Un-flattening the Earth, and Worms
(or – Aristotle Vindicated at the End of a Flat-Earth)
By Robert J. Blakemore PhD, VermEcology Japan, 10th June, 2017.
Woodblock featured image credit: Hiroshige Utagawa print of Hakone on the Tokaido that artistically demonstrates undulations of land and also shows how people closely follow each other, rarely looking out beyond the pack (as does Hiroshige).
Image of an anaglyptic or anaglyptaic terrain in Colorado River region of USA (source here). Note: An anaglyph is an ornament carved in relief; adj. anaglyptic from Greek: ana – up, gtyphb – to carve. “Anaglypta” is a textured wall covering with stucco relief sold since 1885; its word origin is from the Greek words ‘Ana’ (meaning raised) and ‘Glypta’ (meaning Cameo) (Wikipedia – https://en.wikipedia.org/wiki/Anaglypta); thus anaglypta-like is more properly “anaglyptaic”. Either way, this land is obviously not flat as NASA/NOAA would have it.
Accurate information on the actual surface area of the Earth is surprisingly elusive. Whereas the ocean is horizontally flat, the land has undulating terrain and rugosity adding to its extent. The value of this relates to global primary productivity. It is important too for calculations of our total topsoil resource or, as Darwin (1881: 39) has it in his book on Earthworms: “The vegetable mould [= topsoil humus] which covers, as with a mantle, the surface of the land…” Soils occupy 81% of land that is not yet extreme desert, rock, sand, ice, or waterlogged (19%) [Jackson et al. (1997: tab. 2)]. Freshly calculated herein is an estimate of about (64 x 0.81) or 51.84 Gha total topsoil on a true undulating land surface area (of 64 Gha). This plus level ocean surface area (36 Gha) give Earth’s new total sunlit surface area as 100 Gha.
Calculating planetary values of primary productivity, carbon storage in soils, global biomass and such like, along with proper allocation of funds, may require a doubling or likely quadrupling of land to realize a relative ratio of soil : sea as 64 : 36 rather than the oft-quoted yet erroneous 29% vs. 71%. Earthworm counts are revised accordingly to give staggeringly high figures of 2.6 quadrillion with a massive biomass of 8-16 Gt, truly as masters of earth.
This study builds on earlier work by the author (e.g. Blakemore, 2010, 2012, 2016, 2017). Base data are from sources such as US’s National Geographic (Ref. May, 2017) that has land area as “148 million square kilometers (57 million square miles)” and the oceans “almost three fourths [3/4 or 75%] of the Earth” to give a total surface area of 148 + 444 = 592,000,000 sq km or 59.2 Gha! More normal NASA/NOAA estimates are around 14.8-15.1 Gha land (29.2%) and 36.2 Gha ocean (70.8%) to total about 51 Gha (or 139,434,000 sq mi) for Earth’s (flat) surface.
However, none of these figures include topographical relief or true undulating surface area. In other words, they ignore that land is naturally hilly. The reasoning, from NASA and NOAA, I believe, is that the Globe is so large that slight bumps such as the Alps, Andes, Atlas, Ethiopian Highlands, Himalayas, Pyrenees, Rockies, Transantarctic Mountains and Australia’s slight Great Dividing Range are insignificant. What these geographers and astronomers fail to appreciate is that primary productivity that provides for all ecological Life on Earth operates at the biological scale of a leaf. Average leaf size reportedly ranges from 0.011 to about 39.5 cm2 (Ref.) but I can find no datum for the topographical topsoil surface area that supports plants.
My online enquiries of the literature and with institutions or academics over the last 5 years or so is that they do not have this basic value. I have contacted NASA, NOAA, USGS, National Geographic, universities and individual authors of satellite and geological surveys (Ref.). None have been able to provide even an estimate of the true undulating topography of the Earth. For example, authors of recent papers were unable to provide information on global/regional topography: neither Dr Fiachra O’Loughlin (2016), Dr Christian Hirt author of other papers on SRTM (Ref.), his colleague Prof. Michael Kuhn, Dr Hayakawa et al. (2008), Dr Tadano (firstname.lastname@example.org), nor Dr Kenneth Falconer <email@example.com> (pers. comms.).
