the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Mar 2024
Spatially aggregated climate indicators over Sweden (1860–2020), Part 1: Temperature
Abstract. Climate indicators are useful tools to synthesise climate information from multiple station time-series into a single national indicator. The method applied should be spatially representative and robust over time. We introduce a new method, based on Empirical Orthogonal Functions (EOF) during the calibration period 1961–2018, in order to reconstruct the climate indicator for temperature in Sweden for the full 1860–2020 period of available observations.
The new method delivers results in good overall agreement with the reference method (i.e. arithmetic mean from selected stations in the reference network). Discrepancies are found prior to 1900, primarily related to the reduced number of active stations: the robustness of the indicator estimation is assessed by an ensemble computation with added random noise, which confirms that the ensemble spread increases significantly prior to 1880.
The present study establishes that the 10-year running averaged temperature indicator rose from −1.03 °C in 1903 to +1.19 °C in 2010 (with respect to a mean value of 4.64 °C over the 1961–2018 calibration period), i.e. an increase by +2.22 °C in a century. The temperature difference between 1860 and 2020 was largest for winter (DJF) averages (+3 °C) and minimal for summer (+2 °C).
The leading EOF patterns illustrate the spatial modes of variability for climate variability, with a predominantly homogeneous, mono-modal distribution for temperature. For precipitation, the first EOF pattern displays more pronounced regional features (maximum over the West coast), which is completed by a north-south seesaw pattern for the second EOF. We illustrate that EOF patterns calculated from observation data reproduce the major features of EOF calculated from GridClim, a gridded data-set over Sweden, for annual and seasonal averages. The leading EOF patterns vary significantly for seasonal averages (DJF, MAM, JJA, SON) for temperature.
Finally, future developments of the EOF-method are discussed for calculating regional aggregated climate indicators, their relationship to synoptic circulation patterns and the benefits of homogenisation of observation series.
The EOF-based method to compute a spatially aggregated indicator for precipitation is presented in a companion article (Sturm, 2024a). The code and data for this study is available on Zenodo (Sturm, 2024b).
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RC1: 'Comment on egusphere-2024-582', Anonymous Referee #1, 13 Apr 2024
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Summary. Official climate indicators to characterise long-term climate change in Sweden are compiled by averaging station data belonging to a suitable network. The manuscript explores an alternative method to define long-time series climate indicators based on deriving spatial patterns of Empirical Orthogonal Functions during a recent period and reconstructing the past temperature field from the available more sparse observations of longer time series. The main conclusion of the manuscript is that the alternative method yields very similar results to the conventional method but has some additional advantages.
Recommendation: The manuscript's objective is sound, but it requires deep revisions, both in its structure and in the methods. Overall, the manuscript, especially the description of the data sets and station networks, is disorganized and confusing—it can be better presented to help the reader. Also, the last disunion section contains parts that would better fit the introduction, and the introduction fails to provide a suitable context about reconstruction methods for the reader.
Perhaps more importantly, the EOF-based method contains some technical errors that need to be addressed, although I believe these changes would not strongly impact the final results.
Main points:
1) The definition of climate indicators is actually a field reconstruction method, for which many alternatives exist in the literature. Estimating area averages and spatially resolved fields based on point observations has a long tradition in climatology and palaeoclimatology. For instance, the EOF-based method presented here has clear similarities with the hockey-stick reconstruction method by Mann et al. (Nature,1998), but also with other variants, for instance, principal Components Regression by Luterbacher et al. (2002,10.1007/s00382-001-0196-6). Concerning more recent periods, the GISS, BEST or HadCRUT data sets use different methods to estimate area averages that could also be applied here. The introduction should provide more context to the reader to frame the present method in that context. Perhaps the author may want to check the paper by Smerdon ( 10.1002/wcc.149), although that paper is focused on paleoclimate reconstruction methods.
