Graded 6 October 2026
Can Adobe PDF Extract API preserve math in a document with equations?
Adobe PDF Extract API preserved the equations in the three-page PDF as linked figure images in the generated Markdown. The page shows each equation in place with its number beneath it, and the figure images keep fractions, superscripts, subscripts, and absolute-value bars intact; there are no LaTeX, MathML, or $ delimiters.
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# Tarnbeck Institute of Hydrology A one-dimensional model of tidal attenuation in the Braithe channel Technical note TIH/TN/18 · January 2026 R. K. Sandiman and H. Vale # 1 Introduction The tide entering the Braithe is attenuated over the eleven kilometres between the bar and Braithe Bridge, and the attenuation is large enough to matter to anyone predicting water levels in the upper estuary. This note sets out the one-dimensional model the Institute has used since 2018, states the approximation on which the working formula rests, and compares the result with the gauge record at three stations. Nothing here is new. The intention is to have the derivation, the assumptions and the coefficients in one place, because the formula has been quoted in Partnership papers without them. # 2 Governing equations Take the channel as a single reach of slowly varying cross-section and neglect lateral inflow. Conservation of mass gives  (1) where A is the cross-sectional area below the free surface and Q the discharge through it. Conservation of momentum, with friction represented in the Manning form, gives  (2) in which η is the surface elevation above mean sea level, n is Manning's coefficient, R the hydraulic radius R = A/P for wetted perimeter P, and g the acceleration due to gravity. The friction term is the only nonlinear one that matters over the range of interest. # 3 Attenuation of the leading harmonic For a channel of nearly uniform depth the leading semidiurnal harmonic decays close to exponentially with distance upstream, so that  (3) with η0 the amplitude at the bar, ω the angular frequency of the harmonic, k the wavenumber and μ the attenuation coefficient. Linearising the friction term by the Lorentz method and collecting terms gives  (4) where c is the frictionless wave speed and h the mean depth. The second expression is the friction parameter; it is small in the lower reach and approaches unity above Harrowby Reach, which is where the exponential form begins to fail. # 4 Application to the Braithe Taking the mean depth as eleven metres below the bar and four metres at the bridge, with Manning's coefficient at the value fitted in 2018, the formula reproduces the observed amplitude at Vardenne Quay to within four per cent and at Harrowby Reach to within nine. At Braithe Bridge it overestimates the amplitude, and the discrepancy grows through the spring tides, which is the behaviour the friction parameter predicts. A two-reach treatment with separate depths would probably remove most of the error at the bridge. It has not been attempted here because the gauge record above Harrowby Reach is too short to fit a second coefficient with any confidence. # 5 Coefficients Manning's coefficient is not constant with depth in a channel of this kind, and the single fitted value used above is a compromise. Fitting the 2018 record with a depth-dependent form gives  (5) with n∞ the deep-water value and b a bed constant. The fit is better in the lower reach and no better at the bridge, which suggests that the error there is not in the friction term at all. The two constants were fitted to the 2018 record and have not been refitted since. Refitting on the four years now available would be worth doing; the Institute's expectation is that the deep-water value will move very little and the bed constant appreciably, because it is carrying the shallow reaches where the record has improved most. # 6 Limitations Three limitations should be stated plainly. The first is the one-dimensional assumption, which fails where the channel divides above Harrowby Reach. The second is the neglect of the freshwater inflow, which is small in summer and not small after rain. The third is the linearisation itself, which is a poor approximation once the friction parameter approaches unity - that is, in exactly the reach where the model is least accurate. The error measure quoted in the previous section is  (6) taken over the spring-neap cycle at each gauge, with ηo the observed amplitude and ηm the modelled one. It is a crude measure and it flatters the model at the bar, where the amplitude is large and the absolute error is not. None of this is an argument against using the formula, which is quick, transparent and good enough for the purposes the Partnership puts it to. It is an argument for quoting it with the reach and the tidal range attached, which the papers that quote it have not always done. # References Sandiman, R. K. (2018). Tidal propagation in the Braithe: a first fit. Tarnbeck Institute internal report TIH/IR/09. Vale, H. and Croyde, P. (2021). The Harrowby Reach gauge, 2015 to 2020. Journal of Estuarine Hydrology 44, 218-31. Prosser, A. (2009). Friction coefficients for the Braithe channel. Braithe Harbour Board, unpublished.