Apparently, Australia has its terrain plotted, the first country to have this data, and at 1 arc-second detail. But my efforts to obtain a summary from published reports or direct enquiries thus far have been unanswered (Ref.1, Ref.2, Ref.3).
SRTM shaded anaglyptaic relief of Zagros mountains (Wikipedia).
The Landsat programme started in 1972 and the most recent Shuttle Radar Topography Mission (SRTM) was in 2000. This SRTM DET had over 80% of the Globe covered (or about 11.956 Gha of 15 Gha flat land) to 90 m scale from 60 degrees N to 56 degrees S (excluding the holarctic and Antarctica, itself 1.4 Gha) – https://www2.jpl.nasa.gov/srtm/coverage.html. Resampled SRTM data to 250 m resolution is recently available from CGIAR (http://srtm.csi.cgiar.org/) here – http://gisweb.ciat.cgiar.org/TRMM/SRTM_Resampled_250m/. Originally at 3 arc-seconds, which is 1/1200th of a degree of latitude and longitude, or about 90 metres (295 feet), new data are released of 1 arc-second, or about 30 metres (98 feet) from NASA – https://www2.jpl.nasa.gov/srtm/.
Exaggerated image below is of flat Tokyo Bay to hilly Mt Fuji (Ref.).
Another estimation of bare-earth removes vegetation from US satellite data (Ref.), but this too gives no total topographic areas.
Paint, Pythagoras, Perfect Mt Fuji and Paradox
Surprisingly, the closest estimate I can find is from a paint manufacturer (Resene.co.nz Ref.) that allows for a 200 m2 corrugated sheet having 10.5% larger surface area (= 221 m2), and Anaglypta or Stucco textures (i.e., bumpy like the Earth) having surface area 40-100% that of the base area.
In lieu of compiled topography, pythagorean geometry can be used to multiply a flat “foot-print” just as the hypotenuse on a triangle is longer than the base:-
In a simple 3-D example, we may calculate that a near perfect cone such as Mt Fuji has surface skin just larger than its footprint, and as Japan itself is about 73% mountainous we may envisage a topography much above the reported flat surface area (0.0378 Gha).
Satellite imagery of western Japan with Mt Fuji example (fig. 1 from Hayakawa et al., 2008), but yet no surface area estimations.
Coarse topographical profile of Mt Fuji (Ref) has about 12.5% greater 2-D relief distance than linear distance that translates as ~12.5% greater 3-D surface area, itself multiplied at finer resolution.
Especially Mt Fuji scoria has irregular pore spaces thus of mandelbrotic surface area, just as a pair of our lungs are said to have internal surface area the size of a tennis court.
Another 2-D corollary is the “Coastline Paradox” or Richardson effect (Ref.) whereby decreasing scale increases length; e.g., Britain’s same coastline increases with finer resolution of observation from 2,800 km to more than 17,800 km, or a six fold increase precisely due to terrain (so a 4 fold increase is perhaps entirely reasonable for 3-D land).
Extrapolating a “flat-Earth” global land figure of 15 Gha, multi-3-D anaglyptaic stucco variations may double this to 30 Gha (as for paint). An increasingly smaller scale, say metric, of irregular, micro-relief rugosity may easily double this again to 60 Gha (as for coastline). As a paradoxical fractal the true surface area of land can be infinitely expanded, here I simply round it up to ~64 Gha for want of a reasonable land estimate to balance the unchanged mean sea-level area of just 36 Gha. This relates to an important measure of insolation defined as solar irradiance with energy measured in watt-hours per square metre (Wh/m2) or in the Langley which is 1 calorie per square centimetre (= 41,840 J/m2). These are both defined for horizontal area values and the latter cm2 scale is approximately the same size as an earthworm burrow or cast. This is an appropriate level of observation for measuring basic ecological interactions locally and then extrapolating to a global value (as is routinely done by NASA, UN, FAO, IPCC, etc.). Thus a revised estimate of true land surface area as exposed to the radiant Sun is 15 x 4 = 60 Gha rounded up to 64 Gha, with 81% or 51.84 Gha total topsoil supporting plants upon which we depend, on the Globe that itself has a newly realized surface area of 100 Gha.
