Home > Uncategorized > City Size and SUHI

City Size and SUHI

In the course of putting together data for my kriging project with the CRN stations, I got another idea related to a small but potentially important corner of the concerns over UHI in the global temperature index. For clarity I suppose I should make it clear that my position is that the UHI bias is probably low, less than .1C decade. That’s basically what Zeke and I found in our AGU poster work ( with help from Nick Stokes, Matt Menne and Claude Williams ). Nevertheless some people persist in claiming that the bias is bigger and further than the bias can even be found in small cities and towns. There isn’t much peer reviewed science to back up this claim, but there are a few “studies”  here and there looking at the problem. Here is short incomplete bibliography.  Torok 2001  http://www.warwickhughes.com/climate/seozuhi.htm; Spenser  http://www.drroyspencer.com/2012/04/regional-u-s-population-adjustments-to-surface-temperatures-since-1973-still-little-warming/;  Warwick Hughes .http://www.warwickhughes.com/blog/?p=575http://solberg.snr.missouri.edu/gcc/heatisland09.pdfhttps://ams.confex.com/ams/Annual2006/techprogram/paper_100595.htm; Not exactly what I would call compelling arguments, but rather some interesting observations. One reason this matters relates to the definitions of “urban” and “rural” that we use for studying the possibility of bias in the global temperature record. The argument, I have found, usually proceeds like this.  The records of UHI for a large city such as Tokyo, Phoenix, or New York are shown and one might see figures for UHI that are 2,3 or even 9C. The reasonable inference from this is that these types of bias may be in the global temperature record.  For a bit of background have a look at this   http://www.nasa.gov/topics/earth/features/heat-island-sprawl.html Dr. Imhoff and his team do some great work and much of it has inspired me to dig a little deeper into the issue. Results like Imhoff’s on large cities create some concern that this UHI bias may be in the record. There are a few things we need to note. The UHI measured in these studies is typically SUHI, that is, the surface urban heat island, while thermometers measure the air temperature 2 meters above this surface. If  SUHI were simply related to the air temperature above the surface, then this would not be a issue, however, air temperature is not simply related to the surface temperature although it can explain a good portion of the variance. The second issue with satellite measures of SUHI is that they are biased to capture the worst case. SUHI and UHI are modulated by the synoptic weather conditions. So, for example, on cloudy days or rainy days the heat islands that develop tend to be smaller than those on sunny days. Sensing the Land surface temperature requires a cloud free day. Hence the satellite measures will be biased high, or rather they will tend to capture the worst SUHI days. This approach is fine for understanding the human health concerns related to UHI and heat waves–another project I am working on,  but one should not be surprised to find that even large cities don’t see  9C heat islands every day of the year. SUHI and UHI vary by weather and by season and by location. The other thing to note about Imhoff’s study is that it tended to focus on large cities.  A comprehensive look at large cities was conducted by Peng who looked at 419 cities around the world http://cybele.bu.edu/download/manuscripts/peng-uhi-est-2012.pdf.  Some interesting findings that tend to confirm some of the things I’ve thought. First, if you look at annual figures for SUHI ( or UHI ) you will come up with numbers typically less than 3C and second there appears to be a threshold to the bias at the high end. Peng argues, for example, that for these large cities that SUHI is insensitive to population density. Since these are all cities over 1 million it might be more precise to say that there is a threshold effect above certain densities.  That’s consistent with what Oke already understood in 1973 when he fit maximum UHI with a log curve. Imhoff, appears to have found something similar in his studies focusing on impervious area as opposed to population density. In his study of 38 large US cities he found a similar log type relationship with the impervious area of a city. That single variable explains 71% of the variance in SUHI. and There are some interesting constrasts between Peng and Imhoff’s work that will take this post in a different direction that center around finding different driver for daytime SUHI and nighttime SUHI, but I’m going to focus on the rather small number of data points for cities less than 10 sq km in size.  