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K. Sandiman and H. Vale ", "TextSize": 10.399993896484375, "attributes": {"Placement":"Block"} }, { "Bounds": [73.70100402832031,682.0473937988281,155.3800048828125,698.9322052001953], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 523, "Page": 0, "Path": "//Document/Sect[2]/H1", "Text": "1 Introduction ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.375} }, { "Bounds": [73.70100402832031,605.3800048828125,522.7848358154297,678.0429992675781], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 524, "Page": 0, "Path": "//Document/Sect[2]/P", "Text": "The tide entering the Braithe is attenuated over the eleven kilometres between the bar and Braithe Bridge, and the attenuation is large enough to matter to anyone predicting water levels in the upper estuary. This note sets out the one-dimensional model the Institute has used since 2018, states the approximation on which the working formula rests, and compares the result with the gauge record at three stations. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.70100402832031,569.6156005859375,523.7706451416016,598.4900054931641], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 525, "Page": 0, "Path": "//Document/Sect[2]/P[2]", "Text": "Nothing here is new. The intention is to have the derivation, the assumptions and the coefficients in one place, because the formula has been quoted in Partnership papers without them. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.70100402832031,532.6773986816406,197.75059509277344,549.5621948242188], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 526, "Page": 0, "Path": "//Document/Sect[3]/H1", "Text": "2 Governing equations ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.5} }, { "Bounds": [73.70100402832031,499.79859924316406,516.7237548828125,528.6730041503906], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 527, "Page": 0, "Path": "//Document/Sect[3]/P", "Text": "Take the channel as a single reach of slowly varying cross-section and neglect lateral inflow. Conservation of mass gives ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [263.22483825683594,437.00059509277344,335.5469055175781,476.7852020263672], "ClipBounds": [263.22483825683594,440.9009552001953,333.7518310546875,473.1289520263672], "ObjectID": 528, "Page": 0, "Path": "//Document/Sect[3]/Figure", "attributes": { "BBox": [263.5089999999909,442.9059999999881,332.14599999999336,472.90499999999884], "Placement": "Block" }, "filePaths": ["figures/fileoutpart0.png"] }, { "Bounds": [263.22483825683594,437.00059509277344,335.5469055175781,476.7852020263672], "ClipBounds": [263.22483825683594,440.9009552001953,333.7518310546875,473.1289520263672], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": false, "monospaced": false, "name": "GGEIDJ+STIXGeneral-Regular", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 528, "Page": 0, "Path": "//Document/Sect[3]/Figure", "Text": "∂A ∂t + ∂Q ∂x =0 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [263.5089999999909,442.9059999999881,332.14599999999336,472.90499999999884], "Placement": "Block" } }, { "Bounds": [509.6820068359375,451.34559631347656,524.1251983642578,465.0850067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 529, "Page": 0, "Path": "//Document/Sect[3]/P[2]", "Text": "(1) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":11.875,"TextAlign":"End"} }, { "Bounds": [73.70100402832031,410.30059814453125,524.1978149414062,439.1750030517578], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 530, "Page": 0, "Path": "//Document/Sect[3]/P[3]", "Text": "where A is the cross-sectional area below the free surface and Q the discharge through it. Conservation of momentum, with friction represented in the Manning form, gives ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [189.22483825683594,344.5733947753906,409.9833068847656,389.0184783935547], "ClipBounds": [189.22483825683594,347.4029541015625,407.7518310546875,383.6309509277344], "ObjectID": 531, "Page": 0, "Path": "//Document/Sect[3]/Figure[2]", "attributes": { "BBox": [189.4719999999943,349.1899999999878,406.6629999999859,383.38799999999173], "Placement": "Block" }, "filePaths": ["figures/fileoutpart1.png"] }, { "Bounds": [189.22483825683594,344.5733947753906,409.9833068847656,389.0184783935547], "ClipBounds": [189.22483825683594,347.4029541015625,407.7518310546875,383.6309509277344], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": false, "monospaced": false, "name": "GGEIDJ+STIXGeneral-Regular", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 531, "Page": 0, "Path": "//Document/Sect[3]/Figure[2]", "Text": "∂Q ∂t + ∂ ∂x( Q2 A ) + gA ∂η ∂x + g n2 Q |Q| A R4/3 =0 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [189.4719999999943,349.1899999999878,406.6629999999859,383.38799999999173], "Placement": "Block" } }, { "Bounds": [509.68299865722656,359.52760314941406,524.1262054443359,373.2669982910156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 532, "Page": 0, "Path": "//Document/Sect[3]/P[4]", "Text": "(2) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":13.375,"TextAlign":"End"} }, { "Bounds": [73.70199584960938,302.20640563964844,524.1627807617188,346.8768005371094], "ClipBounds": [73.70199584960938,302.20640563964844,524.1627807617188,345.677001953125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 533, "Page": 0, "Path": "//Document/Sect[3]/P[5]", "Text": "in which η is the surface elevation above mean sea level, n is Manning's coefficient, R the hydraulic radius R = A/P for wetted perimeter P, and g the acceleration due to gravity. The friction term is the only nonlinear one that matters over the range of interest. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.70050048828125,265.2814025878906,278.0505065917969,282.16619873046875], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 486, "Page": 0, "Path": "//Document/Sect[4]/H1", "Text": "3 Attenuation of the leading harmonic ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.375} }, { "Bounds": [73.70050048828125,232.40260314941406,523.1818389892578,261.27699279785156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 487, "Page": 0, "Path": "//Document/Sect[4]/P", "Text": "For a channel of nearly uniform depth the leading semidiurnal harmonic decays close to exponentially with distance upstream, so that ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [221.13800048828125,188.6046600341797,377.3040008544922,209.8997344970703], "ClipBounds": [221.13800048828125,190.10498046875,375.2518615722656,205.7329864501953], "ObjectID": 488, "Page": 