Ironically, earthworm activity both raises small mounds and fills in hollows in soils, for example levelling out the preserved trenches from the Western Front of WW1 of 100 years ago (pers. obs., Ref.). As with other land surfaces, soil uneven-ness (rugosity or tortuosity) is an important factor with many methods of study but no assessible area examples (Ref.).
DSM and DTM from SRTM and LAI?
Wikipedia (2017) gives information on DSM a Digital Surface Model representing the Earth’s surface including all objects on it, in contrast to the 3-D Digital Terrain Model (DTM) that represents “bare ground surface without any objects like plants and buildings.” – https://en.wikipedia.org/wiki/Digital_elevation_model#/media/File:DTM_DSM.svg. See Wiki fig.:-
Essence of the present essay is that I can find compiled data neither for DTM nor DSM.
An estimate of effective DSM is possible if we apply a terrestrial Leaf-Area-Index (LAI). This is a dimensionless quantity that characterizes plant canopies defined as the one-sided green leaf area perpendicular to flat unit ground surface area (LAI = leaf area / ground area, m2 / m2). LAI ranges from 0 (bare ground) to ~47 (dense forests) and a “global” average from Asner et al. (2003) is 4.5 (including deserts and tundra). These authors state that “LAI is a key variable for regional and global models of biosphere-atmosphere exchanges of energy, carbon dioxide, water vapour, and other materials.” Surely it is just as important to have estimates of global DTM and DSM too?
From the conventional flat-Earth view, a rough estimate of DSM is of 15 Gha DTM x 4.5 LAI = 67.5 Gha (plus 36 ocean = 103.5 Gha). From my new topographical calculation DSM is of 64 Gha land DTM x 4.5 = 288 Gha which is an important measure related to global photosynthesis potential (plus a lesser ocean contribution of 36 = 324 Gha). Since LAI is for one side of the leaf, then a total for both sides of a leaf presumably gives 64 x (4.5 x 2) = 576 Gha DSM on land plus flat 36 Gha for oceans = 612 Gha global DSM estimate. Alternatively, since the LAI source data is already for hypothetical flat bases, a DSM may be taken as original 67.5 x 2 (for LAI x 2) = 135, plus (65-15) = 49 for terrain micro-relief and 36 for ocean to give just 220 Gha. Then again, as global DSM is from average LAI for a biome times the biome area, and my contention is that terrain substantially increased all biomes, thus my first figure of 324 is probably correct.
Either way, topography is an important factor. Cities occupy about 3% of flat land area with additional parks, gardens, verges, etc. that would add to these very rough estimates of DSM, superficially obtainable from SRTM satellite data too. Actual land surface areas form an intricate boundary layer with the atmosphere (and with water at its edges). At finer scale, plant spines and leaf stomatal voids (as with villi & alveoli in animals) make surfaces theoretically infinite. Townscapes are no less complex than landscapes.
Effects of non-Flat-Earth on Biodiversity and Primary Productivity?
Most of us assume that national and international organizations such as National Geographic or NASA/NOAA/IPCC/UGS/BGS/METI/JAXA/UN, etc. have their facts checked and are a reliable source for the most current information Why is it then that they seem to yet promote a flat-Earth model of the World? All the calculations of total land area, primary productivity from biomes and basic carbon budgets that I find seem to be based upon a flat 2-D view of land, disregarding topography, and mostly ignore below-ground biomass too. Ocean bathymetry in contrast is exquisitely mapped and, although sunlight penetrates several metres, water absorbs >90% of solar energy, epipelagic phytoplankton just 7% (Ref.). Productivity in the open ocean is restricted due to insufficient minerals as a truly wet desert. In contrast to the oceans, forests provide cool shade precisely because land plants compete intensely to absorb the Sun’s energy for photosynthesis. Primary sources of global carbon budgets seem to be authors such as Batjes, Haughton, Jackson and Jobbágy, all of whom give a land area total of ~15 Gha on a globe of around 51 Gha. However, as this is for an idealized flat surface whereas it is self-evident that the land is hilly. With topological consideration all land areas may be doubled and at finer resolution, possibly to the metre or centimetre scale, likely doubled again as is proposed in the current work.
