A database of in situ water temperatures for large inland lakes across the coterminous United States

Abstract

Water temperature dynamics in large inland lakes are interrelated with internal lake physics, ecosystem function, and adjacent land surface meteorology and climatology. Models for simulating and forecasting lake temperatures often rely on remote sensing and in situ data for validation. In situ monitoring platforms have the benefit of providing relatively precise measurements at multiple lake depths, but are often sparser (temporally and spatially) than remote sensing data. Here, we address the challenge of synthesizing in situ lake temperature data by creating a standardized database of near-surface and subsurface measurements from 134 sites across 29 large North American lakes, with the primary goal of supporting an ongoing lake model validation study. We utilize data sources ranging from federal agency repositories to local monitoring group samples, with a collective historical record spanning January 1, 2000 through December 31, 2022. Our database has direct utility for validating simulations and forecasts from operational numerical weather prediction systems in large lakes whose extensive surface area may significantly influence nearby weather and climate patterns.

Full text

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SCIENTIFIC DATA | (2024) 11:282 | https://doi.org/10.1038/s41597-024-03103-8
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A database of in situ water
temperatures for large inland
lakes across the coterminous
United States
Troy Sorensen
 ✉ speyKelleyKessler





and forecasting lake temperatures often rely on remote sensing and in situIn situ


the challenge of synthesizing in situ lake temperature data by creating a standardized database of




simulations and forecasts from operational numerical weather prediction systems in large lakes whose

Background & Summary
Accurately representing spatial and temporal variability of lake surface water temperatures in numerical
weather prediction (NWP) systems has been shown (particularly for Earth’s largest lakes) to improve short-
and long-term forecasts of regional precipitation, air temperature, and surface wind velocity1–4. us, realistic
representation of lake conditions is crucial for the development of the next generation of climate and weather
forecast models5,6. e database we introduce here was developed to support this advancement by providing in
situ validation data for a broader project sponsored by the National Oceanic and Atmospheric Administration
(NOAA) through its Joint Technology Transfer Initiative (JTTI). e parallel NOAA JTTI project is designed to
optimize representation of lake surfaces in the NOAA Unied Forecast System (UFS) by exploring the sensitiv-
ity of UFS lake models to alternative lake bathymetric data sets7. Specically, the NOAA JTTI project evaluates
potential impacts of a new global lakes bathymetric dataset (GLOBathy) on simulations of lake surface temper-
ature, and temperature depth proles, in UFS 1-D lake models8. It is informative to note that these models are
currently operationalized within NOAA’s High-Resolution Rapid Refresh model, or HRRR9, which simulates
lake physics using a 1-D lake model included in the Community Land Model v4.510 with a 3-km horizontal
resolution, and 10 vertical (depth) layers.
Following an iterative in situ monitoring platform selection protocol (details below) we obtained near-surface
and subsurface lake temperature data from 134 sites across 29 lakes which (through the parallel NOAA study
referenced above) can be used to validate HRRR lake model simulations. We solicited and stored temperature
data at the highest temporal resolution available, which varies from site to site; at some sites, data is available at
sub-hourly resolution and, at others, at relatively coarse (e.g. semi-annual or monthly) resolution. Of the 134
1School for Environment and Sustainability, University of Michigan, Ann Arbor, 48104, USA. 2Department of
Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, 48109, USA. 3Coastal Survey
Development Laboratory, National Ocean Service, NOAA, Silver Spring, 20910, USA. 4Great Lakes Environmental
Research Laboratory, NOAA, Ann Arbor, 48108, USA. ✉e-mail: trsoren@umich.edu


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sites in our database, 84 include temperature measurements across multiple depths, allowing for comprehensive
validation of HRRR 1-D lake column model simulations.
While the lakes presented here represent a subset of all lakes in the HRRR model, we believe that, because
they are among the model domain’s largest lakes (by surface area; see methods below), they might be expected
to have the most profound impacts on surrounding terrestrial weather and climate dynamics. We note that
the Laurentian Great Lakes are not included in the NOAA UFS study because they are represented through a
separate 3-D modeling framework11,12 operated through NOAA’s National Ocean Service (NOS). In situ data
for validating Laurentian Great Lakes 3-D models is collected and utilized separately and specically for the
NOS modeling initiative, and is therefore not addressed here. Ultimately, the goal of our database is to provide
an organized, easily-accessible aggregation of in situ lake temperature prole data that can be used not only to
support validation for the NOAA UFS 1-D lake model experiments, but to serve as a resource for related lake
model validation and empirical data analysis studies as well (see Figs. 1 and 2).