0, "Path": "//Document/Sect[4]/Figure", "attributes": { "BBox": [221.15099999999802,191.39599999999336,373.90499999999884,205.55599999999686], "Placement": "Block" }, "filePaths": ["figures/fileoutpart2.png"] }, { "Bounds": [221.13800048828125,188.6046600341797,377.3040008544922,209.8997344970703], "ClipBounds": [221.13800048828125,190.10498046875,375.2518615722656,205.7329864501953], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "FKVMUH+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 488, "Page": 0, "Path": "//Document/Sect[4]/Figure", "Text": "η(x, t) = η0 e−μx cos (ωt − kx) ", "TextSize": 13.399993896484375, "attributes": { "BBox": [221.15099999999802,191.39599999999336,373.90499999999884,205.55599999999686], "Placement": "Block" } }, { "Bounds": [509.68150329589844,193.57760620117188,524.1246948242188,207.31700134277344], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 489, "Page": 0, "Path": "//Document/Sect[4]/P[2]", "Text": "(3) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":4.75,"TextAlign":"End"} }, { "Bounds": [73.68989562988281,159.5045928955078,523.9461059570312,189.7198028564453], "ClipBounds": [73.68989562988281,159.5045928955078,523.9461059570312,188.37899780273438], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 490, "Page": 0, "Path": "//Document/Sect[4]/P[3]", "Text": "with η0 the amplitude at the bar, ω the angular frequency of the harmonic, k the wavenumber and μ the attenuation coefficient. Linearising the friction term by the Lorentz method and collecting terms gives ", "TextSize": 10.600006103515625 }, { "Bounds": [189.63800048828125,713.0648040771484,406.04100036621094,755.5887451171875], "ClipBounds": [189.63800048828125,714.2109527587891,406.04100036621094,753.4389495849609], "ObjectID": 459, "Page": 1, "Path": "//Document/Sect[4]/Figure[2]", "attributes": { "BBox": [189.59199999999691,715.1749999999884,404.3839999999909,753.2129999999888], "Placement": "Block" }, "filePaths": ["figures/fileoutpart3.png"] }, { "Bounds": [189.63800048828125,713.0648040771484,406.04100036621094,755.5887451171875], "ClipBounds": [189.63800048828125,714.2109527587891,406.04100036621094,753.4389495849609], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "HJTXDD+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 459, "Page": 1, "Path": "//Document/Sect[4]/Figure[2]", "Text": "μ= ω c ( χ 2(1 + χ2)) 1/2 , χ= 8 n2 c η0 3π h4/3 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [189.59199999999691,715.1749999999884,404.3839999999909,753.2129999999888], "Placement": "Block" } }, { "Bounds": [509.6809997558594,727.5955963134766,524.1242065429688,741.3350067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 460, "Page": 1, "Path": "//Document/Sect[4]/P[4]", "Text": "(4) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":14.625,"TextAlign":"End"} }, { "Bounds": [73.69999694824219,669.014404296875,523.2947540283203,712.4850006103516], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 461, "Page": 1, "Path": "//Document/Sect[4]/P[5]", "Text": "where c is the frictionless wave speed and h the mean depth. The second expression is the friction parameter; it is small in the lower reach and approaches unity above Harrowby Reach, which is where the exponential form begins to fail. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.69999694824219,632.0894012451172,224.84579467773438,648.9741973876953], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 462, "Page": 1, "Path": "//Document/Sect[5]/H1", "Text": "4 Application to the Braithe ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.5} }, { "Bounds": [73.69999694824219,555.4219970703125,523.79931640625,628.0850067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 463, "Page": 1, "Path": "//Document/Sect[5]/P", "Text": "Taking the mean depth as eleven metres below the bar and four metres at the bridge, with Manning's coefficient at the value fitted in 2018, the formula reproduces the observed amplitude at Vardenne Quay to within four per cent and at Harrowby Reach to within nine. At Braithe Bridge it overestimates the amplitude, and the discrepancy grows through the spring tides, which is the behaviour the friction parameter predicts. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":6.625} }, { "Bounds": [73.69999694824219,505.0614013671875,524.1247406005859,548.5319976806641], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 464, "Page": 1, "Path": "//Document/Sect[5]/P[2]", "Text": "A two-reach treatment with separate depths would probably remove most of the error at the bridge. It has not been attempted here because the gauge record above Harrowby Reach is too short to fit a second coefficient with any confidence. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.69999694824219,468.11940002441406,150.60879516601562,485.0041961669922], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 465, "Page": 1, "Path": "//Document/Sect[6]/H1", "Text": "5 Coefficients ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.5} }, { "Bounds": [73.69999694824219,435.2406005859375,524.0918731689453,464.11500549316406], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 466, "Page": 1, "Path": "//Document/Sect[6]/P", "Text": "Manning's coefficient is not constant with depth in a channel of this kind, and the single fitted value used above is a compromise. Fitting the 2018 record with a depth-dependent form gives ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [252.63800048828125,372.7763977050781,343.35264587402344,412.0249938964844], "ClipBounds": [252.63800048828125,374.3429718017578,343.35264587402344,408.5709686279297], "ObjectID": 467, "Page": 1, "Path": "//Document/Sect[6]/Figure", "attributes": { "BBox": [252.5899999999965,376.90899999999965,341.025999999998,408.3469999999943], "Placement": "Block" }, "filePaths": ["figures/fileoutpart4.png"] }, { "Bounds": [252.63800048828125,372.7763977050781,343.35264587402344,412.0249938964844], "ClipBounds": [252.63800048828125,374.3429718017578,343.35264587402344,408.5709686279297], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "GAXFQP+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 467, "Page": 1, "Path": "//Document/Sect[6]/Figure", "Text": "n(h) = n∞ + b h1/3 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [252.5899999999965,376.90899999999965,341.025999999998,408.3469999999943], "Placement": "Block" } }, { "Bounds": [509.6809997558594,385.6275939941406,524.1242065429688,399.36700439453125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 468, "Page": 1, "Path": "//Document/Sect[6]/P[2]", "Text": "(5) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":12.5,"TextAlign":"End"} }, { "Bounds": [73.68940734863281,343.7425994873047,523.5523376464844,373.4627990722656], "ClipBounds": [73.68940734863281,343.7425994873047,523.5523376464844,372.61700439453125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 469, "Page": 1, "Path": "//Document/Sect[6]/P[3]", "Text": "with n∞ the deep-water value and b a bed constant. The fit is better in the lower reach and no better at the bridge, which suggests that the error there is not in the friction term at all. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":6.625} }, { "Bounds": [73.68940734863281,278.7857971191406,523.4876861572266,336.85260009765625], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 471, "Page": 1, "Path": "//Document/Sect[6]/P[4]", "Text": "The two constants were fitted to the 2018 record and have not been refitted since. Refitting on the four years now available would be worth doing; the Institute's expectation is that the deep-water value will move very little and the bed constant appreciably, because it is carrying the shallow reaches where the record has improved most. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.70100402832031,241.8513946533203,149.27999877929688,258.7362060546875], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 435, "Page": 1, "Path": "//Document/Sect[7]/H1", "Text": "6 Limitations ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":4.5} }, { "Bounds": [73.70100402832031,165.1840057373047,524.1914672851562,237.8470001220703], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 436, "Page": 1, "Path": "//Document/Sect[7]/P", "Text": "Three limitations should be stated plainly. The first is the one-dimensional assumption, which fails where the channel divides above Harrowby Reach. The second is the neglect of the freshwater inflow, which is small in summer and not small after rain. The third is the linearisation itself, which is a poor approximation once the friction parameter approaches unity - that is, in exactly the reach where the model is least accurate. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":8.5} }, { "Bounds": [73.70100402832031,144.0157928466797,293.58740234375,158.29400634765625], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 437, "Page": 1, "Path": "//Document/Sect[7]/P[2]", "Text": "The error measure quoted in the previous section is ", "TextSize": 10.600006103515625, "attributes": {"LineHeight":12.75,"SpaceAfter":18} }, { "Bounds": [263.63800048828125,721.4080963134766,333.00245666503906,760.127197265625], "ClipBounds": [263.63800048828125,722.2109527587891,332.7518768310547,753.4389495849609], "ObjectID": 404, "Page": 2, "Path": "//Document/Sect[7]/Figure", "attributes": { "BBox": [263.62899999998626,724.2949999999837,329.9869999999937,753.2129999999888], "Placement": "Block" }, "filePaths": ["figures/fileoutpart5.png"] }, { "Bounds": [263.63800048828125,721.4080963134766,333.00245666503906,760.127197265625], "ClipBounds": [263.63800048828125,722.2109527587891,332.7518768310547,753.4389495849609], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "CELNPC+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 404, "Page": 2, "Path": "//Document/Sect[7]/Figure", "Text": "ε= |ηo − ηm| ηo ", "TextSize": 13.399993896484375, "attributes": { "BBox": [263.62899999998626,724.2949999999837,329.9869999999937,753.2129999999888], "Placement": "Block" } }, { "Bounds": [509.6809997558594,732.235595703125,524.1242065429688,745.9750061035156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 405, "Page": 2, "Path": "//Document/Sect[7]/P[3]", "Text": "(6) ", "TextSize": 10.199996948242188, "attributes": {"LineHeight":12.25,"SpaceAfter":11.375,"TextAlign":"End"} }, { "Bounds": [73.69999694824219,677.014404296875,523.0552062988281,721.6847991943359], "ClipBounds": [73.69999694824219,677.014404296875,523.0552062988281,720.4850006103516], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 406, "Page": 2, "Path": "//Document/Sect[7]/P[4]", "Text": "taken over the spring-neap cycle at each gauge, with ηo the observed amplitude and ηm the modelled one. It is a crude measure and it flatters the model at the bar, where the amplitude is large and the absolute error is not. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":6.5} }, { "Bounds": [73.71060180664062,626.6537933349609,523.7929534912109,670.1244049072266], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 409, "Page": 2, "Path": "//Document/Sect[7]/P[5]", "Text": "None of this is an argument against using the formula, which is quick, transparent and good enough for the purposes the Partnership puts it to. It is an argument for quoting it with the reach and the tidal range attached, which the papers that quote it have not always done. ", "TextSize": 10.600006103515625, "attributes": {"SpaceAfter":18} }, { "Bounds": [73.69999694824219,589.7194061279297,133.6508026123047,606.6042022705078], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 410, "Page": 2, "Path": "//Document/Sect[8]/H1", "Text": "References ", "TextSize": 12.199996948242188, "attributes": {"SpaceAfter":7.375} }, { "Bounds": [73.69999694824219,571.6824035644531,520.3056030273438,584.8829956054688], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 411, "Page": 2, "Path": "//Document/Sect[8]/P", "Text": "Sandiman, R. K. (2018). Tidal propagation in the Braithe: a first fit. Tarnbeck Institute internal report TIH/IR/09. ", "TextSize": 9.800003051757812, "attributes": {"LineHeight":11.75,"SpaceAfter":4.875} }, { "Bounds": [73.69999694824219,540.283203125,513.5142059326172,566.6844024658203], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 412, "Page": 2, "Path": "//Document/Sect[8]/P[2]", "Text": "Vale, H. and Croyde, P. (2021). The Harrowby Reach gauge, 2015 to 2020. Journal of Estuarine Hydrology 44, 218-31. ", "TextSize": 9.800003051757812, "attributes": {"LineHeight":13.25,"SpaceAfter":6.5} }, { "Bounds": [73.69999694824219,522.0845947265625,475.1177978515625,535.2852020263672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 413, "Page": 2, "Path": "//Document/Sect[8]/P[3]", "Text": "Prosser, A. (2009). Friction coefficients for the Braithe channel. Braithe Harbour Board, unpublished. ", "TextSize": 9.800003051757812, "attributes": {"LineHeight":11.75} } ]