For example, a much-cited study (Whitman et al., 1998 Ref.) of prokaryotes [Monera (simple bacteria) and Archaea] estimated their total cellular Carbon biomass as around 450 Pg (= 450 Gt) that they claimed equalled the carbon storage in land plants. [Incidentally, they assume a leaf-area-index (LAI) of 10, much above that quoted herein]. Their allocation of prokaryotic mass was approximately 50 : 50 ocean to land. But their table 2 of land estimates is for flat-earth biome areas (total 12.3 Gha) multiplied by numbers of microbe cells sampled from each biome. Thus it is likely that terrain will at least double the land count and thus the total biomass by at least one third. Moreover, a recent ocean assessment (Kallmeyer et al., 2012) reduced microbial biomass on the seafloor (due to real paucity in actual deep ocean cores) from their original 303 billion tonnes of C to 4.1 billion tonnes representing just 0.6% of Earth’s total living biomass. Thus land’s allocation is yet again greatly increased proportional to that of the ocean.
The UNEP (2002: tab. 2.1) “World Atlas of Biodiversity” has total carbon content of Earth as 100,000,000 Gt, allocated as in the following Table:
|In sedimentary rock||organic||16,000,000|
|Active carbon near surface||40,000|
|Dissolved inorganic carbon in sea||38,000|
|Organic carbon in soil (0-1 m)||1,500|
|Atmospheric CO2 carbon||750|
|Biomass on land||560|
|Biomass in sea||8|
Note: Bacteria were not included and sea biomass, given as 5-10, is here rounded to 8 Gt. If bacterial data from Whitman et al. (1998: tab. 5 Ref.) and Kallmeyer et al. (2012) of 231 Gt and 6.3 Gt in land and sea, respectively, is included it gives total biomass (560 + 231) = 791 Gt on land and just (8 + 6.3) = 14.3 Gt in sea. [Carbon is ~50% of oven-dry weight]. Biomass on land is just for plants and may be doubled for underground stores (roots + fungi) and doubled again for topography. Nevertheless, it shows at most 1.7% of living biomass in the sea to >791 Gt or >98.6% on land. In stark contrast, Dr Sylvia Earle (2009) claims that ocean is “home for about 97% of life in the world, maybe in the universe.”
This relates to total nett primary productivity (NPP), with the contribution of land currently put at somewhere around 50%, yet with correct terrain and subterranean figures this would be increased, possibly by a factor of four, to about 80% giving a more likely ratio of soil : sea as greater than 4 : 1.
Earthworms and other C-based Life Doubled on and in Un-flattened Earth
Most calculations of terrestrial fauna & flora (plants, microbes, fungi & animals) based upon flat-Earth biomes or habitats now require revision and this would affect the relative ocean proportions too. Although the total animal biomass appears to be insignificant in comparison to land plants (UNEP 2002: 11) just considering megadrile (true) earthworms, my recent calculations (Ref., Ref.) of 1.3 quadrillion worms with fresh weight biomass 4-8 Gt on a flat-Earth, may be doubled for terrain to 2.6 quadrillion and a staggering 8-16 Gt! If correct, earthworms would be truly masters of the earth (as Darwin, 1881 told us). This compares to a recent best estimate of global fish “wet weight” of just 1-2 Gt (Ref., Ref.) and casts glib comments about worms being good fishing bait in a whole new light.
