HadEX3 - initial steps

With IPCC AR6 now in full swing, development of HadEX3 is occurring in earnest. In fact, I've been gently getting on with bits and bobs over the last year or so.  The largest bits were the calculation of the decorrelation length scale, and also the angular distance weighting gridding scheme.  These were tested on three different datasets which will go into HadEX3.

The European Climate Assessment and Dataset (ECAD) is coordinated by KNMI and now has partner datasets in Latin America (LACAD) and Southeast Asia (SACAD).  They have already calculated indices from the data they have sight to (not all can be shared in its raw, daily form).  These indices need converting to a standard format and the metadata checked.

The Global Historical Climate Network Daily (GHCND) is a large collection of daily observations.  I've so far just taken a subset of US stations which form part of their Historical Climate Network dataset (HCN).  These daily observations needed reformatting and then passing through the code which calculates the indices.  

Finally, as we are encouraging individuals, national meteorological services and organisations to submit any data or indices they have to this dataset, we also used some Spanish stations to include and process in our initial test.

There have been a number of codes which calculate the ETCCDI climate indices, in IDL, Fortran and R.  As different codes will, despite the best efforts of the scientists and programmers involved, have subtle differences in the methods and thresholds, an attemp has been made to take the best aspects of all of these and create a single codebase, freely available to calculate these indices.  The Climpact2 software uses the RClimdex software and wraps this to allow both for the processing of netCDF files of gridded temperature and precipitation values, but also batch processing of raw station files. 

Once the indices have been calculated, we do some quick checks to ensure that there were sufficient daily observations to actually produce the indices, that there are at least 20 years of data without too many long gaps and that the end of a station series occurs after 1950.  We still get a large number of stations that could contribute to the dataset from these three sources (Fig 1.), so in some parts of the world (or for some data sources) we may be able to be more exacting in our data requirements.  The large gaps where we have no data as yet are a more urgent aspect to address.

Fig 1.  Stations used for two example indices (top - PRCPTOT, bottom - TX90p) from the first test run of HadEX3.

Although we do not expect changes to occur in a linear way, showing the linear trends over the recent period give a good summary of the dataset and allows comparison with HadEX2 and others using the ETCCDI indices.  Two examples are in Fig. 2, but as is clear, the spatial coverage has some very large gaps.  The nature of the ADW gridding scheme is that it interpolates into areas with low station density, increasing the apparent coverage, especially for the temperature indices.

Fig 2. Linear trends for two example indices based on their annual values over 1951-2017 (top - PRCPTOT, bottom - TX90p) from the first test run of HadEX3.  Please note these are preliminary plots, with gaps in the spatial and temporal coverage.

We still have decisions and choices to make, some of those parameters which will result in small differences in the final data files.  There are parallel versions that we could create, with smaller gridbox sizes, other gridding methods, more- or less restrictive selection and quality control settings.  Watch this space.

Oh, and please get in touch if you have data that could contribute towards this dataset!  We'd be very happy to have you on board.

Uncertainties and methods within the HadEX family

It appears to be very simple.  Just take daily temperature values (maxima and minima) along with daily precipitation values, calculate the ETCCDI indices and then convert these point based quantities into a space-filling version.  However, this latter stage is relatively complex, even when the space filling version uses a simple latitude-longitude grid.  And many alternate methods exist - tri-polar grids, triangular meshes, Voronoi tessellation, each with their own quirks, pros and cons.