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"weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 520, "Page": 0, "Path": "//Document/Sect/Title", "Text": "Tarnbeck Institute of Hydrology A one-dimensional model of tidal attenuation in the Braithe channel ", "TextSize": 15.0, "attributes": { "LineHeight": 16.125, "SpaceAfter": 5.5 } }, { "Bounds": [73.69999694824219, 741.0646057128906, 236.1811981201172, 753.4570007324219], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "ObjectID": 521, "Page": 0, "Path": "//Document/Sect/P/Sub", "Text": "Technical note TIH/TN/18 \u00b7 January 2026 ", "TextSize": 9.199996948242188, "attributes": { "Placement": "Block" } }, { "Bounds": [73.69999694824219, 725.856201171875, 194.16319274902344, 739.6882019042969], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": true, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-ItalicMT", "subset": true, "weight": 400 }, "HasClip": false, "ObjectID": 522, "Page": 0, "Path": "//Document/Sect/P/Sub[2]", "Text": "R. K. Sandiman and H. Vale ", "TextSize": 10.399993896484375, "attributes": { "Placement": "Block" } }, { "Bounds": [73.70100402832031, 682.0473937988281, 155.3800048828125, 698.9322052001953], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 523, "Page": 0, "Path": "//Document/Sect[2]/H1", "Text": "1 Introduction ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.375 } }, { "Bounds": [73.70100402832031, 605.3800048828125, 522.7848358154297, 678.0429992675781], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 524, "Page": 0, "Path": "//Document/Sect[2]/P", "Text": "The tide entering the Braithe is attenuated over the eleven kilometres between the bar and Braithe Bridge, and the attenuation is large enough to matter to anyone predicting water levels in the upper estuary. This note sets out the one-dimensional model the Institute has used since 2018, states the approximation on which the working formula rests, and compares the result with the gauge record at three stations. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.70100402832031, 569.6156005859375, 523.7706451416016, 598.4900054931641], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 525, "Page": 0, "Path": "//Document/Sect[2]/P[2]", "Text": "Nothing here is new. The intention is to have the derivation, the assumptions and the coefficients in one place, because the formula has been quoted in Partnership papers without them. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.70100402832031, 532.6773986816406, 197.75059509277344, 549.5621948242188], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 526, "Page": 0, "Path": "//Document/Sect[3]/H1", "Text": "2 Governing equations ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.5 } }, { "Bounds": [73.70100402832031, 499.79859924316406, 516.7237548828125, 528.6730041503906], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 527, "Page": 0, "Path": "//Document/Sect[3]/P", "Text": "Take the channel as a single reach of slowly varying cross-section and neglect lateral inflow. Conservation of mass gives ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [263.22483825683594, 437.00059509277344, 335.5469055175781, 476.7852020263672], "ClipBounds": [263.22483825683594, 440.9009552001953, 333.7518310546875, 473.1289520263672], "ObjectID": 528, "Page": 0, "Path": "//Document/Sect[3]/Figure", "attributes": { "BBox": [263.5089999999909, 442.9059999999881, 332.14599999999336, 472.90499999999884], "Placement": "Block" }, "filePaths": ["figures/fileoutpart0.png"] }, { "Bounds": [263.22483825683594, 437.00059509277344, 335.5469055175781, 476.7852020263672], "ClipBounds": [263.22483825683594, 440.9009552001953, 333.7518310546875, 473.1289520263672], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": false, "monospaced": false, "name": "GGEIDJ+STIXGeneral-Regular", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 528, "Page": 0, "Path": "//Document/Sect[3]/Figure", "Text": "\u2202A \u2202t + \u2202Q \u2202x =0 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [263.5089999999909, 442.9059999999881, 332.14599999999336, 472.90499999999884], "Placement": "Block" } }, { "Bounds": [509.6820068359375, 451.34559631347656, 524.1251983642578, 465.0850067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 529, "Page": 0, "Path": "//Document/Sect[3]/P[2]", "Text": "(1) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 11.875, "TextAlign": "End" } }, { "Bounds": [73.70100402832031, 410.30059814453125, 524.1978149414062, 439.1750030517578], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 530, "Page": 0, "Path": "//Document/Sect[3]/P[3]", "Text": "where A is the cross-sectional area below the free surface and Q the discharge through it. Conservation of momentum, with friction represented in the Manning form, gives ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [189.22483825683594, 344.5733947753906, 409.9833068847656, 389.0184783935547], "ClipBounds": [189.22483825683594, 347.4029541015625, 407.7518310546875, 383.6309509277344], "ObjectID": 531, "Page": 0, "Path": "//Document/Sect[3]/Figure[2]", "attributes": { "BBox": [189.4719999999943, 349.1899999999878, 406.6629999999859, 383.38799999999173], "Placement": "Block" }, "filePaths": ["figures/fileoutpart1.png"] }, { "Bounds": [189.22483825683594, 344.5733947753906, 409.9833068847656, 389.0184783935547], "ClipBounds": [189.22483825683594, 347.4029541015625, 407.7518310546875, 383.6309509277344], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": false, "monospaced": false, "name": "GGEIDJ+STIXGeneral-Regular", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 531, "Page": 0, "Path": "//Document/Sect[3]/Figure[2]", "Text": "\u2202Q \u2202t + \u2202 \u2202x( Q2 A ) + gA \u2202\u03b7 \u2202x + g n2 Q |Q| A R4/3 =0 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [189.4719999999943, 349.1899999999878, 406.6629999999859, 383.38799999999173], "Placement": "Block" } }, { "Bounds": [509.68299865722656, 359.52760314941406, 524.1262054443359, 373.2669982910156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 532, "Page": 0, "Path": "//Document/Sect[3]/P[4]", "Text": "(2) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 13.375, "TextAlign": "End" } }, { "Bounds": [73.70199584960938, 302.20640563964844, 524.1627807617188, 346.8768005371094], "ClipBounds": [73.70199584960938, 302.20640563964844, 524.1627807617188, 345.677001953125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 533, "Page": 0, "Path": "//Document/Sect[3]/P[5]", "Text": "in which \u03b7 is the surface elevation above mean sea level, n is Manning's coefficient, R the hydraulic radius R = A/P for wetted perimeter P, and g the acceleration due to gravity. The friction term is the only nonlinear one that matters over the range of interest. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.70050048828125, 265.2814025878906, 278.0505065917969, 282.16619873046875], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 486, "Page": 0, "Path": "//Document/Sect[4]/H1", "Text": "3 Attenuation of the leading harmonic ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.375 } }, { "Bounds": [73.70050048828125, 232.40260314941406, 523.1818389892578, 261.27699279785156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 487, "Page": 0, "Path": "//Document/Sect[4]/P", "Text": "For a channel of nearly uniform depth the leading semidiurnal harmonic decays close to exponentially with distance upstream, so that ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [221.13800048828125, 188.6046600341797, 377.3040008544922, 209.8997344970703], "ClipBounds": [221.13800048828125, 190.10498046875, 375.2518615722656, 205.7329864501953], "ObjectID": 488, "Page": 0, "Path": "//Document/Sect[4]/Figure", "attributes": { "BBox": [221.15099999999802, 191.39599999999336, 373.90499999999884, 205.55599999999686], "Placement": "Block" }, "filePaths": ["figures/fileoutpart2.png"] }, { "Bounds": [221.13800048828125, 188.6046600341797, 377.3040008544922, 209.8997344970703], "ClipBounds": [221.13800048828125, 190.10498046875, 375.2518615722656, 205.7329864501953], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "FKVMUH+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 488, "Page": 0, "Path": "//Document/Sect[4]/Figure", "Text": "\u03b7(x, t) = \u03b70 e\u2212\u03bcx cos (\u03c9t \u2212 kx) ", "TextSize": 13.399993896484375, "attributes": { "BBox": [221.15099999999802, 191.39599999999336, 373.90499999999884, 205.55599999999686], "Placement": "Block" } }, { "Bounds": [509.68150329589844, 193.57760620117188, 524.1246948242188, 207.31700134277344], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 489, "Page": 0, "Path": "//Document/Sect[4]/P[2]", "Text": "(3) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 4.75, "TextAlign": "End" } }, { "Bounds": [73.68989562988281, 159.5045928955078, 523.9461059570312, 189.7198028564453], "ClipBounds": [73.68989562988281, 159.5045928955078, 523.9461059570312, 188.37899780273438], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 490, "Page": 0, "Path": "//Document/Sect[4]/P[3]", "Text": "with \u03b70 the amplitude at the bar, \u03c9 the angular frequency of the harmonic, k the wavenumber and \u03bc the attenuation coefficient. Linearising the friction term by the Lorentz method and collecting terms gives ", "TextSize": 10.600006103515625 }, { "Bounds": [189.63800048828125, 713.0648040771484, 406.04100036621094, 755.5887451171875], "ClipBounds": [189.63800048828125, 714.2109527587891, 406.04100036621094, 753.4389495849609], "ObjectID": 459, "Page": 1, "Path": "//Document/Sect[4]/Figure[2]", "attributes": { "BBox": [189.59199999999691, 715.1749999999884, 404.3839999999909, 753.2129999999888], "Placement": "Block" }, "filePaths": ["figures/fileoutpart3.png"] }, { "Bounds": [189.63800048828125, 713.0648040771484, 406.04100036621094, 755.5887451171875], "ClipBounds": [189.63800048828125, 714.2109527587891, 406.04100036621094, 753.4389495849609], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "HJTXDD+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 459, "Page": 1, "Path": "//Document/Sect[4]/Figure[2]", "Text": "\u03bc= \u03c9 c ( \u03c7 2(1 + \u03c72)) 1/2 , \u03c7= 8 n2 c \u03b70 3\u03c0 h4/3 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [189.59199999999691, 715.1749999999884, 404.3839999999909, 753.2129999999888], "Placement": "Block" } }, { "Bounds": [509.6809997558594, 727.5955963134766, 524.1242065429688, 741.3350067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 460, "Page": 1, "Path": "//Document/Sect[4]/P[4]", "Text": "(4) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 14.625, "TextAlign": "End" } }, { "Bounds": [73.69999694824219, 669.014404296875, 523.2947540283203, 712.4850006103516], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 461, "Page": 1, "Path": "//Document/Sect[4]/P[5]", "Text": "where c is the frictionless wave speed and h the mean depth. The second expression is the friction parameter; it is small in the lower reach and approaches unity above Harrowby Reach, which is where the exponential form begins to fail. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.69999694824219, 632.0894012451172, 224.84579467773438, 648.9741973876953], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 462, "Page": 1, "Path": "//Document/Sect[5]/H1", "Text": "4 Application to the Braithe ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.5 } }, { "Bounds": [73.69999694824219, 555.4219970703125, 523.79931640625, 628.0850067138672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 463, "Page": 1, "Path": "//Document/Sect[5]/P", "Text": "Taking the mean depth as eleven metres below the bar and four metres at the bridge, with Manning's coefficient at the value fitted in 2018, the formula reproduces the observed amplitude at Vardenne Quay to within four per cent and at Harrowby Reach to within nine. At Braithe Bridge it overestimates the amplitude, and the discrepancy grows through the spring tides, which is the behaviour the friction parameter predicts. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 6.625 } }, { "Bounds": [73.69999694824219, 505.0614013671875, 524.1247406005859, 548.5319976806641], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 464, "Page": 1, "Path": "//Document/Sect[5]/P[2]", "Text": "A two-reach treatment with separate depths would probably remove most of the error at the bridge. It has not been attempted here because the gauge record above Harrowby Reach is too short to fit a second coefficient with any confidence. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.69999694824219, 468.11940002441406, 150.60879516601562, 485.0041961669922], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 465, "Page": 1, "Path": "//Document/Sect[6]/H1", "Text": "5 Coefficients ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.5 } }, { "Bounds": [73.69999694824219, 435.2406005859375, 524.0918731689453, 464.11500549316406], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 466, "Page": 1, "Path": "//Document/Sect[6]/P", "Text": "Manning's coefficient is not constant with depth in a channel of this kind, and the single fitted value used above is a compromise. Fitting the 2018 record with a depth-dependent form gives ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [252.63800048828125, 372.7763977050781, 343.35264587402344, 412.0249938964844], "ClipBounds": [252.63800048828125, 374.3429718017578, 343.35264587402344, 408.5709686279297], "ObjectID": 467, "Page": 1, "Path": "//Document/Sect[6]/Figure", "attributes": { "BBox": [252.5899999999965, 376.90899999999965, 341.025999999998, 408.3469999999943], "Placement": "Block" }, "filePaths": ["figures/fileoutpart4.png"] }, { "Bounds": [252.63800048828125, 372.7763977050781, 343.35264587402344, 412.0249938964844], "ClipBounds": [252.63800048828125, 374.3429718017578, 343.35264587402344, 408.5709686279297], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "GAXFQP+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 