Total Life on Earth may be similarly elevated. Biomass carbon from data above amounted to (plants 560 + bacteria 231 =791 C x 2) = 1,582 Gt on hilly land, plus 14.2 C in level sea to give (1,582 + 14.2) = 1,596.2 Gt biomass C. As noted herein, however, an ignored sub-surface biomass (i.e., the rhizosphere of VAM fungi & roots) may double land proportion (Ref1., Ref2.), with perhaps 50% of below-ground allocation released as extra-root C (Ref3.). For roots, Mokany et al. (2005: 95; Ref1.) say: “Our results yield an estimated global root stock of 241 PgC, a similar value to that proposed by Robinson (2004), but about 50% higher than the 160 PgC estimated by Saugier et al. (2001). This dramatic increase in estimated global root carbon stock corresponds to a 12% increase in estimated total carbon stock of the worlds vegetation (from 652 to 733 Pg)”. Searching their sources, the value 652 Pg is likely above-ground vegetation from Saugier et al. (2001) of 492 Pg, plus Robinson’s (2004) estimate of 160 Pg root (492 + 160 = 652). And 733 is seemingly from the same above-ground value plus their own estimate of 241 Pg root carbon (492 + 241 = 733). [Cf. Haughton (2003, 2007) has above-ground plants as 550 ± 100 Pg].
Thus a total above- and below-ground land vegetation may reasonably be accepted as 733 Gt C which, along with bacteria gives (733 + 231) 964 Gt. And Robinson (2004) estimates at least 15 Gt C for soil mycorrhizal fungal hyphae (964 + 15 = 979). This terrestrial carbon of 979 may be doubled for terrain to give 1,958 Gt land C plus total ocean carbon of 14.2 (1,958 + 14.2)= 1,972.2 Gt living carbon.
As C is universally about 50% dry weight, a new value is (1958 x 2) = 3,916 Gt on land plus (14.2 x 2 ) = 28.4 Gt in sea to give a total of about 3,944.4 Gt dry biomass. If water content is taken as 50% [~30% in wood (Ref1.) and 40-70% in bacteria (Ref2., Ref3.) has median value ~50%] then this value is doubled again to ~7,888.8 Gt plus an extra 16 Gt worms and 2 Gt wet fish gives a substantial new total for Earth’s living, respiring and reproducing fresh weight of ~7,906.8 Gt. Let’s round it up to 8 Teratonnes (Tt, terra-tons?) of biomass, mainly on land.
These data compare to Vaclav Smil (2011, Ref.) of total dry biomass of Life on Earth he estimated as 1,600 Gt (here more than doubled to 3,944.4) comprising: 1,100 Gt (land) plants, 500 Gt bacteria, 10 Gt protists, 5 Gt fungi, and just 2.5 Gt for other animals. This would translate as ~800 Gt carbon (here doubled to about 1,972.2) comprised: 550 Gt land plants (here 733), 250 Gt bacteria (here 237), 5 Gt protists, 2.5 Gt fungi (here 15) and 1.75 Gt animals (here 9 Gt dry weight for just worms and fish). As a cross-check, total biosphere carbon is put at between 1 to 4 Trillion tons (Ref.), with the current estimate of around 1,972.2 Gt C in the mid-range.
Soil organisms and organic C
Total terrestrial carbon is estimated as 1,958 Gt in soil supported organisms plus 4 Gt in earthworms (including soil and microbes in their intestines). Another 2,300 is in soil organic matter [= SOM or humus at 0-3 m depth according to NASA, 2011; Ref. that surprisingly omits from original (Ref.) nett soil C uptake of 3 Gt per annum!] which, if doubled for terrain, gives (2,300 x 2 = 4,600 plus 1,962) = 6,562 Gt active carbon stored on land, compared to ~1,000 Gt C in oceans with ~2 Gt C ocean uptake (NASA, 2011; Ref.).
The soil faunal component may be reasonably free of double-counting as a recent meta-analysis (Ref.), if factual, had: “microbial biomass carbon representing 0.6–1.1% of soil organic carbon and 1–20% of total plant biomass carbon… Approximately 50% of total animal biomass can be found below ground…“. Regrettably, these latter authors did not compile any total values, but they did show (tab. 1, fig. 4a), against common perception, that earthworms are especially dominant in tropical forest biomes. Whereas terrain likely doubles soil volume (plus other soil carbon adjustments as commented on below), deep ocean sediments are considerably reduced by the Kallmeyer et al. (2012) study and, overall, ocean net productivity is unquestionably low from data presented in the current report and from NASA (2011; Ref.) that shows 120 Gt respiration, and thus O2 production, on land to 90 Gt in sea, or a ratio of 4 : 3 for soil : sea.