The more complex a method is, the more choices there are as to what techniques and settings to use.  Different choices could result in different results and outcomes - and so contribute to the overall uncertainty (range) in the dataset.  Choices in the techniques and methods contribute to the structural uncertainty, whereas settings within these methods to the parametric uncertainty.  A number of groups have assessed aspects of these parametric and structural uncertainties in products using the ETCCDI indices

Limitations of the indices

Before I get onto the studies themselves, I thought I'd highlight some of the limitations that the indices themselves have.  All the indices are available as annual values, and some have monthly versions as well.  Therefore, for long-timescale events (heatwaves being a clear example), if they span two years (in the case of the southern hemisphere) or two months, there is the risk of double counting as well as missing the event entirely.  Double counting could arise where the maximum temperatures are highest on the last day of one month and the first day of another - resulting in twice the number of anomalously warm months than if the event had occurred in the middle of a month.  And for indices which only start counting once a time-threshold has been exceeded, then if an event is split so that this threshold is not exceeded in either month, but would do if it had occurred in the middle of a month.

It would be difficult to define simple indices where this would not be the case.  Though versions could be made to have "years" running from July to June, and months from 15th of one to the 14th of the other, coordinating these systematically is likely to be complex.  It is probably easier to be aware of these issues than to reset how many folk automatically mark the passage of time.

Quick outline of the "HadEX methods"

Once the indices themselves have been calculated on each daily station time series, for each index (and month if these versions exist), the correlation coefficient is calculated for each station pair along with their separation.  Using these, a "decorrelation length scale" (DLS, also known as the "correlation decay distance") can be determined, by plotting all the separations and correlations for all stations. In fact these are done in latitude bands to take into account some of the zonal patterns.

Fig 1. The DLS calculation for TXx in the latitude band 30-60N.  The vertical dotted lines show the minimum (200km) and maximum (3000km), and the magenta dashed line the value derived from the exponential decay (cyan curve).  The red points are the binned values calculated from all distance-correlation values for each pair of stations (blue points).

These correlation values are averaged in bins of 100km separation, and an exponential decay fitted to these, as shown in Fig 1.  Where this decay drops by a factor of 1/e is taken as the DLS.  A minimum of 200km is used in cases where this curve drops steeply.

Then, to convert the point observations into gridded values, this DLS is used to select stations within this distance of the grid box centre.  If there are three or more, then an angular distance weighting (ADW) method (Shepard 1968) is used to obtain the value for a grid box.  The datasets also provide the number of stations that went into this calculation, to give some indication as to the reliability of the final value.

Data Completeness

In many cases where trends are presented from the HadEX datasets, only grid boxes which have values in at least 90% of the years considered are plotted ("90% completeness").  However, over a long period, this means improved data availability in recent decades cannot be included.  Percentile based indices are less susceptible to changes as they require data over a reference period to normalise the values, but others can show substantial changes.

Fig 2. (a) Coverage and (b) Globally averaged timeseries for CDD in HadEX2 for different data completenesses.  All lines in (b) have been normalised to 1961-90.  Therefore the larger number of short period stations contributing to the increased number of grid boxes during this period results in the early part of the record appearing to be biased low..

Uncertainties in the methods

Given the number of choices in the settings used as well as the methods themselves, we carried out an assessment into the effect these had on the final results.  The full details are in Dunn et al. (2014).

There were a number of choices and settings which had limited effect on the results, across all indices: the weighting function for the ADW gridding, the number of stations within a DLS when gridding, only selecting long-term stations, and the fitting of the DLS decay curve.  Even when only selecting grid boxes with stations within their bounds (non-interpolative), the quasi-global timeseries didn't show exceptional differences.

Two aspects that we investigated did result in larger changes for some of the indices: the gridding method used, and the overall number of stations in the network.  For the latter, we randomly subsampled the station network to result in 25, 50 or 75 percent of the stations and repeated this 100 times.  Unsurprisingly , the fewer stations which contribute to the dataset, the more uncertain the global annual timeseries become.

But it is the gridding method which had the largest impact. Along with the ADW method we used a reference station method (Hansen & Lebedeff, 1987) which also interpolates, and two methods which do not: the climate anomaly method (Jones et al., 1994) and a first difference method (Peterson et al., 1998).  The timeseries for PRCPTOT in Fig. 3 show how in the early part of the record, the long-term behaviour is very different between the four methods.