Also, reconstruction methods may target area averages (an easier task) or spatially resolved fields. Obviously, the latter are more challenging but provide more information. In the present study, the objective is clearly a spatially aggregated climate indicator, yet the author has chosen to apply a climate field reconstruction. The introduction should also explain the reasons for this choice, which, in principle, is not optimal for the target at hand.
2) Methodological aspects. As explained in a more detailed way below, the application of the EOF-based method is not totally correct. For instance, the method described here reconstructs the expansion temporal coefficients by projecting the available station observations onto the EOF patterns. However, when restricted to the location of the available observations, the EOF patterns are not orthogonal anymore- they are only orthogonal over the full set of stations in which they were calculated. Thus, the way to 'reconstruct' the expansion coefficients is another one in the case of gappy data, as described in the book by von Storch and Zwiers (1999) Statistical Analysis in Climate Research. I believe that this methodological error is not determinant and that the application of the correct method will yield similar results. However, the methods need to be correctly applied in a published paper.
Particular points
3) The title is not very informative. The reader cannot infer that an alternative method is being applied and compared to the official method
4) The introduction is very short and, as I wrote before, does not provide context. This is mainly a methodological study, and so the reader would expect a summary of the existing methods, their deficiencies and strengths and the reason the author has chosen the EOF-based method in the introduction.
5) The times scale of the targeted climate indicators is not stated after the middle of the manuscript. So the reader cannot know if this study is targeting, daily, monthly, annual means
6) Table 1 includes one entry, Gridclim, and year of maximum that are described much later in the manuscript and not in the caption. This is confusing
7) (e.g. if increasing nearby urbanisation leads to the station no longer)
This sentence seems incomplete.
8) The lower plot in Fig. (1) indicate
indicates
9) line 85 'The present study focuses on annually-resolved climate indicators
This paragraph is a repetition of a previous paragraph.
10) subsequently downscaled at 2.5 km with MEPS
what is MEPS ?
11) 'The GRIDC LIM project (Andersson et al., 2021), performed by SMHI, combines the regional European reanalysis UERRA
(Schimanke and Service, 2019; Schimanke et al., 2019) with station observations'
How are they combined? It would be helpful to have a summary here.
12) GridClim-sub is used for the gap-filling of M ORA calibration data-set (338
for temperature)
gap-filling (temporal) , what does 338 mean ? Stations?
13) ..'corresponding to the M ORA reference network SMHI-ref (39 for temperature)'
At this stage in the manuscript, the MORA reference network is only defined in Figure caption 1, and not in the main text, if I am not mistaken. Anyway, I had to unsuccessfully search the text several times for an explanation of MORA reference network, and so the reader will feel quite irritated.
Does 39 refers to the number of stations? if yes, please state clearly 39 stations. Table 1, however, indicates an initial number of 8 and a maximum of 35, so 39 does not match either. Table 1 seems to indicate that this reference network is not frozen in time, so I am really confused.
14) The explanation for the MORA reference network comes *after* the previous paragraph. This needs to be amended.
15) 'In the present study, the original method was emulated by selecting the individual station with the longest record in eachmeta-station, without coupling and homogenisation. Hence, the emulated reference network in this study has sparser data coverage, thereby slightly different result, than the climate indicator provided by SMHI. In the results section, this data-set is referred to as GridClim-sub.'
I am totally confused here. In my understanding so far, the GridCLIM data set is a gridded data set resulting from a combination of stations and reanalysis for the period 1961–2018. So, it is not per se a station data set. Why is now the emulated reference station network denoted GridCLIMsub? Are the gridcells selected according to the position of the reference network? GridCLIMsub would cover only 1961-2018, so how can it emulate the reference network since 1860?
In the previous section, GrdCLIMsub was defined as the subset of gridcells co-located with the calibration network, not the reference network.
The data description needs to be much better organised and presented in the right order in the manuscript. Presently, it is confusing.
