (Fig. S2). The RMSESS values of the winter monthly temperature fields are in general positive, except Australia (Fig. S1). However, the skill of the temperature reconstruction is negative in large parts of North America and Europe, especially from June to August (Fig. S2). In the winter sea-level pressure fields, an improvement can be seen mainly over Europe and Asia (Fig. S1), while in the summer months the effect of precipitation on the pressure fields is mixed (Fig. S2). The winter seasonal skills of exp_R are shown in the Supplement (Figs. S3 and S4), while summer seasonal skills are shown in Figs.
Summer season RMSESS values of precipitation
The assimilation of wet days (exp_W) resulted in mainly positive correlation differences of all three variables (Figs.
Doubling the correlation length scale parameter of precipitation resulted in a very similar correlation skill of precipitation (Figs.
The same experiment with a doubled localization length scale parameter was conducted with the assimilation of the number of wet days. Correlation coefficients of precipitation in the exp_W_2L experiment remained high (Figs.
The distributions of the skill matrices of the presented experiments over the extratropical Northern Hemisphere are summarized as box plots (Fig. S5). Increasing the localization length scale parameter positively affected the reconstructed temperature and sea-level pressure fields in terms of correlation, especially in boreal winter. The sea-level pressure and temperature RMSESS values are less affected by the applied localization. However, the RMSESS of the precipitation reconstruction decreased in the experiments with a doubled localization length if precipitation amounts were assimilated.
Summer season correlation differences between the analysis of exp_TP and the CCC400 model simulation ensemble means: precipitation
Summer season RMSESS values of exp_TP
In the next experiment different observation types such as temperature, sea-level pressure, and precipitation amounts were combined (Fig.
Relative precipitation anomalies over Europe in 1842. Monthly relative precipitation anomaly fields between April and September from exp_TP
Six stations in the GHCN-Daily dataset in Europe fulfilled the requirement to have continuous data in 1842. These stations, with their starting year in parentheses, are the following: Prague (1804), Jena (1826), Bologna (1813), Genoa (1833), Mantova (1849), and Armagh (1835). Using all available data in the 71-year time window centered on 1842, the precipitation amounts and the number of wet days were converted to anomalies. We calculated the relative precipitation anomalies for the months between April and September from exp_TP, exp_R, exp_W, and 20CRv3.
In the exp_R experiment (when only the precipitation amount was assimilated) the period between April and August in central Europe is characterized by negative relative precipitation anomalies (Fig.
These monthly relative anomaly fields were compared to the 20CRv3 reanalysis. As mentioned above, no precipitation data were used in 20CRv3. The relative precipitation anomaly fields of 20CRv3 and exp_R show similar precipitation patterns over the central region from France to western Ukraine. A precipitation deficit from April to August and a wet September are reproduced in 20CRv3 (Fig.
The drought over Europe in exp_R stands out even better on a seasonal timescale (June–July–August) (Fig. S10). Except northern Europe, Spain, and the southern part of France and Italy, negative relative precipitation anomalies define Europe (Fig. S10). Despite assimilating precipitation amount data from only six stations the obtained precipitation pattern is very similar to the reconstruction made by
Outcome of the Shapiro–Wilk test for normality for precipitation
In weather forecasting, there have been many attempts to make use of precipitation measurements from radar
Hence, the question remains as to whether the errors of precipitation amounts and the number of wet days are normally distributed, a fundamental assumption of EKF. In Fig.
Another advantage of the number of wet days over precipitation amounts is lower representativity error (see Sect.
Assimilating monthly precipitation information such as precipitation amounts and the number of wet days, in general, shows positive improvements in all variables compared to the CCC400 model simulations when correlation is analyzed. The RMSESS of precipitation from both the exp_R and exp_W experiments is negative at the high northern latitudes and over large parts of Asia, especially in the winter season. As discussed earlier, precipitation observations are not error-free.
