ModE-RA (ensemble members and statistics) and ModE-RAclim (ensemble statistics) are uploaded to NOAA and to the World Data Center for Climate (WDCC) at Deutsches Klimarechenzentrum in Hamburg, Germany. The two climate reconstructions are in NetCDF4 format; the NetCDF4 files cover the whole period per variable. Ensemble statistics include the mean (monthly anomalies with respect to the period 1901 to 2000), maximum, minimum and spread in terms of one standard deviation from the ensemble mean. The observation feedback archive files are available in tsv format (one file per 6 months), which contain all relevant information of the input data, how the input data were processed, and useful feedback information from the DA system. A detailed list of all information stored in the feedback archive has been published with the dataset.

The ModE-RA paleo-reanalysis is identical to the ModE-Sim simulations in areas far away from any assimilated observations, especially at the beginning of the reconstruction period. With time, more and more observations are available, suggesting that the reconstruction becomes more skillful. Therefore, the users first should ensure how reliable the paleo-reanalysis is for a given region and time period. This can be achieved by looking at the ensemble spread and the differences between ModE-Sim and ModE-RA. Among the reconstructed variables, the ones with observational input data are the most realistically estimated. We encourage the users to make use of the ensemble members and not only the ensemble mean.

ModE-Sim was generated in two phases (1420–1850 and 1850–2009) with different boundary conditions. In the earlier period, ModE-RA is based on ModE-Sim Set 1420-3, and in the later period on ModE-Sim Set 1850-1. ModE-RA is not split into the two periods of the ModE-Sim prior because the assimilated observational time series lead to a smooth transition between the two periods of the ModE-Sim sets.

ModE-RA was generated by transforming both model simulations and observations to 71-year running anomalies. Hence, users should be aware that the centennial-scale variability is the model response to forcings. Therefore, we see great potential for future research, particularly in terms of intra-annual to multi-decadal variability. We provide monthly anomalies with respect to the 1901 to 2000 climatology and the model climatology for the 1901 to 2000 period. Be aware that the model climatology includes model biases. Therefore, we recommend using anomalies instead of absolute values.

Furthermore, because of the employed setup, unrealistic values (such as negative precipitation) can occur if absolute values are generated by adding back a climatology. This is especially an issue in arid regions where monthly precipitation is not normally distributed. Precipitation is consistent in the periods of 1421–1800 and 1900–2009 when the observational network is quite stable, but in the 19th century, when many of the observation time series start, a trend is introduced in some arid land regions and tropical oceans. Hence, in the case of the reconstructed precipitation fields, the early and late period should be looked at separately.

ModE-RAclim should be seen as a sensitivity study and is only a side product of the project. ModE-RAclim does not contain centennial scale climate variability. For most users, the main product ModE-RA therefore should be used for regular studies on past climate. The main differences between ModE-RAclim and ModE-RA are on the model side: ModE-RAclim uses 100 randomly picked years from ModE-Sim as a priori state. Thereby, stationarity in the covariance structure is assumed, and the externally-forced signal in the model simulations is eliminated. In combination with ModE-Sim and ModE-RA it can be used to distinguish the forced and unforced parts of climate variability seen in ModE-RA.

ModE-RA makes use of several data compilations and assimilates various direct and indirect sources of past climate compared to 20CRv3. Hence, if monthly resolution is sufficient for the planned study, ModE-RA may have higher quality already from 1850 backwards to analyze past climate changes and can be viewed as the backward extension of 20CRv3.

(Cf. ModE-RA paper Usage notes. )

Anomalies:

The anomaly map function shows the spatial distribution of climate anomalies averaged over a user-selected year range and month range. For example, June, July, August (JJA), 1501 to 1600 if your focus is boreal summer in the 16th century. The anomalies are created from 3 data products:

1. Annual Means – a timeseries of annual means for each point on the map, created by averaging absolute ModE values across the selected month range.
2. Reference Means – a single reference mean for each point on the map, created by averaging annual means across a chosen reference year range.
3. Annual Anomalies – a timeseries of annual anomalies for each point on the map, created by subtracting the reference means from the annual means.

