Earth observation by constellations of CubeSats: New opportunities and challenges
Rasmus Houborg
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11/15/2018
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CubeSats
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- [00:00:00.690]Thank you.
- [00:00:02.400]Let's see how long I last in South Dakota with the winters.
- [00:00:07.270]All right, so this talk is gonna be about CubeSats.
- [00:00:12.020]It's really kind of an exciting new area I think,
- [00:00:13.940]and I started looking into those new kind of sensors
- [00:00:17.610]about two or three years ago,
- [00:00:19.020]and it really, really excited my passion for doing science.
- [00:00:23.450]This talk is really about how to exploit
- [00:00:27.132]this type of new resource using an agnostic sensor data
- [00:00:32.540]fusion approach that takes into consideration
- [00:00:36.860]other more traditional sensor types like Landsat
- [00:00:40.470]and Sentinel Two.
- [00:00:42.230]So, it's really an exciting area
- [00:00:44.170]for remote sensing and accu-culture monitoring
- [00:00:45.780]as I see it with these new observational paradigms
- [00:00:49.460]and the general proliferation of sensor data.
- [00:00:53.221]There's so much new data coming alive.
- [00:00:55.150]And then who would imagine that today we are able
- [00:00:59.290]to do daily imaging at three minute solution globally?
- [00:01:02.260]So, that wasn't something that you would imagine feasible
- [00:01:04.410]just a few years ago.
- [00:01:05.960]Obviously, these new data sources
- [00:01:07.570]doesn't come without limitations.
- [00:01:09.840]And as I see, you need to use it.
- [00:01:12.000]With other more conventional resources.
- [00:01:20.150]This talk is about kind of presenting this technique,
- [00:01:23.200]for integrating these different data sources,
- [00:01:25.690]but it's also kind of...
- [00:01:28.396]I also want to show or demonstrate,
- [00:01:30.130]how to evaluate how good our SmallSat data really is.
- [00:01:32.680]Is it really useful for doing scientific analysis?
- [00:01:36.023]Delivering products of sufficient quality,
- [00:01:38.670]for doing science and application for case and studies.
- [00:01:47.120]There we go
- [00:01:48.380]So the end idea, the CubeSat.
- [00:01:51.377]And for those who don't know it,
- [00:01:54.645]it's a small satellite that has a single unit size
- [00:01:57.130]of 10 times 10 centimeters
- [00:01:59.690]and a mass list of one point three kilograms.
- [00:02:04.070]The basic concept is really to expand the observation
- [00:02:07.330]potential by launching flocks of these small CubeSats
- [00:02:11.461]that are based on a very cheap commercial
- [00:02:14.820]after-shelf components, which makes constellations
- [00:02:18.330]of hundreds of these in space economically feasible.
- [00:02:23.170]I'm doing configure these in a number
- [00:02:25.356]of comparable sizes to increase
- [00:02:27.380]potential application fields,
- [00:02:29.280]including the three U, six U, and 12 U sizes;
- [00:02:34.060]and the last number of companies that kind of
- [00:02:35.760]taking up on this new technology,
- [00:02:37.860]including Planet Labs and Astro Digital
- [00:02:40.120]and a number of other kind of companies.
- [00:02:43.060]My work has focused on using data from Planet.
- [00:02:52.800]So, they operate the largest constellation
- [00:02:55.270]of CubeSats in space.
- [00:02:57.473]They adopted three U standard
- [00:03:01.200]and about four kilograms per CubeSat,
- [00:03:04.100]currently have around 150 active CubeSats in space
- [00:03:09.100]and that kind of facilitates daily imagining
- [00:03:12.820]at three to four meter resolution.
- [00:03:16.590]So for instance, when we look at commercial satellites,
- [00:03:19.640]they will take years to produce and cost you a fortune.
- [00:03:23.250]Planet can produce 40 satellites in just one week
- [00:03:26.690]at a tiny fraction of that cost.
- [00:03:28.940]So, this is a completely new, really a game changing
- [00:03:31.430]kind of resource that we're looking at here.
- [00:03:35.580]Obviously, the special kind of resolution
- [00:03:38.480]is a bit limited.
- [00:03:40.330]It's only four bands that are quite broad
- [00:03:42.640]in the red, green, blue, and the infrared.
- [00:03:51.527]All right.
- [00:03:56.400]I just want to show this animation
- [00:03:57.798]just to show how they orbit in space.
- [00:04:01.304]The cubes assign a center corner as orbit
- [00:04:04.343]and they orbit in a train.
- [00:04:06.380]It's pretty unique and it gives you this very high,
- [00:04:09.332]unprecedented spatiotemporal frequency.
- [00:04:19.301]And the spatial advantage is superior
- [00:04:21.702]to that what you can achieve
- [00:04:23.194]from conventional system like Landsat.
- [00:04:25.370]This compares the Landsat 30 meter
- [00:04:27.090]with the Planet Scope, which is the Planet's CubeSat data,
- [00:04:30.820]three meters in data and you can really appreciate
- [00:04:33.182]the enhanced spatial resolution.
- [00:04:35.342]You're able to resolve individual trees
- [00:04:38.750]and shadows from the planet data,
- [00:04:41.410]as well as intra field variability
- [00:04:45.460]that you won't be able to see with LandSat-like information.
- [00:04:52.770]But at the same time, these CubeSats
- [00:04:54.233]are not without limitations.
- [00:04:56.580]As mentioned, they're more spatially limited,
- [00:04:58.990]they only have four bands,
- [00:05:01.029]and they have significant overlap in the visible domain.
- [00:05:06.950]This shows an average spatial response
- [00:05:08.963]of a selection of CubeSats
- [00:05:11.000]compared to that of LandSat eight.
- [00:05:12.560]Kinda the shading around each of these curves
- [00:05:15.840]represent the standard deviation
- [00:05:17.330]between each individual CubeSats.
- [00:05:19.830]Each CubeSat has a unique spatial response
- [00:05:23.020]and you need to account for that difference
- [00:05:25.620]when you wanna create a continuous
- [00:05:28.480]or consistent time series of data.
- [00:05:31.220]As you can see, it's quite different
- [00:05:32.870]from the spatial response you get from LandSat,
- [00:05:34.663]that has much narrow bands,
- [00:05:37.210]particularly in the visible domain.
- [00:05:39.490]And this will result in inconsistencies
- [00:05:41.380]or if you compare a common spatial metric,
- [00:05:43.860]like the NDVI, it will not be consistent
- [00:05:46.160]between the CubeSat and a LandSat observation.