We collected lake temperature data from a variety of sources, each requiring a dierent approach, ranging from
scraping online federal agency repositories to collaborating with and soliciting data from local water qual-
ity monitoring organizations. Federal agency repositories from which we collected data include the NOAA
National Data Buoy Center (NDBC)13, the United States Geological Survey (USGS) National Water Information
System (NWIS)14, and the Water Quality Portal (WQP) - a cooperative service maintained and sponsored by
USGS and the United States Environmental Protection Agency15. e temperature data we collected from local
organizations is unlikely to be included in the aforementioned federal repositories. It is informative to note that
any data we have collected for a given lake in our study may be aggregated across one or more of these sources
(for a summary, see Table1). It is also informative to note that data quality, spatiotemporal resolution, and tem-
poral continuity can vary greatly from source to source (see Fig.3); some sources provide quality-controlled data
throughout a lake’s depth prole at high temporal resolution, while others provide relatively sparse temperature
data collected by local ad hoc or citizen-based groups with little documentation on quality control methods.
Feedback from database users has highlighted that direct examination of the data signicantly aids in under-
standing its characteristics, especially for individual lakes or sites. Accordingly, we’ve included a scriptwithinthe
database repository to facilitate the creation of data plots for each site.
One of the most important design features of the parallel NOAA lake model simulation study made possible
by our database was a focus on evaluating historical lake temperature simulations in 29 of the largest (by surface
area) lakes across the continental United States (CONUS). A second important design feature of the NOAA lake
model study was a focus on assessing lake model simulation results from just one calendar year (following a
Fig. 1 Map of the coterminous United States indicating the location of all 29 lakes in our study (blue polygons;
magnied slightly to improve clarity). For 9 representative lakes, we also include an overlay of in situ monitoring
sites (each represented by a blue ‘x’), lake boundaries, and the corresponding 3 km × 3 km HRRR lake model
pixels (yellow grids). e 9 representative lakes are, from top le advancing clockwise, Lake Washington,
Flathead Lake, Devils Lake, Red Lake, Oneida Lake, Lake Okeechobee, Lake Tawakoni, Lake Mead, and Mono
Lake. See Fig.5 for corresponding details for all 29 lakes in our study.
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model spin-up period) given the relatively high computational expense of running the HRRR model at CONUS
scale. erefore, the collective criteria for including a monitoring platform in our database is that it comes from
one of the largest lakes across CONUS for which there is at least one in situ temperature observation within a
recent calendar year. e selection of a common recent calendar year, in turn, is intended to maximize the total
number of temperature data points across the selected lakes and monitoring platforms.
e results of our manual and iterative selection process identied 2019 as the calendar year that maxi-
mizes the total number of in situ observations across the largest CONUS lakes. Based on our analysis of federal
databases and conversations with individual (i.e. local) database managers, it is our understanding that 2019
was (for the purposes of our study) an “optimal” year for aggregating lake temperature data because many in
situ monitoring platforms were discontinued in 2020 at the onset of the pandemic. As a result of this selection
criteria, our database includes data from monitoring platforms for which there was at least one measurement
(and, typically, many more measurements) in 2019. However, in order to support any future related empirical
and model validation studies we also included any and all data available over a historical period from January
1, 2000 through December 31, 2022, although data availability may vary greatly for years other than 2019 (see
Table2).
We used the R Statistical Soware (v4.2.116) to extract and store variables from each monitoring platform
including sample collection date and time (UTC), coordinate location, depth (m), and water temperature (C).
Details on our nal data formatting are included in the Data Records section. Details on how we extracted data
from each source are included in the subsections below, with related metadata summarized in Tables1, 2.
 e NDBC is located within NOAA’s National Weather Service, and
is responsible for collecting, managing, and distributing meteorological and oceanographic data from a network
of buoys and coastal stations located in oceans, coastal waters, and large lakes (including the Great Lakes, which
are not included in this database). All data is quality controlled and publicly available here: (https://www.ndbc.
noaa.gov/).
 e USGS NWIS is a comprehensive database containing
a wide range of water-related data including streamow, groundwater levels, and water quality data including lake
temperatures. Lakes that met our study’s criteria were found manually using the online NWIS mapper (https://
maps.waterdata.usgs.gov/mapper/), and their data was accessed using the dataRetrieval17 package in R by spec-
ifying site identication numbers, desired date ranges, and the parameter code for water temperature. Note that
the WQP (described in detail below) includes data from the NWIS, but at a much lower temporal resolution.
 e WQP is a centralized repository maintained by the United States EPA
and the USGS, integrating data from multiple agencies and organizations18. Data from sites in the NWIS are
included in the WQP, but typically at a lower resolution. us data was extracted directly from the NWIS wher-
ever there was overlap with the WQP, and the WQP was instead used to extract data aggregated from other
sources.
Depth (m)
0
2
4
6
8
10
12
14
Temperature (°C)
Fig. 2 Representative example (from Oneida Lake, NY) of the relationship between in situ station locations