The goal for this project is to   focus  on small city SUHI using Imhoff’s approach and then perhaps Peng’s approach. My goal at the outset was to get something on the order of 100 to 500 small cities less than 10 sqkm in size. Along the way we will also see the limitations of some datasets for these types of studies. In due course we will see the limitations of using Grump population data ( Like Spenser uses ) for small  areas and low population areas and we will see some difficulties in using Modis Urban. The Modis limitation is something I’ve struggled with before specifically in our AGU poster and then later in the Berkeley earth UHI paper. There were two basic issues. First, the Modis calibration was done on cities of 100K people or more. Given the size of the Modis pixel it is likely ( as one can see plowing through thousands of small cities) that Modis will miss small urban/town areas and identify areas as rural when in fact they are “small towns” or villages. The other issue with Modis that no one has pointed out is that I think some northern latitudes have snow cover where there are cities, so that Alaska, for example, is mis represented as more rural than it actually is. Checking the dates for when the Modis images were taken provides some confirmation of this. It appears this wasn’t caught in the calibration testing since all the cities used for calibration are at latitudes below 50 ( As I recall, I need to recheck all of this!) There are also some software goals in this project. There is a new Modis package in R that I am eager to use and some landscape statistic packages that I’ve always wanted to play with, so it’s a small bit of new science  to learn and a lot of software fun. Let’s get started! Here is a brief synopsis of Imhoff’s approach ( Peng is a bit different but let’s save that till later ). A)  identify the urban areas you want to study. B) identify the biome C) identify the rural area for comparison D) eliminate confounding variables E) process the Modis LST data for various time periods and seasons. F) regressions Along the way, we will learn something about the limitations of various datasets. A) Finding small urban areas. To find small urban/ small town areas  I employed US census data. After banging my head against the wall with census block shapefiles, the collections by state are huge, I took a different path. I downloaded the gazetter files: http://www.census.gov/geo/www/gazetteer/gazetteer2010.html.  Here I took the “Places” file  which is basically a flat file of  places in the US: cities, towns and CDPs or census designated Places. For now I’m working with 2010 data which is read in nicely by R. Later I’ll update with 2000 data which is not so easily read in. placesFile <- “G:\\USCensus\\Gaz_places_national.txt”  Places <- read.delim(placesFile, stringsAsFactors = FALSE) The file contains all the information I need to conduct a quick search for areas that are small and have people. I also know that when I return to the census shapefiles for these areas I’ll have an easier job of finding what I want. Next I impose some limits on the areas I will be looking at. colnames(Places)[13]<-”Lat” colnames(Places)[14]<-”Lon” Places <- Places[Places$Lat < 50 & Places$Lat > 22 & Places$Lon > -130,] Places <- Places[Places$ALAND <= 10000000,] Places <- Places[Places$POP10 < 2500,] Places <- Places[Places$AWATER < 25000,] After changing the names of Lat and lon columns I limit my area of interest to CONUS. I do that for several reasons. I plan on working with NLCD landcover 2006 and Alaska and Hawaii are missing from that. Second, I have some concerns about Modis Landcover (urban) in Alaska. I may return to this selection criteria. Next I use the ALAND metric provided by the US census to select only those areas with less than 10Million sq meters of area or 10sq km. This area is the area of the polygon that defines that area for the census bureau. Again, I’m only using this to narrow a search I will be doing in the satellite data. Next, I limit the population size I am looking at. The Census data will contain many small physical areas that are located within huge urban sprawls and what we are looking for is small cities that are surrounded by rural or un populated areas. Lastly, I limit the amount of water than can be found within the bounding polygon. With this criteria  we get a huge number of sites to look at on the order of  12,000. Plotting these and looking at them on google earth is my typical approach just to get an idea of potential problems any automated selection process will face. The site statistics are as follows: The average population is 600, average number of houses is 275 amount of land in the average area is 2.5m sq meters and the 75% of the sites have less than 100 sq meters of water. After reviewing plots of some of these areas it was clear that I was still not finding what I was looking for so to winnow this collection more I turned to another dataset  of Impervious surface, the global 1km dataset. Moving from a 30 meter dataset to a kilometer dataset makes the search faster.For