- [00:05:49.670]The CubeSat data would be much smaller
- [00:05:51.570]in terms of NDVI and the dynamic range
- [00:05:55.160]will be significantly smaller as well.
- [00:05:57.350]So, you need to correct for that
- [00:05:59.908]in order to make the data really useful,
- [00:06:02.710]and for that purpose, I've developed a CubeSat-enabled
- [00:06:05.510]spatiotemporal enhancement method called CESTEM,
- [00:06:10.190]kinda explores these synergies and cross paths
- [00:06:12.680]from observation by integrating MODIS, LandSat,
- [00:06:16.250]and Sentinel Two as a reference for calibrating
- [00:06:19.180]your CubeSat data.
- [00:06:21.200]It serves as a multi-purpose tool
- [00:06:24.690]for when you're measuring normalization.
- [00:06:27.430]Phenology reconstruction, via NDVI for instance,
- [00:06:30.900]as well as spatiotemporal enhancement
- [00:06:33.210]of biophysical properties, including Leaf Area Index.
- [00:06:42.197]So, this shows you a kind of a conceptual diagram
- [00:06:44.120]of what CESTEM does.
- [00:06:45.310]One one side, you have these satellites,
- [00:06:49.842]the big satellites that cost quite a fortune to build
- [00:06:55.430]and takes quite a bit of time to put into space,
- [00:06:58.360]but they're rigorously calibrated
- [00:07:00.080]and can be regarded as the gold standard,
- [00:07:02.240]but then they're affected by the classical trade off
- [00:07:05.190]between spatiotemporal resolution.
- [00:07:07.370]This simply cannot satisfy both of these conditions.
- [00:07:11.010]So, there's either gonna be high spatial
- [00:07:12.610]or high temporal, rarely both.
- [00:07:15.290]On the other side, you have SmallSats
- [00:07:16.960]that are low cost, high volume system
- [00:07:19.970]that are launched in flocks,
- [00:07:21.970]which gives you a superior spatiotemporal resolution,
- [00:07:24.132]but then again, they were basically built in a garage
- [00:07:26.990]and don't have that same degree of calibration
- [00:07:29.450]as you get from the conventional systems.
- [00:07:32.000]So, these contrasting data sources or data stream
- [00:07:34.720]feed into system, that then applies a number
- [00:07:40.130]of data fusion and machine-learned techniques
- [00:07:42.890]to kind of fix issues in the original data sets
- [00:07:45.880]in order to produce and enhance the high quality product
- [00:07:50.320]that is suitable for doing scientific applications
- [00:07:53.160]and for delivering real insights of real value
- [00:07:56.910]to the end-users.
- [00:08:02.740]All right.
- [00:08:03.720]So, this exemplifies the approach system framework
- [00:08:07.550]for the MODIS, LandSat, and CubeSat.
- [00:08:13.490]The general idea is to use, in this case,
- [00:08:15.717]MODIS and LandSat surface reflectances as a reference
- [00:08:19.490]to calibrate your raw CubeSat data,
- [00:08:22.540]being digital numbers or top of atmosphere reflectances
- [00:08:25.610]into a LandSat-consistent surface reflectances.
- [00:08:30.470]CESTEM has the ability to draw the reference data
- [00:08:32.890]from LandSat data from any scene in the past
- [00:08:36.670]and then it uses down-scaled MODIS data
- [00:08:40.060]to kind of assess or determine the change
- [00:08:44.260]in cover conditions over the various acquisition time spans.
- [00:08:48.820]So, by drawing LandSat data from past images,
- [00:08:52.000]it establishes a map for each individual CubeSat scene
- [00:08:55.770]and then uses that as a training for creating a model
- [00:08:59.070]to predict LandSat-consistent surface reflectances
- [00:09:02.240]at the spatiotemporal resolution of the CubeSat data.
- [00:09:05.823]So, it basically brings your CubeSat data in line
- [00:09:07.870]with your LandSat surface reflectance data,
- [00:09:11.300]then you can then produce a time series
- [00:09:13.770]of a spectral metric, like NDVI.
- [00:09:17.375]And this is kind of a sensor agnostic approach,
- [00:09:19.840]so you can also substitute LandSata eight with Sentinel Two
- [00:09:23.510]and you can even use the system to calibrate
- [00:09:25.660]other sensors that might need calibration,
- [00:09:28.050]be it other CubeSat sensors or be it a UAV sensors.
- [00:09:32.305]There's no requirement in terms of the input
- [00:09:35.200]of the data to be calibrators and can be raw data.
- [00:09:39.310]So, that's a powerful mechanism,
- [00:09:40.700]a powerful element of this approach.
- [00:09:44.017]Let's see.
- [00:09:49.110]All right.
- [00:09:49.943]So, CESTEM has also been extended to map
- [00:09:53.260]biophysical plan buffers group properties
- [00:09:55.690]at a CubeSat resolution and this approach can use
- [00:10:00.120]either LandSat or Sentinel Two.
- [00:10:02.387]It kind of exploits the enhanced spectral resolution
- [00:10:05.460]of those sensors to better retrieve or better constrain
- [00:10:09.030]your inversion process.
- [00:10:11.690]I use a sale prospect model immersion approach
- [00:10:17.160]and kind of combine that spatially enhanced data
- [00:10:19.520]with your enhanced spatial information
- [00:10:23.510]from the CubeSat data.
- [00:10:26.360]And I will show you that a bit later.
- [00:10:29.210]So first, I'll demonstrate the utility of system
- [00:10:33.370]for radiometric normalization
- [00:10:35.410]and this, I will base this on studies in Saudi Arabia,
- [00:10:40.500]an agricultural farming area,
- [00:10:43.820]consistent of an agricultural pivot
- [00:10:46.070]about 800 meters in diameters.
- [00:10:48.160]It's a combination of corn and alfalfa, primarily.
- [00:10:55.760]So, this compares the NDVI from CubeSat and LandSat eight,
- [00:11:01.282]the normalized frequency distribution shows NDVI
- [00:11:05.151]from CubeSat data based on both
- [00:11:07.430]top of atmosphere reflectances and Six S
- [00:11:10.340]corrective surface reflectances
- [00:11:11.760]compares with LandSat eight,
- [00:11:13.470]and you do see a significant shift
- [00:11:15.940]that's definitely not consistent.