The final anomalies shown are the time-averaged annual anomalies. These are plotted using the base R plotting functions along with the coastlines and borders from the maps package. The anomaly timeseries is generated by averaging the annual anomalies for each year. See Appendix 2. for the specific calculations behind each data product.
For reference, the calculations behind each data product are as follows:
The annual mean for a single year and single point on the map is given by the equation
$$Annual \ Mean = \overline{Absolute \ Values \ (M)}$$
where \(\ (M) \) is the selected month range.

The reference mean for a single year and point is given by
$$ Reference \ Mean = \overline{Annual \ Means \ (Y_{ {ref}})}$$
where \(\ Y_{ {ref}} \) is the selected reference year range.

The annual anomaly for a single year and point is given by:
$$ Annual \ Anomaly = Annual \ Mean - Reference \ Mean$$

Note that in the case of ModE-RAclim, the base data is already in anomaly format, so anomalies are merely calculated by subtracting time-averaged anomalies from each other.

The anomalies presented on the anomaly map and in the anomaly map data are given by
$$ Anomaly \ (map) = \overline{Annual \ Means \ (Y)} - \ Reference \ Mean = \overline{Annual \ Anomalies \ (Y)}$$
where \(Y \) is the selected year range.

Anomalies presented on the timeseries map and timeseries data are given by
$$ Anomaly \ (timeseries) = \ (Annual \ Means \ (Lon, \ Lat)) - \ (Reference \ Means \ (Lon, \ Lat)) = \ (Annual \ Anomalies \ (Lon, \ Lat))$$
where Lon and Lat are the selected longitude and latitude range.

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Composites:

ClimeApp’s composite maps show the time-averaged anomalies for a set of non-consecutive years, which can be entered or uploaded by the user. The anomaly reference period can be a fixed set of consecutive years, a custom set of non-consecutive years or an individual reference period generated for each year based on the X (a number of years chosen by the user) years prior. Calculations and plotting are performed in the same way as for anomalies, except for anomalies compared to X years prior (XYP):

1. XYP Reference Means – a set of reference means for each point on the map, one for each user-selected year. Calculated by averaging the X preceding annual means.
2. XYP Annual Anomalies – a set of annual anomalies for each point on the map. Created by subtracting the corresponding reference mean from each annual mean.

To give an indication of the consistency of anomalies over the set of years in the composite, ClimeApp contains a ‘% sign match’ statistical tool. This marks regions where the annual anomalies that form the composite agree in their sign more often than a user-defined threshold, given in percent. For example, for a composite of five years, with anomalies of -1°C, -5°C, 1°C, 15°C and -3°C, the displayed mean would be a positive 1.4°C, but only 40% of the years would match this, since 3 are in fact negative.

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Correlation:

The correlation function allows users to generate a map of correlation coefficients, comparing either ModE variables or user-uploaded timeseries. Using the cor() function from the stats R package (R Core Team, 2022), it can employ either the Pearson or Spearman’s Ranks correlation method. If both variables are in ‘field’ format, i.e. gridded map data, it performs a timeseries correlation of the annual means for each point on the map with the corresponding annual means for the second variable. If one variable is a timeseries however, it correlates each set of annual means with the same timeseries. In addition to the map, ClimeApp also produces a correlation timeseries, showing an annual timeseries of both variables (spatially averaged in the case of ModE variables) and a single correlation coefficient and p-value, calculated from those timeseries. The p-value shows the probability that the correlation was produced by random chance rather than an actual relationship between the variables. p < 0.05 is generally recommended for drawing legitimate conclusions.