the final look at things we will revert back to the 30 meter data, but first we need to find a good selection of small cities that are surrounded by rural environment. I used two versions of the data the standard dataset which contains Isa values from 0 to 100 ( with -1 for water)  and a reformated version of that file where 0 represents no Isa and 1-100 is recoded as 1. This allows me so simply sum to find the number of 1km cells that have any Isa. Places <- cbind(Places, Isa= extract(Isa,cbind(Places$Lon,Places$Lat))) Places <- Places[Places$Isa >= 0,] Places <- cbind(Places, Isa10sqkm = extract(IsaB, cbind(Places$Lon,Places$Lat), buffer = 3000, fun = sum, na.rm= TRUE)) Places <- Places[Places$Isa10sqkm > 0,] Places <- Places[Places$Isa10sqkm <= 36,] The processing above removes and location where water is at the center of the site location and removes those sites that are embedded in areas of other cities. At this stage we are left with 7445 sites which I then review by looking at plots  while counting the total number of 1km Isa cells in a 1/2 degree zone about the site location. for( i in 1:nrow(Places)){ e <- getExtent(IsaB,.5,c(Places$Lon[i],Places$Lat[i])) patch<- crop(IsaB,e) icount <- count(patch,1) Places$IsaCount[i]<-icount fname <- paste(i,”Patch.png”,sep=”_”) fname <- file.path(“Patches”,fname,fsep=.Platform$file.sep) png(fname, 785,785) plot(patch, main= icount ) dev.off() print(i/nrow(Places)) } That code creates 7445 plots of all the potential locations and counts the number of cells in a 1/2 degree zone. I then review those plots. Here is small sample The review of the 7000 plots suggested that if I wanted to find examples where there was a small amount of Isa  in the center of the plot and “non isa” surrounding it that a limit of 1500 total Isa cells in the  1/2 degree zone would go a considerable way toward that goal.  In addition, at this stage I winnowed the sites by Imhoff’s biome criteria. Since the biome that the urban site is embedded in drives the differential in temperature we want to make sure that a city is not in an area where the biome changes. The biome within  1/2 a degree of the site is check to ensure that a city is not in an area where biomes change.  These two cuts through the data reduce the number of sites to examine to  roughly 2400.  At this stage the underlying statistics of the area have not changed with the average population still be around 600 and the average sq km being 2.5. In addition, we now have tagged every site with its biome. The next step was plot all 2400 sites using 30 meter NLCD impervious surface data. The following gives you an idea of the detail available. With  these 2400 sites I figure I have a good chance of finding  a fairly large sample of small cities that I can perform the “Imhoff”  style analysis on. I will say that looking through thousands of maps for small urban areas gives me a good idea of some of the difficulties ahead. It always helps to get really down and dirty with the data. Reviewing the Imhoff approach one should note that he defines Urban areas by NLCD Isa with various zones such as an urban core at 75-100% Isa and then surounding zones at various levels. His cut off is 25% Isa.  One should also note that he checks this against Modis Urban.  That check is the check I turn to next. Why Modis Urban?  The answer lies in the bowels of MODIS LST.  Land Surface temperature data is estimated using a variety of MODIS  products. On critical unknown is emmissivity. That is estimated from Modis Land cover. Simply put, if Modis Land cover doesnt think a pixel is urban it will not apply the correct emissivity and the temperature will not be estimated correctly.  My next step then was to use Modis Land cover to winnow the 2400 sites down to those where Modis thought the small urban area was  “Modis Urban”.  In this next step I add a few more constraints, basically,  steps to ensure that the small urban center is surrounded only by non urban modis pixels. That step reduces the dataset down to 149 stations, mapped below A few things to note.  There are some sites that are located near water which should make an interesting bit of analysis. As I recall recall Imhoff has special handling for water pixels.  There  are  a few more restrictions that Imhoff employs for “rural” pixels  that will probably reduce this set even more and then there are pixels that need to be removed because of altitude differences, but with 150 sites to work with I think I have a manageable number. At this stage I wanted to also check out the  land cover surrounding a station. Imhoff used Biomes  which really dont give a current day view of the land cover rather they give a historical view of things. I may tweak that part of the analysis.  Here are some sample of land cover around the sites. Sites are coded in red..I’m still playing around with ‘rasterVis’  to get legends about land cover to work out