Soil, Carbon and Climate Change (and Worms)
Why does it matter? An immediate answer is that we rely on soil for 98-99.7% of our food, to filter & store water, and for 100% of our timber & natural fibres, so it would be useful to have a measure of just how much soil there is (Ref.). This is important as topsoil erosion rates are >2,000 tonnes per second and soil is also depleted by agri-chemical pollution and urbanization (Ref.). We are rapidly losing this fundamentally vital resource so it may be in our best interests, and in the interests of remaining living organism (i.e., those not already lost to extinction), to get information straight about hills and soils. Earthworm populations and biodiversity are especially important for rebuilding healthy topsoils; they too are rapidly becoming extinct (Ref).
Pimentel & Burgess (2013: 446) report that the Philippines, where >58% of the land has a slope >11%, and in Jamaica where 52% of the land has a slope greater than 20%, soil erosion rates are as high as 400 t/ha/year; thus terrain and micro-relief are important.
Concerning climate change, land area is also most important for carbon budgets as in the Table and data above. In addition to terrain considerations, Blakemore (2016a: 11) noted that: “Soil carbon values require allowance for intractable glomalin adding a further 5-27% to almost all SOC tallies (Comis, 2002). Plus data from deep soils may increase budgets: e.g., Harper & Tibbett (2013) found C up to five times greater in Australian soils at depth >1 m and down to 35 m in some cases. The Walkely-Black [typo for Walkley- Black] method itself underestimates total C with a correction factor of ca. 1.3 often required, whereas latest techniques using mid-infrared (MIR) spectroscopy may give more accurate readings. These three factors combined would surely increase soil SOC totals. Relating to above ground LAI are underground root-area-indices (RAIs) with fine roots a prominent sink for carbon, often much greater than that of vegetation above ground.”
The basic answer to “How much soil is there on Earth?” is still elusive. From NASA’s 2,300 Gt SOC, Blakemore (2016a: 11) estimated 10,000 Gt topsoil SOM but this used the old van Bemmelen (1890) constant (itself recently revised upwards from x 1.724 to x 2.0 – Ref.), and even this is likely an underestimation allowing for glomalin, deep soil data and carbon in fungi, land algae plus living or dead roots (Jackson et al., 1997). We should hope it is well above 10,000 Gt globally as loss from 10% of land that is agricultural of 75 Gt per year (as per Pimentel & Burgess, 2013: 447), gives us (10,000 / 10 / 75 ) just 13 years or until 2030…
Data above should be tempered with knowledge that land degradation due in no small measure to loss of natural soil fertility and excess synthetic Nitrogen (Rockström et al., 2009) costs all of us up to $10.6 trillion each year. But, if sustainable land management (e.g. organic farming and Permaculture that produce more – Ref.1, Ref.2) were fully implemented then we could potentially benefit with $75.6 trillion added to global economy per year through jobs and increased agricultural output (UN’s ELD, 2015).
Over two millennia ago Aristotle told us the Earth was not flat and he also concurred with Plato in recognizing that soil erosion and loss of humus and earthworms is catastrophic to civilization (Ref.). Leonardo da Vinci’s observation 500 years ago that “We know more about the movement of celestial bodies than about the soil underfoot” seemingly still rings true. And NASA seems to be more distracted by Mars, Venus or on some other blue dot many light years away, to worry about a bit of dirt on Earth?