(top subgure; each represented by a blue ‘x’ and labeled with its site code), HRRR pixels (yellow squares), and
corresponding temperature data for each station in 2019.
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WQP data can also be accessed in R via the dataRetrieval package, similar to procedures used with the
NWIS. Due to the immense amount of data provided by the WQP, users can search for sites that meet certain
criteria before requesting a specic site’s data. We used this functionality to search for all sites of type “Lake”,
“Reservoir”, or “Impoundment” containing any water temperature data in the year 2019. Once we had a large
list of sites meeting this criteria, we used ArcGIS to lter out any sites not located on a lake over 30 km2. is
le us with a much shorter list of site names which we could then use to query the data of each site individually.
e format for reporting depths of observations varies across dierent sites within the WQP. Some sites were
not given a depth value and were instead reported as “near-surface”; we recorded these as a depth of 0.1 m. Other
sites report depth values to a very high precision (<0.1 m). We rounded these depth values to the nearest 1 m for
sites containing temperature values throughout a prole of 5 m or deeper, and to the nearest 0.5 m for sites with
a shallower prole of less than 5 m. In either case, values of 0 m were then shied to 0.1 m as the sensors included
in the WQP only record bulk temperature.
 In addition to the well-known and established described in the sections above, we gathered
data from a multitude of other websites and local sources, including the following:
• Flathead Lake - from the Flathead Lake Bio Station (FLBS) site (https://bs.umt.edu/apps/weather/) which
includes surface water temperatures at four sites. All sites have downloadable data dating back to 2011, and we
omitted periods of data reporting extremely egregious lake temperature values ( < −50 C).
• Lake McConaughy - provided directly by Nate Nielsen of the Central Nebraska Public Power and Irrigation
District (CNPPID). While data at Lake McConaughy is available in the WQP, we were able to obtain higher
spatial and temporal resolution data from the les shared with us directly by the CNPPID.
• Lake Mendota - provided online by the Space Science & Engineering Center at the University of Wiscon-
sin-Madison (https://metobs.ssec.wisc.edu/data_download/). We extracted the data at an hourly resolution,
though other resolutions are available for download as well.
• Mono Lake - provided directly by Dr. Robert Jellison of the University of California (UC) Santa Barbara and
the Mono Lake Committee (https://www.monolake.org/).
Lake Name Latitude Longitude Size (km2)
Data provider
NDBC NWIS WQP Other
Champlain 44.632771 −73.301921 979.6 X X X
Clear 39.048421 −122.808826 136.8 X
Devils 48.049741 −98.978507 311.7 X
Flathead 47.893863 −114.130567 463.1 X
Great Salt 41.169322 −112.539431 3962.2 X X
Houston 29.975492 −95.141341 22.5 X
Lewisville 33.121048 −96.979931 51.4 X
Malheur 43.331553 −118.792309 146.1 X
Marion 33.484218 −80.315048 228.7 X
McConaughy 41.248835 −101.792336 66.3 X X
Mead 36.090574 −114.748057 90.2 X
Mendota 43.108566 −89.419588 33.8 X
Mono 38.011535 −119.015838 174.1 X
Okeechobee 26.949621 −80.802608 1317.4 X
Oneida 43.206771 −75.907717 193.7 X
Pontchartrain 30.18727 −90.119927 1655.3 X X
Red 48.035195 −94.916255 1123.5 X
Sakakawea 47.752826 −102.184397 942.1 X
Sebago 43.861237 −70.551793 105.1 X
Seneca 42.66719 −76.920011 141.2 X
Tah oe 39.100468 −120.034368 483.8 X
Tawakoni 32.881902 −95.987976 111.2 X
Upper Klamath 42.428961 −121.934868 271.4 X X
Utah 40.220629 −111.824294 321.3 X
Walker 38.699737 −118.71699 119.2 X
Washington 47.625051 −122.25055 61.8 X
Winnebago 44.021601 −88.409584 512.4 X
Winnipesaukee 43.609695 −71.341321 116.6 X
Tab le 1. Metadata associated with each lake included in the database. “Latitude” and “Longitude” indicate the
center point of the lake and “Size” indicates the surface area as provided by the HydroLakes dataset27. e “Data
provider” column indicates which data source or sources provided data for each lake; see Table2 for select
summary statistics associated with the data for any given lake and data source.
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• Oneida Lake - provided by Dr. Lars Rudstam at the Cornell University Biological Field Station19. While
Oneida Lake temperature data is also available through the Knowledge Network for Biodiversity (https://knb.
ecoinformatics.org/), the high resolution temperature prole data provided by Dr. Rudstam is not available
online.
• Pyramid Lake - provided by Jennessy Toribio, a sheries biologist at Pyramid Lake Fisheries (PLF). PLF data
is sampled monthly, and while there is no exact time specied in the raw data, the PLF stated that readings are
typically taken in the late morning. We therefore assigned a timestamp to each recording of 10am local time.
• Sebago Lake - publicly available through the Portland Water District (https://www.pwd.org/
sebago-lake-monitoring-buoy).
• Lake Tahoe - provided from two contacts; Dr. Gerardo Rivera at the National Aeronautics and Space Admin-
istration (NASA) Jet Propulsion Laboratory (JPL) provided data from three sites at an extremely high tem-
poral resolution, but only for shallow proles in September 2019. Dr. Shohei Watanabe of the UC Davis
Tahoe Environmental Research Center (TERC) provided monthly temperature proles dating back to 2010
throughout the entire depth prole of Lake Tahoe, but only at a single site. e original TERC data includes
temperature measurements at every meter to a depth of 480 m. Our nal database includes these temperature
measurements at meter intervals to a depth of 50 m, and at 10-meter intervals from 50 m to 480 m (the origi-
nal higher resolution data is available in the Raw_data section of our database).
• Lake Washington - provided online by King County, WA (https://green2.kingcounty.gov/lake-buoy/Data.
aspx). All values from March 2009 were omitted due to noticably incongruous data.
• Lake Winnipesaukee - provided online by the New Hampshire Department of Environmental Services
(https://www4.des.state.nh.us/rivertraksearch/search.html).