The site stats  now look like this:  Population ranges from  141 to 2417  with a mean of 999 and a median of 879.   The size of the community according to cadastral boundaries is from rounghly .5 sqkm to 10 sq km  with a mean of around 3km.  and the population density according to census figures runs from 36 people per sq km to 1200.

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  1. Evan Englund
    October 2, 2012 at 11:49 PM | #1


    Are you familiar with GPW and GRUMP?



    • Steven Mosher
      October 3, 2012 at 12:00 AM | #2

      yes Evan, one of the things I’ve been auditing is GRUMP. been using it for a couple years and the figures it gives for low population areas are sometimes wrong. They are wrong because they spread the population out evenly over space. Landscan which distributes population according to physical parameters such as the presence of roads and slopes is thought to be more accurate. So I started looking at the source data for GRUMP which is US census data to see if I could figure out where it was going wrong.

      In fact in this current data set I have I’ve already done the comparison between Grump population for these sites and the census data ( the actual source inputs for GRUMP )
      Of course Roy Spenser never checked on the sources for Grump or GPW before he used it
      and Mckittrick as well has made similar mistakes. They find a GIS dataset and never check the manual for how it was built.

      For example, when you check NLCD land cover and find croplands, and check google earth and find croplands and check Grump and find people living in the middle of wheat field that should give you some idea about trusting the veracity of that data at 1km.

      So, yes I check GRUMP I check GPW I check Hyde population and I check the data that uses Landscan population as part of its regression models. At some point I may swicth to Landscan but its not open data

  2. Evan Englund
    October 3, 2012 at 3:48 AM | #3

    Sorry, Steve.

    I commented after a quick skim and missed that you mentioned GRUMP. My view on UHI in general is that it is a real phenomenon that we might call anthropogenic local warming. That is an issue not because the data are erroneous, but because the urban areas are oversampled. The proper way to deal with this is NOT to correct, adjust or homogenize the data, but rather to stratify the spatial estimation. If we had true population density on a 1km grid, we could easily divide the land area into population density tiers, and krige only within tiers. Of course, pop. density is only a proxy for UHI-ness, but at least a reasonable one. Census-based maps like GWP or GRUMP may be crude, but stratification doesn’t have to be perfect to be useful. ISA sounds equally reasonable as a proxy, and may be a better way of classifying stations.

    Hopefully this won’t be (much of) an issue when kriging with CRN data. Or will it?

    I’ve looked at the papers on the BEST methods, They managed to make it complicated enough that I didn’t understand all the detail. But I think i follow the gist of it and see mostly positives and no major problems. I’ll email you with some comments in a day or two.


    • Steven Mosher
      October 4, 2012 at 10:27 PM | #4

      No problem Evan.

      A while back I did some regressions of temperature trend against the Isa Area it was significant in the US.

      My sense on population is this> If you look at the energy balance equation for the urban enviroment you will of course see a term for anthro heating. The problem is that figure has been estiimated from 100watts to 1500 watts. Also population is co linear with ISA.. err
      unless the people are living outside buildings on the grass. In any case stratification is kinda what I was shooting for.. once I get a bunch of data assembled.

    • mwgrant
      October 20, 2012 at 12:01 AM | #5

      Evan (and Steve),

      [Steve, my apologies as this is off-topic per posting, but is mentioned by Evan. I was unable to find emails for you or Evan or I would have gone that route. ]

      Because you have been looking at the BEST papers and given your extensive background over the years in geostatistics, I have a couple of questions/comments regarding the BEST papers. I found the discussion difficult to follow, but that may in part reflect a bias of my own ‘expectations’ as a result of exposure and practice in a context of contaminant hydrology. I think that the BEST application is a different beast–at least compared to what I have seen.

      1.) I was surprised to see no presentation or discussion of local error estimates within the formal kriging process. Or maybe I just missed something in the short discussion under spatial uncertainty. It seems to me that given uneven coverage in observations really suggests taking a look at local error estimates–error maps. What was your read on the topic?

      Steve: I guess I’m a little confused by what you mean by the local error map. The nugget is .46C per month and the error for estimating any
      temperature at an arbitrary lat/lon/elv is 1.6C.

      2.) Regarding the oversampling of some areas–are cell declustering or polygonal declustering viable here? a manual judgement process?

      over sampling is not an issue as far I can see. We’ve done some test with synthetic data, that will get posted in due course.
      basically if you have more samples in a given area that is going to be handled in the regression and the correlation length. You start
      by collecting all the data and running a regression where temperature is a function of lat/lon/elevation and a seasonal component.
      The residual of that ( weather) gets interpolated via kriging

      3.) I think time will show anisotropy is to important to ignore, and that will be incorporated. In addition to the latitude aspect, many important geographical features, e.g., mountain ranges, are oriented and have a physical scale not unlike the typical correlation lengths seen in the data.
      yes. basically you are talking about improving the fit of the regressions and explaining more of the temperature in terms of physical
      geography. I’ve played around with this a lot. The more work you do here the smaller the error in the predicted temperature.