- [00:11:18.258]You can see the same tendency in the tendency scatter plots
- [00:11:22.400]as significant bias between your LandSat and CubeSat NDVI,
- [00:11:28.000]even after you correct for the atmospheric effects,
- [00:11:31.664]there's significant bias and a mean absolute deviation
- [00:11:34.190]of around 25% on average for this given day,
- [00:11:40.090]but then when you apply the system algorithm,
- [00:11:42.260]you're really able to kinda bring
- [00:11:43.690]these different data sets together.
- [00:11:46.830]They now align quite nicely and you would use
- [00:11:48.540]significantly reduced bias to basically eliminate the bias
- [00:11:53.090]and end up with a mean absolute deviation
- [00:11:54.580]of around two percent for this particular day.
- [00:12:02.130]And you can also apply this to the individual spatial bands
- [00:12:05.660]and this shows an independent validation
- [00:12:06.890]of the system derived reflectances
- [00:12:10.450]against day coincident LandSat eight reflectances
- [00:12:13.880]and then again, you see you're able to quite accurately
- [00:12:16.900]reproduce the LandSat eight data using this approach.
- [00:12:29.892]So now, I'm looking into how to use this
- [00:12:32.990]for reconstruction phenology via NDVI
- [00:12:36.490]and this shows a time series of an alfalfa field
- [00:12:40.387]in Saudi Arabia.
- [00:12:41.670]It's a six month period.
- [00:12:44.006]We have different time series here.
- [00:12:45.699]The blue one...
- [00:12:46.877]Sorry.
- [00:12:48.570]Yeah, the blue one is the system correct time series
- [00:12:51.240]and the red's kind of a square of the LandSat eight data,
- [00:12:56.240]and then I'm mostly showing the original,
- [00:12:58.820]uncorrected CubeSat data.
- [00:13:00.960]You have the top of atmosphere reflectances,
- [00:13:02.413]as well as the surface reflectances
- [00:13:04.340]corrected via Six S, and you can clearly see
- [00:13:06.990]how the original data is really quite noisy
- [00:13:09.360]over this site, but when you apply the CESTEM algorithm,
- [00:13:13.160]you are able to kind of reproduce a sensible
- [00:13:15.790]and meaningful time series that tracks what you see
- [00:13:19.127]in LandSat quite nicely.
- [00:13:29.090]And below is just an animation,
- [00:13:30.680]kind of can see what's going on in the spatial domain
- [00:13:34.500]for this specific pivot.
- [00:13:36.550]Again, you can see there's quite a bit of fluctuation
- [00:13:38.840]in the top of atmosphere data
- [00:13:41.150]whereas the CESTEM corrected data is more stable in time,
- [00:13:44.420]it's more consistent, what you would expect
- [00:13:47.592]to observe in real time, in a real kind of setting.
- [00:13:53.156]Let me just see.
- [00:13:55.890]And this shows a fast forward animation of that,
- [00:13:58.552]showing the CubeSat data before and after applying CESTEM
- [00:14:04.325]and, in this case, you can also get a good appreciation
- [00:14:06.680]of the noise in the original data and the capacity
- [00:14:09.820]of CESTEM to correct for that and produce
- [00:14:12.599]a meaningful NDVI time series.
- [00:14:27.825]This one.
- [00:14:31.710]Yeah, might work.
- [00:14:32.543]All right.
- [00:14:39.180]So, we also done some studies of alfalfa
- [00:14:43.000]in Southern California that I will show next.
- [00:14:46.846]So, this is another alfalfa site, multicolored alfalfa,
- [00:14:50.420]a 10 month period, and again showing the raw CubeSat data
- [00:14:55.530]in black and then the corrected CESTEM corrected data
- [00:14:58.770]in while circles, and the Sentinel Two data,
- [00:15:02.570]so I used Sentinel Two data in this case
- [00:15:04.586]as a reference for calibrating the CubeSat data
- [00:15:07.970]and you can see that the corrected data
- [00:15:11.050]quite nicely matches the Sentinel Two data
- [00:15:14.400]and produce a more realistic time series.
- [00:15:18.050]It kind of corrects some of the dips and peaks
- [00:15:20.240]you see in the raw data.
- [00:15:24.063]And you also get an appreciation of, even with Sentinel Two,
- [00:15:26.850]over this clear sky site, you do have quite a few
- [00:15:29.440]observations, but you're still gonna miss critical periods
- [00:15:33.330]of the growing seasons and the growing season,
- [00:15:36.002]you have 10 growing season over a 10 month period,
- [00:15:39.299]it's a really kind of rapid kind of finale
- [00:15:41.690]that you need really frequent observations
- [00:15:44.640]to capture sufficiently.
- [00:15:48.930]This just highlights one of these growing seasons
- [00:15:51.220]and you can get a feel of the spatial and temporal
- [00:15:54.669]advantages of the CubeSat versus the, in this case,
- [00:15:58.560]20 meter Sentinel Two data.
- [00:16:10.540]And in this case, I've run it with one system
- [00:16:14.210]with both LandSat and Sentinel Two independently,
- [00:16:17.200]so I'm just seeing how they compare.
- [00:16:19.860]If I do that and you get a pretty good agreement,
- [00:16:22.250]fairly consistent results in both cases,
- [00:16:26.020]I would expect some disagreement because LandSat
- [00:16:28.687]and Sentinel Two themselves are not consistent
- [00:16:31.077]in terms of the spectral configuration.
- [00:16:33.360]You also have BIDF effects.
- [00:16:35.630]Ideally, I would probably run CESTEM
- [00:16:38.337]kinda using a combined harmonized Sentinel Two
- [00:16:40.570]LandSat eight data set as input,
- [00:16:42.490]as that will give me more training data
- [00:16:44.590]and that will be a more consistent data set
- [00:16:47.080]for doing the reference sampling,
- [00:16:49.590]but that's the next step.
- [00:16:52.660]So now, turning to Nebraska,
- [00:16:56.920]looking at corn and soybean sites.
- [00:17:00.690]So, this is a corn site, this is the NE one site
- [00:17:04.490]in Mead in 2017.