In addition to assimilating only precipitation amounts or only the number of wet days, the effect of assimilating them in combination with other types of instrumental measurements was also tested. Correlation and RMSESS metrics were calculated using the reconstruction based on temperature and sea-level pressure data (exp_TP) as a baseline. The exp_TP experiment shows a clear positive impact on the correlation values of all three variables in both seasons. Due to the high skill of temperature and sea-level pressure reconstructions, further improvements with the assimilation of precipitation amounts or the number of wet days are mainly seen in the precipitation field. Assimilating the precipitation amount or the number of wet days has a small impact on the temperature and sea-level pressure correlation skills. If only precipitation information is available from a given region, its affects the reconstruction of the other fields more; for example, over northern and western Australia, where no temperature observations are assimilated, precipitation information improved the skill of the temperature field in boreal winter (Fig. S4). The RMSESS values of all variables from exp_TPR and exp_TPW are very similar in winter, indicating that both types of precipitation data perform similarly. Moreover, assimilating the precipitation amount or wet day records has a mainly positive effect in the regions where temperature observations are absent. However, sea-level pressure fields suggest that with the assimilation of precipitation observations the skill of the pressure reconstruction decreased in the regions with available sea-level pressure measurements. In general, assimilating precipitation amounts (exp_TPR) performs worse than assimilating wet days (exp_TPW) in summer. The better performance of wet days in summer is expected due to lower spatial variability. However, even wet day records have a negative effect on the sea-level pressure RMSESS, especially in Europe. To minimize this negative effect, ignoring or limiting the cross-covariance updates between precipitation and other variables will be tested in future experiments.
A case study was conducted to test how well precipitation amounts and wet day records are able to reproduce a severe drought event in Europe. Only a sparse network with six stations provided data from 1842. In the model simulations (CCC400) the precipitation anomalies are much smaller compared to the reconstructed precipitation fields in the exp_R and exp_W experiments, indicating that with the assimilation of six stations this drought event is reconstructed. The reconstructed precipitation anomaly fields are very similar in the case of both precipitation amounts and the number of wet days (Fig.
Based on the historical sources gathered by
As the application of data assimilation techniques has become more widespread in the field of paleoclimatology, more and more different observational sources, such as early instrumental measurements, documentary records, and various types of proxy records, have been used in the assimilation process. In this paper, new observation data sources – precipitation amounts and the number of wet days – were tested in an offline ensemble-based Kalman filter framework. The experiments in which only precipitation amounts (exp_R) and only wet day records (exp_W) are assimilated performed similarly in winter, but in summer exp_W has better skill in the case off all three examined variables. Moreover, the results of the exp_W_2L experiment suggest that the localization used for wet days could be increased, by which a better use of observation data can be achieved. In the exp_TPR and exp_TPW experiments, the skill of the two reconstructions was compared to exp_TP to examine the effect of adding precipitation data to the assimilated observations. In general, both precipitation amounts and the number of wet days had a rather positive impact on the temperature reconstructions in winter, while in summer only the number of wet days had an overall positive effect on temperature. The skill metrics of sea-level pressure clearly indicate that precipitation data should be used if pressure measurements are not available from a given region. Therefore, it might be better to limit how precipitation data can update the other fields of the state vector, for example with the implementation of an asymmetric localization function, in forthcoming experiments. The reconstructed monthly precipitation fields of the severe 1842 drought in Europe are mostly in agreement with documentary data, showing that precipitation amounts or wet day records can be useful sources in a paleoclimate data assimilation framework.
The atmospheric model simulations, CCC400, are available at the World Data Center for Climate through the Deutsches Klimarechenzentrum (DKRZ) in Hamburg, Germany (
The supplement related to this article is available online at:
All authors were involved in the design of the study and contributed to writing the paper. VV conducted the experiments and performed most of the analyses. The model wet day field, the assimilated precipitation amounts, and the wet day data were prepared by YB. YB helped with the analysis. JF developed the original code.
The authors declare that they have no conflict of interest.
The CCC400 simulation was performed at the Swiss National Supercomputing Centre CSCS.
This research has been supported by the Swiss National Science Foundation (grant no. 162668) and the European Commission – Horizon 2020 (grant no. 787574).
This paper was edited by Chantal Camenisch and reviewed by two anonymous referees.