Our database is deposited in “Deep Blue Data”, the University of Michigan’s institutional data repository20. It
can be accessed here: https://doi.org/10.7302/7gnd-mj10. e database contains sub-directories for each lake.
Within the sub-directory for each lake is the R script used to extract all data for that lake, a metadata table with
the latitude/longitude location and depth of each temperature sensor, and a directory containing the tempera-
ture data for each sensor in csv format with two columns for the date/time (in UTC) and the temperature (C).
Each sensor’s data lename is formatted as ABCXX_YY.csv where ABC is a three letter code for the lake, XX is
a unique numerical identier for the latitude/longitude location of the site, and YY is a numerical identier for
the depth of that sensor. A more detailed explanation of the directory structure is included in a README le
within the database.
Technical Validation
e data we collected from federal agency repositories (e.g. NDBC, NWIS, and WQP) and some local sources
were subjected to repository-specic quality control methods, each of which is described in detail in the respec-
tive repository’s literature and (if available) web-site. Regardless, we visually inspected all data at all depths
and removed data points or time periods periods with egregiously erroneous values for a very small number
of sites (as described in the Methods section). Additionally, to ensure overall data reliability, we validated our
in situ temperatures against remote sensed surface temperature data from the Moderate Resolution Imaging
Fig. 3 Representative time series (showing only 2018 through 2022 for clarity) of temperature data from ve
surface (or near-surface) sensors in our database. is time series underscores dierences in temporal resolution
and continuity across dierent sensors and lakes; a more comprehensive summary of temporal and spatial (i.e.
depth) resolution and continuity is included in Table2, and the database repository includes a script to visualize
the data of each individual sensor. Year labels on x-axis are positioned at the beginning of a calendar year.
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Spectroradiometer (MODIS), which has a spatial resolution of approximately 1 km21. We used MODIS Terra
and Aqua land surface temperature products, which collectively provide up to four surface water temperature
observations per day, per 1-km grid cell, to validate our in situ observations.
We recognize there are challenges to comparing gridded remote sensing temperature data to in situ data,
especially along lake shorelines where there is a potential for land contamination22. To address this challenge,
we ltered (i.e. removed, prior to validation) in situ sites within a 1-km buer of any lake shoreline, leaving 79
of our total 134 in situ sites for validation. en, because the original intent of our database was to validate (in
the parallel NOAA study) HRRR lake models for only the calendar year 2019, we interrogated surface tem-
perature data for MODIS pixels corresponding to each selected in situ site location in calendar year 2019 via
NASA’s AppEEARS data portal (https://appeears.earthdatacloud.nasa.gov/). Specically, the products obtained
via AppEEARS were MOD21A1D.06123, MOD21A1N.06124, MYD21A1D.06125, and MYD21A1N.06126. It is
informative to note that the MODIS data obtained through AppEEARS has quality thresholds of 0 (poor), 1
Lake Name Sites Sensors Observations Depth Coverage Historical Coverage
NDBC data summary
Champlain 3 3 45981 1 m 2019–2020
Mead 2 2 285564 0.5 m 2016–2021
Pontchartrain 1 1 1155458 0.6 m 2008–2022
NWIS data summary
Champlain 1 1 15327 1.5 m 2019–2020
Great Salt 1 1 80214 0.1 m 2018–2022
Houston 1 4 64564 0.9 m–4.3 m 2014–2022
Malheur 1 1 18039 0.5 m 2018–2020
Seneca 1 3 39046 1.8 m–29.6 m 2018–2020
Upper Klamath 1 1 68402 1 m 2007–2022
WQP data summary
Champlain 10 407 4954 1 m–100 m 2000–2021
Clear 6 24 246 0.15 m–10 m 2014–2022