- [00:17:07.640]Again, you see the raw CubeSat data
- [00:17:12.370]compared to the CESTEM corrected data
- [00:17:14.640]and the Sentinel Two data as well
- [00:17:17.000]and then you have a good consistency between the CESTEM
- [00:17:18.917]and the Sentinel Two data
- [00:17:20.620]and clearly your CubeSat data adds a lot of information
- [00:17:25.340]between your Sentinel Two acquisitions
- [00:17:28.920]that could be quite useful, even thought not a whole thing
- [00:17:32.400]is happening in this case, but if you had to experience
- [00:17:35.740]some kind of stress, this model kind of disturbance,
- [00:17:39.542]the CubeSat data would be really helpful
- [00:17:41.635]determining the exact timing of that even.
- [00:17:47.446]And yes, you do have significant gaps
- [00:17:49.800]in your Sentinel Two record,
- [00:17:51.060]such as during the green up and during senescence
- [00:17:54.930]and these are periods where a lot of things are going on,
- [00:17:58.020]where we really need information to tell what is going on,
- [00:18:01.589]so this is where data from CubeSat can be really helpful.
- [00:18:08.190]With CubeSats, they have issues with clouds too
- [00:18:11.188]and so I'm always been looking into technique
- [00:18:13.806]to correct for that.
- [00:18:16.000]I've been using some automated image feature recognition,
- [00:18:20.810]optic-based feature recognition techniques for doing that
- [00:18:26.402]and while it does a pretty good job
- [00:18:29.000]in identifying the main structures,
- [00:18:30.850]you still have areas where we don't really
- [00:18:34.930]capture the contamination, particularly from the shadows.
- [00:18:38.340]It can be quite difficult.
- [00:18:41.410]So in those cases, we're gonna get a contaminated signal
- [00:18:44.747]that's not really that useful,
- [00:18:46.800]so I also been trying to correct for that using some...
- [00:18:52.090]Let me see.
- [00:18:54.568]There we go.
- [00:18:55.401]Using some...
- [00:18:56.234]Okay.
- [00:18:58.619]All right.
- [00:19:00.090]Using some gap-filling techniques.
- [00:19:01.770]So, the image on your left is the gap-filled one
- [00:19:10.073]and you can see, compared to the previous one,
- [00:19:12.480]in this case you get rid of the cloud shadows
- [00:19:16.220]and you get a realistic-looking image
- [00:19:21.090]compared to the one that has not been cloud-filled
- [00:19:25.230]or corrected for these cloud shadows.
- [00:19:28.590]So, it seems to be working pretty well for this case
- [00:19:33.174]and this is just another case,
- [00:19:34.007]this is the NE one and NE two fields
- [00:19:36.402]where you can see the shadows in one image
- [00:19:39.014]is removed than the other image,
- [00:19:42.910]in addition to the cloud-detected areas
- [00:19:45.470]being restored with real values.
- [00:19:51.120]So, this is the time series that include
- [00:19:55.280]the gap-filled data points.
- [00:19:57.060]So, I think I've added about 10 scenes.
- [00:19:59.870]In principle, I could apply these techniques
- [00:20:01.780]to add daily imagery, but at the moment
- [00:20:04.477]I'm just kinda filling the scenes that I have,
- [00:20:07.940]but I could apply to get a daily time series
- [00:20:11.507]of CubeSat-scale data if I wanted to,
- [00:20:15.370]but you can see here how it kind of restores the signal.
- [00:20:18.465]You have the regional top of atmosphere reflectance data
- [00:20:21.619]on one side and you have the CESTEM-corrected
- [00:20:24.209]surface reflectance data has been corrected
- [00:20:26.611]and you can see how it is able to remove the shadow
- [00:20:29.270]in this case in NE two.
- [00:20:32.566]In this case, you don't have any data
- [00:20:34.740]in the original data, but you're able to restore it
- [00:20:36.785]using my gap-filling approach.
- [00:20:41.020]Same in this case.
- [00:20:42.310]A lot of contamination going on in the original data,
- [00:20:45.270]but then are able to get a pretty
- [00:20:46.790]realistic-looking image like that.
- [00:21:00.790]Right, so I've also been looking at validating
- [00:21:03.410]these time series from Planet
- [00:21:06.900]using data that Trenton has provided,
- [00:21:12.210]as been mentioned by the Arable Mark's penetrometer.
- [00:21:16.410]Obviously, the spatial conflation is not identical
- [00:21:20.021]between Sentinel Two and the Arable Mark,
- [00:21:25.310]but still fairly comparable,
- [00:21:27.360]at least in giving idea about the phenology.
- [00:21:29.740]Is it realistic?
- [00:21:30.946]Is it realistic what we see from Planet?
- [00:21:32.680]From the CESTEM-corrected Planet data.
- [00:21:35.650]It's also used as the metric for evaluating
- [00:21:37.782]the raw data from Planet.
- [00:21:41.360]So, this is a validation of a soybean in Mead, Nebraska,
- [00:21:47.910]comparing the CESTEM-corrected surface reflectances
- [00:21:50.700]against the institute observations in 2018
- [00:21:55.007]and you get a pretty good fit.
- [00:21:56.680]Some bias is going on.
- [00:21:58.080]It could be due to different spacial conflation.
- [00:22:00.290]It could also be a scale issue,
- [00:22:01.830]it could be an issue with the observation time, as well,
- [00:22:08.060]but that apart, you get a pretty good correlation.
- [00:22:10.380]Point nine eight seven for this site.
- [00:22:13.420]And when I compare it to the...
- [00:22:15.766]So, Planet also produces a surface reflective product
- [00:22:21.530]that I'll show you here, in blue,
- [00:22:24.800]and there's obviously quite a significant amount
- [00:22:26.890]of scatter in that product.
- [00:22:29.070]It does kinda reduce the bias a little bit,
- [00:22:31.860]which might be something to do with the more
- [00:22:34.190]similar spectral configuration.
- [00:22:36.211]It has broader bands, more comparable to the Arable Mark,
- [00:22:39.330]but then you have some significantly pronounced scatter.
- [00:22:45.830]This is another soybean site,
- [00:22:48.380]comparing the institute observations
- [00:22:50.370]against the CESTEM-corrected surface reflectances
- [00:22:52.710]during 2018 and, in this case,
- [00:22:55.160]the agreement is quite exceptional.
- [00:22:56.850]It's point nine nine.
- [00:23:00.480]So, yeah.
- [00:23:01.840]So, this might indicate that...
- [00:23:04.370]I think it's difficult maybe.
- [00:23:05.550]The bias can be a bias due to different kind of instruments.