Fig 3. Long term behaviour of PRCPTOT for the 4 methods. FDMr is the first difference method, but run with a reverse time axis.

As well as investigating the temporal differences, we wanted to investigate the spatial ones.  As both the short and long term behaviour is of interest, we looked both at the correlation coefficients using de-trended data on the grid box level (Fig. 4a) and also the spread of the trends (Fig 4b.)  As different methods have difference coverage, the colours show how many of the methods result in a particular grid box being filled, from one (just HadEX2) to all four.  The more intense a colour, the higher the correlation coefficients and the more consistent the long-term behaviour.

Fig 4. (a) mean detrended correlation coefficient (r) of each grid box against HadEX2. (b) standard deviation of linear trends normalised by the mean trend. Grey boxes show where only one of the methods fills that particular grid box. 

Regions of the world which high station densities (e.g. North America, Europe, Asia) show both coverage, high correlations and strong agreement between trends.  Whereas those with lower station densities (South America, parts of Africa, central Australia) have less consistent coverage, lower correlations and less good agreement between trends.

Further Regional Assessments

There are two other studies I am aware of who looked at the methods used to convert between point and grid box values, focussing on Australia.  One used GHCND to test seven different gridding or interpolation methods, and compared these against one another, and also to observed datasets (AWAP, TRMM and GPCP).  Contractor et al. (2015) show that there can be considerable difference between the patterns of precipitation, especially at the higher quantiles.

Fig 2. Adapted from Contractor et al (2015).  Annual maximum daily precipitation from the three datasets (top row) and the seven methods (Inverse Distance Weighting, Cubic Spline, Triangulation with Linear Interpolation, Ordinary Kriging, Natural Neighbour Interpolation, Barnes Objective Analysis, Grid Average)

The other study looked at the effect of the order of operation as well the method used.  Avila et al., (2015) used only three different methods (natural neighbour, cubic spline and angular distance weighting) on the south-east corner of Australia.  They investigated the differences if the indices are calculated on the station timeseries and then gridded compared to when the temperature and precipitation values themselves are gridded and then the indices calculated on this gridded dataset (as in HadGHCNDEX).

Fig 3. TXx (top) and Tx1day (bottom) for the three gridding methods (NAT/CSS/ADW) showing the difference between index-then-grid (xgrid) and grid-then-index (gridx) for two spatial resolutions (adapted from Avila et al. 2015).

As can be seen in Fig. 3 there are differences depending on the order of operation, and the magnitude of these varies depending on the method.  These differences are strongest over the topographically varied region along the coast of this part of Australia.  ADW has a high level of smoothing, and loses detail in highly varying regions. However, between the natural neighbour and the cubic spline, the differences are such that it is not easy to tell which provides the better representation of the actual changes.

Summary

As is hopefully clear from these highlights, how a dataset goes from station based observations through to space-filling maps of extremes indices can impact what the data show and what conclusions might be drawn.  Being aware of the choices that went into the dataset algorithms is an important part of being able to assess what they are able to tell you.  Of course, the higher the station density, the easier it is to study changes in indices and variables which only correlate over short distances.  Hence the ongoing programmes to share data, improve the gridding routines, and update the datasets.

References:

Avila, F.B et al., (2015) Systematic investigation of gridding-related scaling effects on annual statistics of daily temperature and precipitation maxima: A case study for south-east Australia, Weather and Climate Extremes, 9, pp.6-16. https://doi.org/10.1016/j.wace.2015.06.003

Contractor, S., Alexander, L. V., Donat, M. G., and Herold, N. (2015) “How Well Do Gridded Datasets of Observed Daily Precipitation Compare over Australia?,” Advances in Meteorology, Article ID 325718, https://doi.org/10.1155/2015/325718.