      4.) Can variants like probability kriging, logistic kriging, cokriging (e.g., proxy data) maybe bring anything to the table?

      I havent played around with co kriging. But i’m not sure how much narrower we can make the intervals on anomaly theya re already damn
      small. The most important thing is getting more historical data. It exists. Needs to be digitized

      So my question to Evan is ‘did any of questions or similar occur to you and how did you work through them?’

      I did raise questions 1-3 at Judith Curry’s blog but it was late in the life of the thread and the sound and fury had moved on a couple of postings (and unfortunately like here–not entirely on topic):

      sorry about that. I run around from place to place and dont always get back to every fight.


      • mwgrant
        October 20, 2012 at 10:43 AM | #6

        Steve, thanks for the reply sharing your thoughts as they now stand. It I have noticed you are quite busy.

        1.) Error maps–clarification

        Here is a link to a part of Isobel Clark’s classic ‘Practical Geostatistics (1979)’:


        Figures 5-9 and 5-11 illustrate the sort of error maps I am thinking off (OK case). When an estimate of a random variable is made for a given location an estimate of the uncertainty (a local kriging standard deviation) in the value estimate is also produced. Like the estimated value for the variable, this uncertainty estimate is a function of location (relative to the sample locations) and can be mapped as in the figures 5-9 and 5-11. In theory you can also do other interesting things like estimate confidence bands around contours of the variable, determine where new observations might be most effective in regards to reducing overall uncertainty, etc. [These things are kind of old school and there are potential difficulties but still they may at least provide insights.]

        Your 0.46 nugget ( number in CE http://judithcurry.com/2012/07/29/a-new-release-from-berkeley-earth-surface-temperature/ is a measure of the “sum of all errors at the average station, including errors due to different instruments, errors due to different observation practices, siting errors, etc. ” I am guessing that for BEST’s universal kriging it also includes the residual from the regression? Again the local uncertainty estimates above are a function of location. So that is what I was getting at. I hope it is a little clearer. (Your nugget answer here confirmed my understanding from the papers–thanks.)

        2.) clustering

        “basically if you have more samples in a given area that is going to be handled in the regression and the correlation length.” I just don’t have a feel for what happens with UK, but what you say makes sense if the correlation function is fit to the residuals from the regression part. But this is not clear to me from the text. (That is an admission, not a question.) If Evan sheds any more light on this particular topic I hope you will have an opportunity to share that.

        3.) Anisotropy

        It will be interesting to see you physical geography results. Its got to be a lot of grinding. I had thought about playing with an area encompassing part of the Great Plains and Rockies for a couple of different years, but wow! one really has to do a lot just to get to the data. (I hadn’t looked at your climate GUI yet.)

        4.) Other kriging variants

        I’ll have to say I don’t know about the prospects of cokriging, logistic kriging, etc. They are possibly more of interest (if at all workable) from the perspective of exploring the relationships between various proxies and temperature estimate-as opposed to the main show of good global temperature estimation.

        Thanks again for you reply. It has been very helpful.

  3. David Unwin
    October 4, 2012 at 1:52 PM | #7

    I am a retired geographer who in the 1970s worked a little measuring UHI using an instrumented vehicle and analysing simple max/min data. My background was that I studied with T.J., Chandler, author of the classic 1965 Climate of London and published a bit on the association between UHI and synoptic ‘weather type’. I have only come across this work via my interest in R. and my experience is only in air temperature at screen height, not the surface radiation temperatures sensed remotely, the quantities you call SUHI..

    Can I make a few observations about the climatology?