- [00:23:08.880]The Arable Mark might not be completely consistent
- [00:23:11.890]between them individually,
- [00:23:13.580]but in this case, they match pretty well
- [00:23:17.210]and when I compare it against the Planet
- [00:23:19.570]surface reflectance product,
- [00:23:21.400]you can see how the diverge is quite significant from there.
- [00:23:25.470]That's significant scatter and has some serious issues,
- [00:23:29.660]so it also indicates and shows you
- [00:23:31.874]or demonstrates that you really need to correct
- [00:23:34.001]the original Planet data if you wanna make it useful
- [00:23:39.370]for scientific analysis.
- [00:23:42.050]This is just a side by side comparison
- [00:23:43.810]between the CESTEM surface reflectance product
- [00:23:45.577]and the Planet surface reflectance product.
- [00:23:48.460]Again, kinda demonstrating the different performances
- [00:23:52.150]of these two products.
- [00:23:55.980]So, this highly calibrated.
- [00:23:58.350]So, once you have a highly calibrate NDVI
- [00:24:00.420]data set like that, You can really start looking
- [00:24:02.370]at intra field dynamics,
- [00:24:04.520]like I'm doing here.
- [00:24:05.570]This is the NE three rain-fed soybean field in 2018
- [00:24:11.910]and we really see in the beginning
- [00:24:13.270]you have a quite homogenous field conditions,
- [00:24:16.140]but then beyond day 180, the curves start to diverge,
- [00:24:20.780]maybe due to some intra field conditions;
- [00:24:26.050]and looking at time series like this,
- [00:24:29.200]having that time of data and a daily kinda frequency,
- [00:24:31.980]it's really useful and powerful for identifying
- [00:24:34.910]those kinda suboptimal conditions
- [00:24:37.970]and taking the necessary preventative measures
- [00:24:40.730]to kind of avoid that progressing any further.
- [00:24:47.050]So, I've mostly been looking at translating
- [00:24:50.370]this spectral information into more quantitative insights
- [00:24:56.120]by using such as Leaf Area Index
- [00:25:00.560]and this really uses...
- [00:25:02.820]The idea is to take advantage of the spectrally
- [00:25:04.840]enhanced data from sensors inside LandSat eight
- [00:25:08.140]and particularly Sentinel Two
- [00:25:10.100]and combine that with the superior spatial
- [00:25:12.650]and temporal resolution of the CubeSat data,
- [00:25:14.930]so really exploiting the synergies.
- [00:25:18.700]In this first example I used, based on the fusion
- [00:25:22.420]of LandSat and CubeSat data with our site in Saudi Arabia.
- [00:25:29.360]So, you can see that the CubeSat data,
- [00:25:31.150]particularly when you progress this,
- [00:25:32.920]you really start to provide close to daily information
- [00:25:37.180]on the layout dynamics and again matches
- [00:25:39.983]the LandSat LAI quite nicely.
- [00:25:44.570]This high-resolution information is really quite beneficial,
- [00:25:48.490]particularly during the green up,
- [00:25:50.210]as well as harvesting.
- [00:25:51.790]You can really get an idea when the actual harvest started.
- [00:25:59.370]When you look at a green up cycle,
- [00:26:00.950]as in the bottom figure, this is an eight day sequence
- [00:26:05.750]of Planet's Scope CubeSat data over an eight day period
- [00:26:10.830]during the green up, and then it's bound by LandSat data
- [00:26:14.310]on day 206 and 230.
- [00:26:17.590]So, you can really get an appreciation
- [00:26:19.633]of what you're gonna miss if you only have LandSat data
- [00:26:22.560]on an eight day visit.
- [00:26:25.092]I should probably mention that in this site,
- [00:26:27.130]you have LandSat data every eight day,
- [00:26:29.180]or this specific farm, due to overlapping swaths.
- [00:26:32.160]But in most cases, you would have a 16 day interval,
- [00:26:37.580]so you're gonna miss a lot of things
- [00:26:39.690]and you can use the CubeSat data to feel out
- [00:26:41.720]that amazing information, in addition to providing
- [00:26:45.920]addition information on the infield stuff and intra field
- [00:26:49.540]dynamics with the enhanced spacial resolution.
- [00:26:55.220]And again, this just highlights the spacial and temporal
- [00:26:59.870]advantages of the daily CubeSat LAI data
- [00:27:04.730]compared to LandSat, so it just shows the timing
- [00:27:08.730]and progression of a harvesting event
- [00:27:11.420]that has commenced on day 181 and terminated on day 183,
- [00:27:16.850]but when you only have LandSat data on one day,
- [00:27:19.290]you're really gonna miss a lot of critical
- [00:27:21.470]day to day variations in this specific case.
- [00:27:29.440]And so, I've also been looking at the constructing
- [00:27:32.330]and producing LAI products while in Mead, Nebraska.
- [00:27:38.880]So, this uses the Sentinel Two data.
- [00:27:43.170]The previous work on LandSat that I used
- [00:27:44.970]is a bit more empirical LAI retrieval approach.
- [00:27:49.130]In this work, I've been using the Pro-Cell model
- [00:27:51.820]so that combines the prospect,
- [00:27:54.090]Leaf Optical Probability model,
- [00:27:55.853]with a sale type of canopy bi-directional reflectance model
- [00:28:00.430]and it uses the Sentinel data to invert that model,
- [00:28:03.570]giving the additional spectral bands in the red edge
- [00:28:06.450]and the shortwave infrared, you can better constrain
- [00:28:10.040]the inversion process.
- [00:28:11.210]It wouldn't be feasible to invert Pro-Cell
- [00:28:13.180]using just the Planet scope, just the CubeSat data,
- [00:28:16.300]given the limited spectral information,
- [00:28:18.650]but I can use that information that I get from Sentinel Two
- [00:28:22.610]as a reference to kind of enhancing the LAI information
- [00:28:26.430]in space and time.
- [00:28:27.920]And this is shown here,
- [00:28:31.040]showing my Sentinel Two retrievals
- [00:28:34.090]and the added spatial temporal information
- [00:28:36.360]of the CubeSat data with this corn field in 2017.
- [00:28:48.370]And then, I've also been looking at validating
- [00:28:50.700]those kind of retrievals using the destructive
- [00:28:55.520]institute measurements from this facility.
- [00:28:59.149]In this plot, I'm just kind of showcasing
- [00:29:01.930]a few time series from any three different points
- [00:29:08.110]in any three, showing both the CESTEM-corrected,
- [00:29:13.710]CESTEM-based LAI, the Sentinel Two LAI,
- [00:29:16.860]and then your field measured LAI as the blue triangles,
- [00:29:23.650]and in general, you get a pretty good agreement
- [00:29:26.930]in this field.