Oceans and Space Diversions and Distractions from the Real Problems on Earth
The Conversation (2017, Ref.) reveals that the entire ocean floor has now been mapped to a maximum resolution of around 5 km and that: “NASA’s Magellan spacecraft mapped 98% of the surface of Venus to a resolution of around 100 metres. The entire Martian surface has also been mapped at that resolution and just over 60% of the Red Planet has now been mapped at around 20m resolution. Meanwhile, selenographers have mapped all of the lunar surface at around 100 metre resolution and now even at seven metre resolution.” And Earth’s global data is available from the 2000 Shuttle Radar Topography Mission (SRTM) and ASTER Global Digital Elevation Model (https://asterweb.jpl.nasa.gov/) with a 1 arc-second, or about 30 meters (98 feet) sampling and some datasets have trees and other non-terrain features removed. But where on Earth is the compiled data for the earth beneath our feet!?
A summary for bathymetry has a surface of 36.066 Gha and a seabed at 2-20 km resolution of 36.138 Gha (difference 0.72 or just about 0.02% but these authors predict they have under-estimated the seabed slopes by more than 50% – so is their true value closer to 72 Gha or just plus 1.44 Gha?) (Costello et al., 2010: tab. 1. Ref.). They claim this as important as it relates to fisheries (that, nevertheless, supply just 0.6% of food!). Regardless, only the surface of the ocean is exposed to sunlight thus the bathymetry is as much an irrelevant diversion as are other planets’ topographies, for calculations of primary productivity and soil carbon here on Earth on which oceanographers and astronomers entirely depend for their survival, along with the rest of us.
This is further exemplified by studies on Rugosity, or small-scale landform Roughness (Ref.), that has been mostly press-ganged into use for marine seascapes and, after oceans, is best worked out for the Moon, Mars and Venus! Indeed where on Earth is earth?
The only worked terrestrial examples I can find are: “a study using a 90m SRTM DEM for the rugged states of Jammu and Kashmir, Rashid (2010) found the 3D and 2D areas differed by nearly 25% (296,513 km2 vs. 222,236 km2, respectively)” (actually by 33%) and “2D Area of One Pixel: 28.40m x 28.40m pixel sloping 60 degrees = 806.56 m2 … 3D Area of Same Pixel: 806.56 m2 / cos(60) = 806.56/0.5 = 1613.12 m2” – this latter being 100% larger or double the area (Ref1., Ref2.). Although the SRTM data used was 90 or 30 m resolution, only ten classes of slope were used in the first example (with large variability) and one in the second, thus they are relatively crude estimations. Finer slope resolution will considerably increase the surface reality to the planimetric model, and refined rugosity more so. A single real-world example is needed.
Flaws in Un-flattening the Earth?
Flaws in my land surface argument are that the estimation of quadrupled topographical land area may be excessive, or it may be an underestimation depending upon what scale is chosen. Double the land’s mantling surface topsoil skin seems reasonable for practical purposes relating to slope and, by the same logic, the craggy micro-relief rugosity of rocks and soil tortuosity may double this again. Who knows? Certainly, the present NASA/NOAA values are wrong. Other criticisms may be that Landsat and other satellites can be set to measure perpendicular values thus terrain is less relevant. And, because land productivity calculation is difficult (compared to ocean or atmosphere), the IPCC (2014) sources estimate carbon contributions based upon total emissions less atmospheric plus oceanic uptakes. The residual difference is ascribed to a land sink which is possibly a quite valid method. Other calculations relating to carbon stored and released from agriculture, forestry and other land-use changes, however, probably do require topography. Moreover, as this is our basic biospheric raft of survival it is surely important to define the fundamental metrics of our shared homeland and, most crucially vital, the amount of our organic topsoils (here estimated, as before, as 81% of the new total land area) remaining thereupon. It seems we are foolhardy to ignore the wisdom and warnings from Plato, Aristotle, da Vinci and Darwin.
The challenge now is for professional geographers or astronomers with the resources to provide more down-to-Earth topographic relief values, starting from sea-level upwards.
Rob Blakemore Draft 27th May, 2017; Final 10th June, 2017 firstname.lastname@example.org
Pdf of the original paper presented here: – Grounded5 .
Drive shared link – https://drive.google.com/file/d/0B1FEBK_Ori41NUltcXRjdDRKM2c/view?usp=sharing .