    If you look at UHI data using the old fashioned comparison approach (which has its faults, read Landsberg on this) what become clear is that the phenomenon isn’t something that is ‘there’ all the time, but which occurs only in some synoptic conditions. These in turn might vary from season to season and by location of the urban areas on the planet. In UK I am reasonably satisfied that the main correlate is the presence of settled anticyclonic weather and UHI are a night-time phenomenon. Chandler attempted to isolate these factors using linear regression, and in my work I simply looked at histograms of the UHI disaggregated by weather type. The issue for climate change studies is the extent to which these UHI incidents contaminate the record by feeding through into the time series. My view is that this is a much more complex problem than is suggested by use of simple corrections based on urban size or population. I should also note that it is by no means uncommon for there to be day-time ‘cold cores’.

    The second issue is what controls the magnitude of the individual UHI when they occur? There is a paper by Tim Oke on this issue as well as work by David Johnson somewhere in the literature, but what happens if you look at any two stations, one urban and one ‘rural’ during heat island incidents? Basically what you see is that there is a divergence in the RATES of heating and cooling that itself leads to both the night time heat island and the day time ‘cold core’, So what causes this difference? We are in very settled conditions (bar some UHI induced ‘urban winds’ that will ventilate the urban area) so advected air isn’t an issue. Oke and his team focussed on the near surface energy balance and there are several possible processes, any one of which could generate the observed difference. If you believe it is the lack of transpiring vegetation then using the local amount of built over surfaces might be best, whereas if you think it is flux divergence in the outgoing thermal radiation then some measure of the local urban geometry might be better, and so on. All I know is that in two cities in England the best correlate of the urban excess (found by traversing) was the urban geometry (the height width ratio of the urban canyons) which suggests flux divergence in the urban canopy.

    So how does city size get a look in? First, I would be very careful in looking at Oke’s paper (and compare it with what is implicit in some of his other later work). The data were a mix of small settlements in Canada to which he added ‘maximum’ observed heat islands gleaned by writing to friends in the same game (Tony Chandler included) and the literature. Second, he attempted to explain the size by reference to an advective model due to Summers in which the UHI was explained by warming of air advected across the city, so ‘population’ was basically a surrogate for ‘area’. The original paper discusses this link but this is the wrong process and I wish I had kept copies of my later correspondence with Tim in which he admits this (see his work on Vancouver). There may be a correlation with population and/or area, but this is most probably due to some co-variate such as the fact that ‘bigger’ cities tend to have more ‘urban’ cores.

    Finally, if you actually measure the air temperature during UHI incidents it is worthwhile simply watching the thermometry as you drive through any city. It quickly becomes evident that there is a rapid response to changes in the nature of the urban surface. Extend out into the country and you find that even very small villages can generate UHI — it all depends on the nature of the urban surfaces (at least in the mid-latitudes) that in turn influence how the net radiation is partitioned. There are several studies that look at the UHI of quite small urban areas (such as airports and out of town supermarkets)

    Hope this helps.

    dave Unwin

    NB as a minor point of presentation, UHI and SUHI should be expressed as temperature differences (K), not as points on the Celsius scale (C)

    • Steven Mosher
      October 4, 2012 at 10:41 PM | #8

      dave. Thanks. I agree with everything you say, especially Tim’s work. I wish I could find my lost copy of his 73 paper.

      1. synoptic conditions. Yes. I try to make this point in various debates with folks who focus on the MAX.

      2 H/W. Yes! I had a discussion with Imhoff about this ( a few words nothing more ) basically
      we can use city/size area and impervious area to get a proxy for the heat storage issues
      and latent/sensible issues, but the flux divergence is going to be dependent on H/W.
      Imhoff suggested trying to get building height from “shadow analysis” which is doable.
      As a quick and dirty estimate I can also look at population and housing units. In residential
      US pop/housing units is approx 2-3. that is, single story homes. When that ratio is
      lower than 2 you will see unihabited houses. when it is greater than 3, you are in a urban
      area of high rise housing where 2000 people live in one housing unit.. I have not tested
      this proxy of height, just an idea for now. I also have some ideas for isolating the
      anthro effect by looking at depopulation. There have been studies done on weekend
      UHI ( decreases ) such that you can infer/estimate/guesstimate anthro heating by looking
      at weekend/weekday deltas. I’ve got some other ideas there as well.

      ” There are several studies that look at the UHI of quite small urban areas (such as airports and out of town supermarkets)
      Hope this helps.”

      If you have links pass them along. I love reading this stuff. Especially Oke

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  1. November 25, 2012 at 10:43 AM | #1

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