- [00:29:29.420]The Planet data is able to kind of track what you see
- [00:29:32.750]quite well, what you see in the institute data.
- [00:29:38.200]So, I think this is pretty encouraging.
- [00:29:41.870]And when I look at a validation,
- [00:29:43.910]this is the field-level validation,
- [00:29:45.610]so I'm kind of being averaged over each of these fields
- [00:29:48.670]over NE one, Ne two, NE three,
- [00:29:50.860]and compared my CESTEM LAI with the measured LAI,
- [00:29:55.870]we get a pretty good agreement for this specific data set.
- [00:30:00.200]So, this is based on data from 2017.
- [00:30:06.150]So, I think one of the next steps is always
- [00:30:07.830]to extend this to pigments.
- [00:30:10.780]I think there's the potential to also retrieve pigments
- [00:30:14.640]like Leaf chlorophyll using this technique,
- [00:30:17.570]particularly from Sentinel Two data
- [00:30:18.990]and then use the CubeSat to enhance that in space and time.
- [00:30:21.570]So, I think that's a critical next step of this work.
- [00:30:26.207]So, a bit of a summary.
- [00:30:30.085]CESTEM is really a cross-platform calibration approach
- [00:30:34.100]that can be used for radiometric normalization,
- [00:30:37.040]for phenology reconstruction,
- [00:30:39.180]as well as higher level biophysical product generation.
- [00:30:42.830]So, it's really a kind of technique
- [00:30:44.170]to enhance data into probability
- [00:30:48.715]and creating a harmonized analysis-ready data set
- [00:30:52.473]that is consistent.
- [00:30:55.433]A key feature is that it uses observations
- [00:30:57.650]from gold standard satellites as a reference,
- [00:31:01.320]so it cannot work without that,
- [00:31:03.890]so it's critical to have the conventional systems
- [00:31:06.680]to calibrate these CubeSat systems.
- [00:31:11.470]A powerful element of CESTEM is that it is quite
- [00:31:14.960]insensitive to the noise level of the input data,
- [00:31:17.900]so it doesn't really matter if you put in digital counts,
- [00:31:20.680]top atmosphere reflectances, or if it's really noisy,
- [00:31:25.010]if there's a lot of noise in the original data,
- [00:31:27.110]it should be able to correct for that,
- [00:31:30.076]and you can extend it to other sensors, like UAVs.
- [00:31:33.950]I see that as a particularly interesting follow-on study,
- [00:31:36.770]kind of apply this technique in an automative matter
- [00:31:40.770]to kind of correct data from collected intra field UAVs
- [00:31:43.580]to surface reflectances without the need
- [00:31:46.934]to do any ground-based calibration work.
- [00:31:50.681]And then, it can also be used to...
- [00:31:55.232]It goes beyond the immediate product of spectral data,
- [00:31:59.220]like the NDVI, you can also kind of extend it
- [00:32:01.720]to produce added-value higher-level products,
- [00:32:04.650]like Leaf Area Index and maybe Leaf chlorophyll,
- [00:32:07.760]that is maybe more useful for a lot of uses,
- [00:32:14.834]particularly as LAI is more directly related
- [00:32:16.960]to crop growth and crop condition.
- [00:32:20.000]And just to finish off, I think the spatiotemporal insight
- [00:32:24.390]that is provided by this type of resource
- [00:32:27.140]really represent a game changer
- [00:32:30.515]in space point monitoring with the precision Ag
- [00:32:34.568]kinda being the obvious application area,
- [00:32:37.380]but you can envision particularly other areas
- [00:32:41.360]that could have potential use of this type of information.
- [00:32:47.440]So, just wanna finish off with just this overview
- [00:32:50.050]of the strengths and weaknesses
- [00:32:52.790]of LargeSats and SmallSats.
- [00:32:55.630]So, I think there's a lot of benefit in both
- [00:32:58.690]of these systems.
- [00:33:00.444]LargeSats, they are rigorously calibrated,
- [00:33:03.682]high radiometric quality, and they operate for a long time,
- [00:33:07.630]so there's a lot of continuity in terms,
- [00:33:10.494]the continuity if very useful,
- [00:33:12.600]but then again, you have also weaknesses.
- [00:33:15.060]Typically, there is a trade off between spatial
- [00:33:17.000]and temporal resolution, the systems are very expensive,
- [00:33:20.970]they take years to produce,
- [00:33:22.740]and once you get them up there,
- [00:33:24.410]the technology is quite old.
- [00:33:27.270]A lot of things happen in five or 10 years,
- [00:33:30.248]particularly in these times.
- [00:33:31.660]So, the SmallSats, they have superior
- [00:33:34.280]spatiotemporal resolution, it's very cheap to produce,
- [00:33:38.060]and you can implement new technology very rapidly.
- [00:33:41.580]As I mentioned before, Planet can kind of turn around
- [00:33:44.460]40 satellites in just one week,
- [00:33:46.650]so they can really very quickly implement new technology,
- [00:33:50.180]that makes this kind of a scheme very powerful,
- [00:33:53.800]but then the calibration accuracy is less,
- [00:33:55.880]is not consistent, as good as what you get
- [00:33:59.324]from the conventional satellite systems,
- [00:34:00.394]and having multiple satellites,
- [00:34:03.170]hundreds of satellites to operate,
- [00:34:05.060]you're gonna run into cross sensor inconsistencies.
- [00:34:09.290]At the moment, the spectral resolution is low.
- [00:34:11.351]That might change in the future.
- [00:34:13.810]There has been a lot of talk about launching
- [00:34:16.640]Sentinel Two-like CubeSats and even hyper-spectral CubeSats,
- [00:34:21.230]but then again, you're gonna continue
- [00:34:23.340]to have shorter lifespan and the continuity
- [00:34:27.130]might be another issue, and the fact that it is
- [00:34:29.990]a commercial company brings up some uncertainties.
- [00:34:34.497]But I think a key issue here is to use these datas
- [00:34:38.850]as in synergy.
- [00:34:40.100]I think that's kind of the key message of this talk.
- [00:34:43.880]The SmallSats should be used to augment
- [00:34:45.820]and complement LargeSat systems.
- [00:34:47.410]They shouldn't be used separately.
- [00:34:49.120]You need to use these together.
- [00:34:51.208]And with that, I can take questions.