Dunn, R.J.H., Donat, M.G. and Alexander, L.V., (2014) Investigating uncertainties in global gridded datasets of climate extremes. Climate of the Past, 10, 2171-2199 https://doi.org/10.5194/cp-10-2171-2014 

Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. In Proceedings of the 1968 23rd ACM national conference (pp. 517-524). ACM. https://dl.acm.org/citation.cfm?id=810616

A historical perspective on HadEX

Climate extremes indices have been used for well over a decade to allow the comparison between extreme climate events in different parts of the world.  As these indices have become more well used, they have allowed the monitoring of changes in extreme events over time.

I thought it might be useful to outline a bit about their history (at least, that which I know) and why there are now plans underway to create an updated global dataset.  If I've missed something out, or got something wrong, please let me know in the comments or via email and I'll correct it.

Despite pressure from many in the climate and meteorological community, not all meteorological data are freely shared across the globe. Usually, however, derived quantities can be shared more easily, allowing the study and assessment of individual phenomena and also the climate on a global basis.  To this end, climate extremes indices get around the problem of restricted access to in-situ data.  By converting daily values of minimum and maximum temperature, and precipitation accumulations (rainfall) to monthly or annual climate extremes, some information can be shared globally.

The other advantage of using climate indices, is that they standardise the way certain extremes are measured.  This has a benefit that like can be compared with like; so that heavy rainfall, for example, uses the same threshold around the globe (be that as an actual depth, or as a percentile of a distribution - both have their advantages).  

The disadvantage of using climate indices is that they reduce the information content as they are by construction some average or single measurement.  This loses some of the detail which might be important in a given situation.  Taking heatwaves as an example, is it the maximum temperature reached in the day, or how high a minimum temperature was at night, or how high above a threshold (and which) or the duration, or combinations thereof?  And is the humidity relevant?  Converting sub-daily or daily observations to a single number for a month or year means some of the "colour" is lost.  But, at least the indices allow the event to be studied if there are data sharing constraints.

The World Meteorological Organisation (WMO)/CLIVAR/JCOMM Expert Team on Climate Change Detection and Indices (ETCCDI) has worked for over a decade to develop a set of indices for use across the globe. They have also developed software and arranged workshops to enable researchers to calculate these indices themselves and contribute to international assessments and fill in data sparse regions.  These indices have been used in the creation of a number of datasets.

The HadEX Family Tree

The first set of indices developed by the ETCCDI numbered just 10, and were assessed by Frich et al. (2002). 

The first global dataset to contain all of the current 27 climate extreme indices recommended by the ETCCDI was HadEX (Alexander et al., 2006).  These indices were presented on a 3.75lon x 2.5lat grid from 1951-2003.  At its launch, it was the most comprehensive, global, gridded dataset of temperature and precipitation extremes based on daily, in-situ data.  HadEX was used in many model evaluation, and detection and attribution studies as well as climate monitoring.  

In 2012, HadEX2 was released (Donat et al., 2012a), which expanded the time span of the data from 1901-2010 and increased the number of in-situ stations contributing to the final gridded product (around 7,000 for temperature and 11,000 for precipitation indices). HadEX2 built on the legacy of HadEX, and was able to incorporate data from a number of new initiatives, primarily led by KNMI: the European Climate Assessment and Datasets (ECAD) and its siblings, in Southeast Asia (SACAD) and Latin America (LACAD).

By incorporating data from a number of different sources, which themselves may have slightly different processing levels, quality control procedures etc., HadEX2 could end up with some regional differences as a result.  Furthermore, HadEX2 has not been updated (bar some minor fixes in the period immediately after its launch), and so it is no longer useful for climate monitoring.  At the expense of spatial coverage, a climate extremes dataset was created from the Global Historical Climate Network Daily dataset (Menne et al., 2012) and is updated annually; GHCNDEX (Donat et al., 2012b).  GHCNDEX has been well used for monitoring extremes in e.g. the BAMS State of the Climate report.