Devils 5 61 228 0.1 m–17 m 2000–2022
Great Salt 4 33 623 0.1 m–10 m 2005–2022
Lewisville 3 46 65 0.1 m–19 m 2006–2022
Marion 7 7 509 0.1 m 2014–2022
McConaughy 1 34 17 0.1 m–33 m 2017–2021
Okeechobee 15 15 1155 0.5 m 2016–2022
Pontchartrain 3 3 305 0.1 m 2008–2021
Red 10 85 1548 0.3 m–9 m 2000–2022
Sakakawea 6 201 431 0.1 m–54 m 2003–2020
Tawakoni 4 56 164 0.3 m–7.9 m 2011–2022
Upper Klamath 6 6 1468 0.1 m 2005–2022
Utah 6 47 457 0.1 m–4 m 2001–2022
Walker 3 52 134 0.1 m–20 m 2006–2022
Winnebago 3 37 197 1 m–21 m 2002–2022
Summary of data from other sources
Flathead 4 4 1864273 0 m 2012–2023
McConaughy 1 32 240 1 m–32 m 2010–2022
Mendota 1 22 20953 0.5 m–20 m 2019–2022
Mono 12 623 553 0.5 m–42 m 2018–2022
Oneida 4 50 1931 0 m–14 m 2000–2020
Pyramid 1 99 76 1 m–99 m 2011–2022
Sebago 1 14 35061 1 m–37 m 2018–2019
Tah oe 4 117 128926 0.5 m–480 m 2010–2021
Washington 1 57 19047 1 m–57 m 2008–2021
Winnipesaukee 1 1 53805 1 m 2016–2022
Tab le 2. Select summary statistics categorized by data source and then by each lake for which the source has
provided data. For each specied data source and lake, “Sites” indicates the number of unique monitoring
platform locations (i.e. latitude and longitude), “Sensors” indicates the total number of temperature sensors at
any depth across all platforms, “Observations” indicates the number of measurements taken though time across
all sensors, “Depth Coverage” indicates the shallowest and deepest sensors, and “Historical Coverage” indicates
the earliest and latest years for which data is available.
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(marginal), 2 (good), or 3 (excellent) for each sensor reading, with each quality threshold corresponding to an
error of >2.0 K, 1.5–2.0 K, 1.0–1.5 K, or <1.0 K, respectively. We only used MODIS data with a quality threshold
of 2 or higher (i.e. reported error of <1.5 K) for our validation.
Fig. 4 Comparison between bulk surface (or near-surface) and skin temperature data from in situ platforms
and (respectively) the nearest MODIS pixel at four representative sites across calendar year 2019. Measurement
depths for in situ platforms are specied in the legend.
Washington
Flathead
Sakakawea
Devils
Red
Winnebago
Mendota
Seneca
Oneida
Champlain
Winnipesaukee
Sebago
Marion
Okeechobee
Pontchartrain
Houston
Tawakoni
Lewisville
McConaughy
Mead
Utah
Great Salt
Mono
Walker
Tahoe
Clear
Pyramid
Upper Klamath
Malheur
Fig. 5 For each lake in our study, a summary of the lake’s shoreline, associated HRRR model pixels (yellow
grids; 3 km × 3 km each), and location of in situ monitoring sites (represented by a blue ‘x’). Some panels (e.g.
Winnebago, Seneca, Champlain) also show HRRR pixels from adjacent water bodies that are not included in
our study.
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A visual comparison between our in situ data and data from each corresponding MODIS pixel (see Fig.4 for
a representative time series from four sites) suggests that the in situ temperatures are generally consistent with
MODIS, with minimal pronounced visible bias. To supplement this visual comparison, we calculated the bias
(relative to MODIS) of each in situ data point, along with the root-mean-square error (RMSE) of each site and
the RMSE across all sites. Specically, for each MODIS data point, we identied the closest in situ value that was
collected within 3 hours of the MODIS observation. If there was no in situ data collected within 3 hours of the
MODIS observation, then that MODIS observation was not used for validation. is approach resulted in 1,808
pairs of in situ and MODIS temperatures. e RMSE and bias across all validation data pairs was 2.780 K and
0.023 K, respectively (with MODIS being slightly warmer on average), and a more detailed assessment of RMSE
and bias for each monitoring platform (Table3) indicates that bias is generally low, especially at sites for which
there is a high number of observations.