16) 'Standard linear algebra methods require the data-set to be complete, without any missing values '
This is not correct. EOFs can be computed from data sets with missing values. The entries in the covariance matrix can be estimated from the pairwise common period of two series. In this case, some usual properties of the covariance matrix are not fulfilled anymore, e.g., all eigenvalues are positive. Still, this is usually not an issue if the number of gaps is not very large. This is explained in section 13.2.8 (Gappy data) of the book Statistical Analysis in Climate Research by Storch and Zwiers (1999)
17) For each station, a linear regression (in least-square sense, i.e. minimising ε)
Please refer here to equation (2)
18) 'By construction, each pattern in the EOF matrix is “orthogonal” to each other, in other words spatially uncorrelated'
This is incorrect. The terms Orthogonal and uncorrelated are only equivalent if the mean value is zero. However, the spatial mean of the EOFs patterns is not zero. Mathematically:
Orthogonality of eigenvectors i and j means SUM_r { x_i(r) x_j(r) } = 0
Non-correlation means SUM_r { (x_i(r)- ) (x_j(r) - ) = 0
The spatial means and are not necessarily zero
'Accordingly, all time expansion vectors (A) are temporally uncorrelated
This is correct, since the temporal expansions are all centred, since the EOFs are computed from anomalies.'
19) Reconstruction of the temporal expansion coefficients. This is a crucial step in the methodology, which is theoretically incorrect. As explained in my main point 2, the expansion coefficients cannot be computed by projecting the available station temperature anomalies onto the EOF patterns since these patterns are not orthogonal over the subset of available stations. Another method needs to be applied here, which is summarised by the following equation:
T (r,t) = SUM_i alpha_i(t) eof_i(r) + epsilon (r,t)
where r denotes the station, i the EOF number and t time. Epsilon is the residual that needs to be minimised
for each time step. This minimisation amounts to the orthogonal projection if the eof_i patterns were orthogonal over the subset of stations. But if the patterns are not orthogonal, as it is now the case, the minimisation involves a usual multivariate regression. One implication is that the expansion coefficients of a particular EOF, say alpha_i(t), depend on how many EOFs are retained: if five are retailed, the results would be different from when 10 are retained. This is also explained in section 13.2.8 (Gappy data) in von Storch and Zwiers.
20) ' The corresponding measurement uncertainty for monthly means are reduced by a facto'
is reduced
'The corresponding measurement uncertainty for monthly means are reduced by a factor √30 '
is reduced
Both statements assume that the daily temperatures are not serially correlated, which is clearly incorrect. The same applies to the monthly means. The number of effective degrees of freedom, and thus of the error reduction, is smaller than 30 or 12, respeectively
21) Normalization of EOF patterns and expansion coefficients.
There is an ambiguity in the text about how the EOF patterns and the corresponding expansion coefficients have been normalized. In principle, this normalization is subjective: the eof patterns can be normalized to unity, and the physical units would be carried by the expansion coefficients, or vice versa. Also, any other option between them is mathematically possible. The reason is an eigenvector of a matrix multiplied by any real number is also an eigenvector. This is irrelevant when reconstructing the temperature anomalies - since only the respective normalization of the patterns and the expansion coefficients need to be consistent. It is, however, relevant when comparing the amplitude of the EOF patterns in separate calculations for GridClim-all and GridClim-ref, for instance. In this case, the amplitude of the of eof patterns can only be meaningfully compared if expansion coefficients have been normalised to unit standard deviation and the physical units are carried by the spatial patterns. Is this the choice adopted in this study?
22) ' For each climate indicator (temperature and precipitation),*
This study should be just about temperature. This is confusing
23) 'As a reminder, Xc represents...'
This paragraph is repetitive and not necessary in a research paper.
24) 'which becomes pregnant when only few stations are active'
pregnant is not the right word here. Relevant is a better choice
25) 4.4 Comparison to studies of historic climate variability in Fennoscandia
I did not see the relevance of this section since this study does not really analyse the historical climate variability processes, amplitudes, forcings, etc.
Citation: https://doi.org/10.5194/egusphere-2024-582-RC1
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