467, "Page": 1, "Path": "//Document/Sect[6]/Figure", "Text": "n(h) = n\u221e + b h1/3 ", "TextSize": 13.399993896484375, "attributes": { "BBox": [252.5899999999965, 376.90899999999965, 341.025999999998, 408.3469999999943], "Placement": "Block" } }, { "Bounds": [509.6809997558594, 385.6275939941406, 524.1242065429688, 399.36700439453125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 468, "Page": 1, "Path": "//Document/Sect[6]/P[2]", "Text": "(5) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 12.5, "TextAlign": "End" } }, { "Bounds": [73.68940734863281, 343.7425994873047, 523.5523376464844, 373.4627990722656], "ClipBounds": [73.68940734863281, 343.7425994873047, 523.5523376464844, 372.61700439453125], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 469, "Page": 1, "Path": "//Document/Sect[6]/P[3]", "Text": "with n\u221e the deep-water value and b a bed constant. The fit is better in the lower reach and no better at the bridge, which suggests that the error there is not in the friction term at all. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 6.625 } }, { "Bounds": [73.68940734863281, 278.7857971191406, 523.4876861572266, 336.85260009765625], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 471, "Page": 1, "Path": "//Document/Sect[6]/P[4]", "Text": "The two constants were fitted to the 2018 record and have not been refitted since. Refitting on the four years now available would be worth doing; the Institute's expectation is that the deep-water value will move very little and the bed constant appreciably, because it is carrying the shallow reaches where the record has improved most. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.70100402832031, 241.8513946533203, 149.27999877929688, 258.7362060546875], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 435, "Page": 1, "Path": "//Document/Sect[7]/H1", "Text": "6 Limitations ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 4.5 } }, { "Bounds": [73.70100402832031, 165.1840057373047, 524.1914672851562, 237.8470001220703], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 436, "Page": 1, "Path": "//Document/Sect[7]/P", "Text": "Three limitations should be stated plainly. The first is the one-dimensional assumption, which fails where the channel divides above Harrowby Reach. The second is the neglect of the freshwater inflow, which is small in summer and not small after rain. The third is the linearisation itself, which is a poor approximation once the friction parameter approaches unity - that is, in exactly the reach where the model is least accurate. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 8.5 } }, { "Bounds": [73.70100402832031, 144.0157928466797, 293.58740234375, 158.29400634765625], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 437, "Page": 1, "Path": "//Document/Sect[7]/P[2]", "Text": "The error measure quoted in the previous section is ", "TextSize": 10.600006103515625, "attributes": { "LineHeight": 12.75, "SpaceAfter": 18 } }, { "Bounds": [263.63800048828125, 721.4080963134766, 333.00245666503906, 760.127197265625], "ClipBounds": [263.63800048828125, 722.2109527587891, 332.7518768310547, 753.4389495849609], "ObjectID": 404, "Page": 2, "Path": "//Document/Sect[7]/Figure", "attributes": { "BBox": [263.62899999998626, 724.2949999999837, 329.9869999999937, 753.2129999999888], "Placement": "Block" }, "filePaths": ["figures/fileoutpart5.png"] }, { "Bounds": [263.63800048828125, 721.4080963134766, 333.00245666503906, 760.127197265625], "ClipBounds": [263.63800048828125, 722.2109527587891, 332.7518768310547, 753.4389495849609], "Font": { "alt_family_name": "STI Extra General", "embedded": true, "encoding": "Identity-H", "family_name": "STI Extra General", "font_type": "CIDFontType2", "italic": true, "monospaced": false, "name": "CELNPC+STIXGeneral-Italic", "subset": true, "weight": 400 }, "HasClip": true, "ObjectID": 404, "Page": 2, "Path": "//Document/Sect[7]/Figure", "Text": "\u03b5= |\u03b7o \u2212 \u03b7m| \u03b7o ", "TextSize": 13.399993896484375, "attributes": { "BBox": [263.62899999998626, 724.2949999999837, 329.9869999999937, 753.2129999999888], "Placement": "Block" } }, { "Bounds": [509.6809997558594, 732.235595703125, 524.1242065429688, 745.9750061035156], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 405, "Page": 2, "Path": "//Document/Sect[7]/P[3]", "Text": "(6) ", "TextSize": 10.199996948242188, "attributes": { "LineHeight": 12.25, "SpaceAfter": 11.375, "TextAlign": "End" } }, { "Bounds": [73.69999694824219, 677.014404296875, 523.0552062988281, 721.6847991943359], "ClipBounds": [73.69999694824219, 677.014404296875, 523.0552062988281, 720.4850006103516], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 406, "Page": 2, "Path": "//Document/Sect[7]/P[4]", "Text": "taken over the spring-neap cycle at each gauge, with \u03b7o the observed amplitude and \u03b7m the modelled one. It is a crude measure and it flatters the model at the bar, where the amplitude is large and the absolute error is not. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 6.5 } }, { "Bounds": [73.71060180664062, 626.6537933349609, 523.7929534912109, 670.1244049072266], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 409, "Page": 2, "Path": "//Document/Sect[7]/P[5]", "Text": "None of this is an argument against using the formula, which is quick, transparent and good enough for the purposes the Partnership puts it to. It is an argument for quoting it with the reach and the tidal range attached, which the papers that quote it have not always done. ", "TextSize": 10.600006103515625, "attributes": { "SpaceAfter": 18 } }, { "Bounds": [73.69999694824219, 589.7194061279297, 133.6508026123047, 606.6042022705078], "Font": { "alt_family_name": "Times New Roman PS", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PS", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPS-BoldMT", "subset": true, "weight": 700 }, "HasClip": false, "Lang": "en", "ObjectID": 410, "Page": 2, "Path": "//Document/Sect[8]/H1", "Text": "References ", "TextSize": 12.199996948242188, "attributes": { "SpaceAfter": 7.375 } }, { "Bounds": [73.69999694824219, 571.6824035644531, 520.3056030273438, 584.8829956054688], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 411, "Page": 2, "Path": "//Document/Sect[8]/P", "Text": "Sandiman, R. K. (2018). Tidal propagation in the Braithe: a first fit. Tarnbeck Institute internal report TIH/IR/09. ", "TextSize": 9.800003051757812, "attributes": { "LineHeight": 11.75, "SpaceAfter": 4.875 } }, { "Bounds": [73.69999694824219, 540.283203125, 513.5142059326172, 566.6844024658203], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 412, "Page": 2, "Path": "//Document/Sect[8]/P[2]", "Text": "Vale, H. and