As described in the Data Records section, our database contains the R scripts that we used to extract and format
data for each lake. Additionally, the database contains example scripts for organizing and visualizing the data.
Received: 15 August 2023; Accepted: 28 February 2024;
Published: xx xx xxxx

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Site Name Lake RMSE Bias NSite Name Lake RMSE Bias N
CHA01_00 Champlain 2.02 −0.32 132 OKE12_00 Okeechobee 1.11 1.11 1
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OKE11_00 Okeechobee 1.47 1.47 1
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reference. Only stations for which an RMSE and bias value could be calculated (see methods above) are listed.
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Acknowledgements
e authors thank the groups and individuals named in the Methods section who helped share lake temperature
data. e authors also thank Stan Benjamin, Eric Anderson, David Yates, Tanya Smirnova, Matthew Casali,
Mike Barlage, Bahram Khazaei, Nina Omani, and Eric James for helpful discussions related to HRRR model
simulation design and validation needs. is reportwas prepared by Troy Sorensenusing Federal funds under
award 018422from NOAA JTTI, U.S. Department of Commerce. e statements, ndings, conclusions, and
recommendations are those of the author(s) and do not necessarily reect the views of the NOAA JTTIor the
U.S. Department of Commerce.
Author contributions
T.S. gathered data, organized the database, developed scripts and methods, created figures, and wrote the
manuscript. E.E. issued feedback on the usability of the database, provided insight on methods and gures, and
assisted with ArcGIS. J.G.W.K. conceptualized the database and gathered data. J.K. provided insight on database
structure and assisted with scripts and gures. A.G. served as the Principal Investigator and provided overall
guidance and technical writing. All authors reviewed the manuscript. Note that while T.S. and E.E. completed
this work at the University of Michigan, T.S. is now aliated with the Colorado School of Mines and E.E. is now
aliated with North Carolina State University.

e authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to T.S.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
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