- [00:34:56.540](audience applauding)
- [00:34:58.710]Hi, nice talk.
- [00:35:00.550]I had a question about the case of clouds or shadows
- [00:35:06.210]where you're creating data,
- [00:35:09.200]where there appeared to be no data.
- [00:35:11.570]So, I wanted to know just a bit more
- [00:35:13.570]about how you do that, 'cause what you're showing
- [00:35:15.570]is spatial detail that seemed to be completely lacking
- [00:35:21.860]in the original condition,
- [00:35:23.530]so I'm missing something in how
- [00:35:26.600]Yeah, I didn't really talk about that.
- [00:35:28.785]So, it basically uses CubeSat data from scenes
- [00:35:36.150]in the past and around the day in question,
- [00:35:41.230]so when given the high frequency of the CubeSat data,
- [00:35:43.967]you're quite likely to get a scene quite close
- [00:35:47.330]to the data.
- [00:35:48.163]At the moment, I'm using five scenes
- [00:35:49.640]surrounding the date in question,
- [00:35:51.800]and then I'm using that in symphony with daily MODIS data.
- [00:35:56.892]So, both incorporating the MODIS data into the interpolation
- [00:36:02.530]and regression, and then also the surrounding CubeSat data.
- [00:36:06.840]It's a bit similar to the Stair Algorithm in some ways
- [00:36:10.570]in how it does it, if you're familiar with that,
- [00:36:13.899]but it does create a land cover
- [00:36:16.050]kind of a cover-specific progression
- [00:36:17.849]to kind of do the interpolation in space and time
- [00:36:23.750]and then it uses some other techniques to kinda
- [00:36:25.830]make it spatially homogenous,
- [00:36:27.810]so sometimes you can have unrealistic gradients
- [00:36:30.710]when you do the gap-filling and I kinda worked
- [00:36:33.900]on refining those techniques to avoid that.
- [00:36:37.541]This is something that I did the last two weeks,
- [00:36:40.070]so just built very new stuff.
- [00:36:41.620]So, probably still need a bit of refining,
- [00:36:44.450]but I think it's really useful to having
- [00:36:46.070]this kind of daily information
- [00:36:48.350]and I need to do some validation of it, of course.
- [00:37:00.660]Thank you.
- [00:37:02.610]That was a nice talk.
- [00:37:05.310]So, you said that the lifespan of a satellite
- [00:37:08.040]is from two to three years
- [00:37:10.440]and you totally depend on LandSat or Sentinel
- [00:37:13.840]or MODIS to calibrate.
- [00:37:17.480]What would be the strategy if both
- [00:37:21.200]the gold standard satellites fail?
- [00:37:23.330]Is it possible to cross-calibrate against
- [00:37:25.620]the own CubeSat constellation
- [00:37:28.917]given the short lifespan of them?
- [00:37:32.525]Is that any plan about that
- [00:37:34.010]or does the company consider to cross-calibrate
- [00:37:39.200]against UAV data?
- [00:37:41.090]Is that a possibility?
- [00:37:42.290]Or you're totally dependent on the LargeSat?
- [00:37:47.710]Yeah, for the initial calibration,
- [00:37:49.070]you will need the LargeSat data,
- [00:37:52.510]but then once you have it calibrated,
- [00:37:54.210]you can then use the CubesSat data to,
- [00:37:56.580]for instance, calibrate the UAV data,
- [00:38:00.080]but the first step, yeah, you're gonna need some kind
- [00:38:03.454]of a highly calibrated system,
- [00:38:05.380]like a conventional satellite, like LandSat and Sentinel Two
- [00:38:09.884]and it shouldn't be an issue,
- [00:38:10.717]because it's gonna be up there for a long time.
- [00:38:13.440]Yeah.
- [00:38:15.430]But maybe at some time they don't need it.
- [00:38:17.090]I don't know.
- [00:38:17.923]Who knows?
- [00:38:21.161]Other questions?
- [00:38:23.620]Making me work over here.
- [00:38:33.150]Hi, great talk.
- [00:38:35.090]So, another variable which is very relevant
- [00:38:38.350]to agriculture production in parallel to LAI
- [00:38:41.300]is fractional PAR.
- [00:38:44.730]Do you think this approach can be extended to that?
- [00:38:47.970]Especially given that it has a higher demand
- [00:38:50.470]for crop modeling and applications such as those?
- [00:38:54.928]FA Par? FA Par, yeah.
- [00:38:56.949]Yeah, I guess.
- [00:39:00.260]I think it's interesting to look into it.
- [00:39:01.930]I've also been considering doing ET with this approach.
- [00:39:07.930]It's a bit more tricky
- [00:39:10.140]because in terms of counting for the change
- [00:39:14.120]between your conventional satellite acquisition
- [00:39:18.290]and your CubeSat acquisition,
- [00:39:20.970]it's easier with spectral data, I think,
- [00:39:22.890]but I think it might be feasible,
- [00:39:26.330]but we'll need a bit of refinement, I think.
- [00:39:32.339]Other questions?
- [00:39:33.958]Oh.
- [00:39:40.820]Good great talk.
- [00:39:42.210]In one of the slides, you showed where you be able
- [00:39:46.860]to invert the prospect in the cell
- [00:39:50.890]to be able to extract a few vegetation traits,
- [00:39:55.735]but maybe I missed some of that talk.
- [00:39:59.850]You didn't mention whether you used the ground truth data
- [00:40:04.220]to validate or train your data set.
- [00:40:06.691]Could you just elaborate that?
- [00:40:09.780]Yeah, I didn't explain that a bit.
- [00:40:11.427]Yeah.
- [00:40:12.860]Sorry.
- [00:40:14.710]No, so I use a random floral forest implementation
- [00:40:16.870]of Pro-Cell, so I use a synthetic training data sets
- [00:40:21.660]that are basically just run the Pro-Cell
- [00:40:23.550]in forward mode to establish the training data
- [00:40:26.580]and then I use a random forest to kind of build
- [00:40:28.930]the model based on that, and then I apply the model,
- [00:40:31.600]so I don't use any institute data.
- [00:40:34.700]I do fix a few parameters,
- [00:40:36.590]like the Leaf mesophyll structure,
- [00:40:39.100]I fix that to be appropriate for maize, in this case,
- [00:40:45.540]but I keep the Leaf angle and chlorophyll
- [00:40:48.750]and Leaf Area Index and most of the other parameters fixed.