A further version was created, based on HadGHCND (Caesar et al., 2006) which slightly adapted methodology used to create the final grids.  The HadGHCND product is gridded maximum and minimum temperature fields, and these have been taken to make a "HadGHCNDEX" dataset.  Although this only exists for the temperature indices, having three datasets all of which have the same goal and product in mind allows the comparison between different methods, and gives users some idea of the uncertainties in these datasets (something for a later blog).

These four datasets (HadEX, HadEX2, GHCNDEX and HadGHCNDEX) have been used to study the change in moderate extremes and individual extreme events for the last decade or so.  The methodology they use has been extended to assess extremes in reanalyses and also climate models (Donat et al., 2014, Sillmann et al., 2013a, 2013b).

HadEX, HadEX2 and HadGHCND are all available from the Met Office Hadley Centre Climate Observations website

References:

Alexander, L. V., et al. (2006), Global observed changes in daily climate extremes of temperature and precipitation, Journal of Geophysical Research-Atmospheres, 111, D05109, doi:10.1029/2005JD006290.

Caesar, J., Alexander, L., and Vose, R, (2006) Large-scale changes in observed daily maximum and minimum temperatures: Creation and analysis of a new gridded data set, J. Geophys. Res., 111, D05101, doi:10.1029/2005JD006280
Donat, M., Alexander, L., Yang, H., Durre, I., Vose, R., Dunn, R., Willett, K., Aguilar, E., Brunet, M., Caesar, J., Hewitson, B., Jack, C., Klein Tank, A. M. G., Kruger, A. C., Marengo, J., Peterson, T. C., Renom, M., Rojas, C. O., Rusticucci, M., Salinger, J., Elrayah, A. S., Sekele, S. S., Srivastava, A. K., Trewin, B., Villarroel, C., Vincent, L. A., Zhai, P., Zhang, X., and Kitching, S (2013a) Updated analyses of temperature and precipitation extreme indices since the beginning of the twentieth century: The HadEX2 dataset, J. Geophys. Res. Atmos., 118, 2098–2118,  doi:10.1002/jgrd.50150

Donat, M. G., Alexander, L. V., Yang, H., Durre, I., Vose, R., and Caesar, J. (2013b) Global land-based datasets for monitoring climatic extremes, Bull. Am. Meteorol. Soc., 94, 997–1006, doi:10.1175/BAMS-D-12-00109.1

Donat, M.G., J. Sillmann, S. Wild, L.V. Alexander, T. Lippmann, and F.W. Zwiers, (2014) Consistency of Temperature and Precipitation Extremes across Various Global Gridded In Situ and Reanalysis Datasets. J. Climate, 27, 5019–5035, doi:10.1175/JCLI-D-13-00405.1

Frich, P., L. V. Alexander, P. Della-Marta, B. Gleason, M. Haylock, A. Klein Tank, T. Peterson (2002), Observed coherent changes in climatic extremes during the second half of the 20th century, Climate Research, 19, 193–212 doi:10.3354/cr019193

Menne, M. J., Durre, I., Vose, R. S., Gleason, B. E., and Houston, T. G. (2012) An overview of the global historical climatology network daily database, J. Atmos. Oc. Technol., 29, 897–910 doi:10.1175/JTECH-D-11-00103.1

Sillmann, J., Kharin, V. V., Zhang, X., Zwiers, F. W., & Bronaugh, D. (2013). Climate extremes indices in the CMIP5 multimodel ensemble: Part 1. Model evaluation in the present climate. Journal of Geophysical Research: Atmospheres, 118(4), 1716-1733. doi:10.1002/jgrd.50203

Sillmann, J., Kharin, V. V., Zwiers, F. W., Zhang, X., & Bronaugh, D. (2013). Climate extremes indices in the CMIP5 multimodel ensemble: Part 2. Future climate projections. Journal of Geophysical Research: Atmospheres, 118(6), 2473-2493. doi:10.1002/jgrd.50188