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Regression:

In ClimeApp, regression operates in a similar way to correlation, performing a multiple linear regression analysis on a set of annual means . Using lm() from the stats R package, one or more independent variable timeseries are fitted to the dependent variable timeseries for each point on the map according to the model
$$ V_{ {Dependent}} = \beta_1 V_{ {Independent \ 1}} + \beta_2 V_{ {Independent \ 2}} + ... + \ Residual$$
where β is the coefficient and α is the intercept. ClimeApp then plots the spatial average of the dependent variable \(\ \beta_1 V_{ {Independent \ 1}} + \beta_2 V_{ {Independent \ 2}} + ... \) and residual as a timeseries. Provided the dependent variable is a field, maps of the coefficients for each independent variable can be produced, as can maps of the p-values and residuals for each year.

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Annual Cycles:

This function shows the spatially averaged monthly ModE values over a given year or set of years. In the case of a set of years, these can be presented individually or as an average.

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Source Analysis and Further Statistical Functions:

The accuracy of ModE-RA is dependent on the availability and reliability of observations to constrain the model ensemble of ModE-Sim. To capture this, ClimeApp includes tools for visualizing the sources used to create ModE-RA and ModE-RAclim and the standard deviation (SD) ratio of the ModE-RA and ModE-Sim ensembles. The ModE-RA sources are presented as a semi-annual map showing the data points assimilated for each half-year, grouped by type and variable. This allows the user to see where proxy, documentary or instrumental observations were integrated into the reconstruction and any gaps in the data. The SD ratio meanwhile, is the standard deviation of the ModE-Sim ensemble divided by the standard deviation of ModE-RA after the assimilation of observations:
$$ SD \ ratio = \frac{\sigma_{ModE-RA \ Ensemble}}{\sigma_{ModE-SIM \ Ensemble}}$$ This gives a value between 0 and 1 for each month and grid point, with 1 showing no constraint (i.e. the ModE-RA output is the same as that of ModE-Sim and entirely generated from the models) and lower values showing increasing constraint by observations, meaning there are either more observations or that they are more ‘trusted’ by the reconstruction. The temporal mean of the SD ratio can be presented in ClimeApp as a contour map or grid-point overlay on the anomaly maps.
On timeseries plots, users have the option to add percentiles and moving averages. The moving averages are calculated using a rolling mean of timeseries values over a number of years selected by the user (default 11). To generate the percentiles, a Shapiro-Wilk test (Shapiro and Wilk, 1965) is first conducted on the timeseries data. If the data is normally distributed, which is rare for ModE timeseries, then percentiles are calculated from the mean and standard deviation of the timeseries using the qnorm() function from the stats package. If the distribution is non-normal, ClimeApp instead finds the value corresponding to the quantile matching the users selection (i.e. for the 0.95 percentile, it returns values that 5% of all values are above/below), using the quantile() function from the stats package.

v1.1 (04.04.2024)

• Option to add GeoPackage-Layers (shape files) on top of field plots

v1.0 (11.03.2024)

• Download / Upload option for metadata
• Information panel for ClimeApp functions
• Helptext as popovers for UI elements

Beta v0.6 (15.02.2024)

• Improved UI (i.e. Hide/Show country borders, Rearranged download sections
• Switch to Annual Cycle when a single year is selected
• Download ModE-RA source data as table
• Loading symbols during plot generation

Beta v0.5 (22.12.2023)

• Download NetCDF files
• Version History

Beta v0.4

• Select single years

Beta v0.3

• Timeseries customization
• Percentiles, maps & statistics based on model constraint change
• Reference line option in timeseries

Beta v0.2 (10.11.2023)

• Use ModE-Sim and ModE-RAclim data
• Create annual cycles method
• View ModE-RA sources
• Download ModE-RA sources maps as image
• Upload User data for correlation and regression
• Reference maps with absolute values, Reference values, and SD ratio for Anomalies and Composites

Beta

• First running version online
• Use ModE-RA data with four variables: Temperature, Precipitation, Sea level pressure, Pressure at 500 hPa geopotential height
• Calculate Anomalies, Composites, Correlations and Regressions (coefficien, p values residuals) as maps and timeseries
• Customize maps and timeseries (title, labelling, add custom points and highlights, statistics)
• Download maps and timeseries plots as images
• Download map and timeseries data in xlsx or csv format