- [00:40:54.060]Yeah, but it's a random forest kind of implementation,
- [00:40:56.780]like a hybrid training.
- [00:41:09.720]Looking forward, I mean, this is a really nice
- [00:41:11.610]framework for filling in gaps and getting a lot
- [00:41:15.050]more information than we could possibly get
- [00:41:16.880]from any one sensor.
- [00:41:19.420]You mentioned hyper-spectral.
- [00:41:21.860]Looking forward to a world of hyper-spectral satellites,
- [00:41:27.070]we may not have the CubeSat version of it
- [00:41:29.610]or we may have it in some limited format
- [00:41:31.838]without the degree of coverage that you have,
- [00:41:35.170]but there would be a different issue, of course.
- [00:41:36.910]We'd be spectrally rich.
- [00:41:39.600]So, do you have any thoughts on a future world
- [00:41:44.160]where these kinds of algorithms might take us
- [00:41:46.660]with a slightly different configuration
- [00:41:48.570]or what objectives me might be able to achieve
- [00:41:53.200]within that future world where hyper-spectral
- [00:41:57.269]starts to come in, but maybe in a different configuration
- [00:42:00.120]than what you're currently using?
- [00:42:03.370]Yeah, well I think it's probably not gonna be daily.
- [00:42:06.070]I don't think so.
- [00:42:07.160]But maybe at some point.
- [00:42:09.740]But I think still you need to do kind of the same thing.
- [00:42:12.300]You're probably still not gonna need
- [00:42:14.339]a conventional hyper-spectral emission
- [00:42:16.790]to do the calibration, unless...
- [00:42:19.360]So, the CubeSat is gonna be at the same issues
- [00:42:21.390]in terms of the absolute calibration accuracy, I think.
- [00:42:26.630]So, I think we need to have a space agency,
- [00:42:33.240]like a real hyper-spectral emission up there
- [00:42:35.380]to kind of provide the necessary reference
- [00:42:38.580]for calibrating, and that might happen and it might not,
- [00:42:43.610]but it hopefully will.
- [00:42:44.780]I think some...
- [00:42:46.280]Or maybe the commercial sector needs to take over,
- [00:42:48.280]I don't know, providing that kind of good reference
- [00:42:51.000]in terms of the hyper-spectral domain.
- [00:42:55.120]But I think it's needed 'cause you can only get
- [00:42:57.290]so much information out of a broad
- [00:43:01.220]multi-spectral bands like this.
- [00:43:05.670]But I think there's so many opportunities
- [00:43:07.207]in the commercial sector at the moment
- [00:43:10.550]in terms of technology and advances
- [00:43:12.650]and you might also...
- [00:43:14.460]Firmware could also be on the table.
- [00:43:17.100]Maybe if they find a business model,
- [00:43:19.213]they might put firmware on a CubeSat in the near future.
- [00:43:22.360]I think it's technologically feasible,
- [00:43:25.530]but if there's an economic benefit of it,
- [00:43:27.470]I think that might be the question at the moment,
- [00:43:29.850]but I think there's many opportunities.
- [00:43:35.229]Speaking of the commercial side of things,
- [00:43:37.660]what's the latency of getting the Planet data
- [00:43:41.250]running it through your algorithm
- [00:43:43.314]and what type of a cost per acre is a producer looking at?
- [00:43:47.380]Any ideas on that?
- [00:43:50.210]The latency, it's about one day.
- [00:43:53.106]I think they make it available within one day,
- [00:43:55.040]but as a researcher, you can get it either free
- [00:43:59.130]or at a very reduced cost,
- [00:44:01.840]but it is a commercial company,
- [00:44:06.373]but they don't kind of make the cost available to you.
- [00:44:10.303]Okay.
- [00:44:11.350]But it's gonna be relatively cheap, I think,
- [00:44:16.390]and maybe it's gonna be...
- [00:44:17.410]In the future, it might be delivered free in some form,
- [00:44:20.600]if the government or some other see the benefit
- [00:44:23.910]in providing that, maybe purchasing that data
- [00:44:26.207]and providing it free to the public or researchers.
- [00:44:31.697]Other questions?
- [00:44:40.710]So on the commercial side,
- [00:44:45.220]from the perspective of the end-user,
- [00:44:48.220]it's a lot of data, considering the time series
- [00:44:51.676]and the pixel size, and I imagine that Planet
- [00:44:56.520]or whatever company owns the constellation
- [00:45:01.261]has some framework to provide this data totally processed,
- [00:45:08.370]so the end-user just gonna use it.
- [00:45:11.154]It's not gonna develop nothing on top of that.
- [00:45:15.500]Is there any strategy to allow scientists
- [00:45:21.720]to work on a broader scale, larger scale?
- [00:45:29.200]Because what I see in remote sensing lately
- [00:45:31.990]is just an increase in the constellation,
- [00:45:35.620]the amount of data, but we still struggling
- [00:45:37.980]to process all that is out there
- [00:45:41.190]and so, with commercial companies taking over
- [00:45:45.400]and closing pretty much a black box on processing data,
- [00:45:51.540]how the scientific community will rely on this data
- [00:45:56.800]to produce science other than just commercial applications?
- [00:46:01.460]So, what is the potential of applying to science
- [00:46:05.030]and open the box?
- [00:46:06.860]Well, I think Planet might be a bit different.
- [00:46:09.930]I think they want that to happen.
- [00:46:11.950]I think they wanna make the product as available
- [00:46:14.490]to as many people as possible
- [00:46:17.242]and even talking about making free code available.
- [00:46:20.510]I think the idea is to make an analysis-ready product
- [00:46:23.493]that can be readily used and maybe having
- [00:46:27.505]some add-on software that can be applied for free,
- [00:46:30.930]open-source software that can be applied for free
- [00:46:33.040]by the user if they need it.
- [00:46:35.790]So, I think that's the direction they're moving,
- [00:46:38.533]if they can make a business model out of it.
- [00:46:40.760]So, it's a commercial company,
- [00:46:42.800]so there needs to be some kind of revenue out of it,
- [00:46:45.940]but I think that's what they want.
- [00:46:51.133]They wanted to make it available
- [00:46:52.510]to as many people as possible.
- [00:46:57.008]Yeah.
- [00:46:58.560]Any last questions for Rasmus?
- [00:47:05.040]Alrighty, well let's thank him one more time.
- [00:47:06.820]Thank you, Rasmus. (audience applauding)
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