Croyde, P. (2021). The Harrowby Reach gauge, 2015 to 2020. Journal of Estuarine Hydrology 44, 218-31. ", "TextSize": 9.800003051757812, "attributes": { "LineHeight": 13.25, "SpaceAfter": 6.5 } }, { "Bounds": [73.69999694824219, 522.0845947265625, 475.1177978515625, 535.2852020263672], "Font": { "alt_family_name": "Times New Roman PSMT", "embedded": true, "encoding": "Custom", "family_name": "Times New Roman PSMT", "font_type": "TrueType", "italic": false, "monospaced": false, "name": "AAAAAA+TimesNewRomanPSMT", "subset": true, "weight": 400 }, "HasClip": false, "Lang": "en", "ObjectID": 413, "Page": 2, "Path": "//Document/Sect[8]/P[3]", "Text": "Prosser, A. (2009). Friction coefficients for the Braithe channel. Braithe Harbour Board, unpublished. ", "TextSize": 9.800003051757812, "attributes": { "LineHeight": 11.75 } } ], "pages": [ { "boxes": { "CropBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125], "MediaBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125] }, "height": 841.8897705078125, "is_scanned": false, "page_number": 0, "rotation": 0, "width": 595.2755737304688 }, { "boxes": { "CropBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125], "MediaBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125] }, "height": 841.8897705078125, "is_scanned": false, "page_number": 1, "rotation": 0, "width": 595.2755737304688 }, { "boxes": { "CropBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125], "MediaBox": [0.0, 0.0, 595.2755737304688, 841.8897705078125] }, "height": 841.8897705078125, "is_scanned": false, "page_number": 2, "rotation": 0, "width": 595.2755737304688 } ] }, "result_zip_entries": [ "structuredData.json", "figures/fileoutpart4.png", "figures/fileoutpart0.png", "figures/fileoutpart2.png", "figures/fileoutpart5.png", "figures/fileoutpart1.png", "figures/fileoutpart3.png" ], "asset_map": { "figures/fileoutpart0.png": "fileoutpart0.png", "figures/fileoutpart1.png": "fileoutpart1.png", "figures/fileoutpart2.png": "fileoutpart2.png", "figures/fileoutpart3.png": "fileoutpart3.png", "figures/fileoutpart4.png": "fileoutpart4.png", "figures/fileoutpart5.png": "fileoutpart5.png" }, "assembler_stats": { "elements": 48, "blocks": 41, "headings": 8, "paragraphs": 27, "list_items": 0, "tables_markdown": 0, "tables_html": 0, "tables_from_csv": 0, "figures": 6, "unmapped_figures": 0, "first_row_promoted": 0 } }
Expected vs. Found
| ✓ | Expected: Equations should be rendered as math markup or an honest fallback, not garbled prose.Found: All six equations appear as linked figure images with intact structure; no LaTeX, MathML, or $ delimiters appear. |
Supporting proof
Proof 1Screenshot
Proof 2Screenshot
Proof 3Screenshot
Proof 4Screenshot
Proof 5Screenshot
Proof 6Screenshot
Proof 7Screenshot
Why this result
The run checked whether the equations stayed as math or a truthful fallback. Adobe returned six figure renditions, and the assembled Markdown placed each image at the equation's spot with its number beneath it; the figure images keep the math structure intact.
Also observed on this row
Flattened captions. The image captions flatten the equation text; the linked images keep the math structure.
Tested by Chandresh Bisht
Configuration and setup
How this tool was set up for the run and what the test needed in place. Each row is a fact from the run's records; a fact the records do not hold is left out, not guessed.
Software that produced the output
Adobe PDF Extract API
Build or version
PDF Services REST (Extract) json_export=240, page_segmentation=55, schema=1.1.0, structure=1.1222.2, table_structure=5
Plan or tier
free tier
Surface
API
Set up before the run
A PDF containing mathematical equations had to be available. The complete PDF was converted to Markdown in one pass with the default Extract pipeline and no flag tuning.
Pipeline
default Extract pipeline
Renditions to extract
renditionsToExtract=tables,figures
Flag tuning
no flag tuning
Tested
By 26 September 2026 · Chandresh Bisht
Connected to
How this scenario is graded
How we decide Pass, Fail and Not gradable. The same rules apply to every tool tested on this scenario.
How results are decided
Each test case gets one result per tool: Pass, Fail or Not gradable. A test case we haven't run yet shows Untested. There are no partial results.
The rules
- Pass: the tool did everything the test expected, and nothing it said contradicts the correct answer.
- Fail: at least one expected behaviour clearly didn't happen; the row says which and quotes the tool.
- Not gradable: our evidence couldn't settle the outcome (for example a record we needed is missing). It is never counted as a fail, and the row says what's missing.
Where this sits in the benchmark
This page is one cell of a larger study: one tool, one scenario. Only this benchmark's frame appears here.
| Level | Name | Scope |
|---|---|---|
| Benchmark | Converting a complex PDF into clean Markdown with a hosted API → | 12 scenarios · 13 tools |
| Capability | Equations & Mathematical Notation → | |
| Scenario | A document containing mathematical equations → | |
| Tool | Adobe PDF Extract API → |
Global scenario definition → · Global capability definition →
History of this result
What has happened to this result since it was first published. Runs and grades are never overwritten: a retest or a re-grade publishes a new result and keeps the earlier one readable.
13 October 2026First publishedConverting a complex PDF into clean Markdown with a hosted API v1
Act on this result
Nothing filed here edits the run or the grade. A challenge opens a review, and a review can produce a new run or a re-grade — which becomes the current result and leaves this one in the history.
This matches what I see
You run the same kind of test against your own setup and get the same behaviour.
Agree →This does not match
Yours behaves differently. Tell us what you got, with a screenshot if you have one.
Disagree →Point out an issue
Something here is wrong — a reference value, a transcription, a grade.
Report an issue →We have fixed this
Tell us what changed and we schedule a rerun of the failing test case. The old result stays as history.
Vendor notice →Filed against this evidenceNothing yet. Challenges, counter-evidence and fix notices appear here with their outcome, and stay on the page after they are resolved.
Cite this result
aidemos.com/benchmarks/pdf-to-markdown-apis/results/adobe-pdf-extract-api/a-document-containing-mathematical-equations · 1 pass · 0 fail · coverage 1/1 · graded 2026-10-06
The same record is available as structured data through the AI Demos MCP server, with the counts, the coverage and every per-test-case reason carried as fields.
Verify the proof files
These files support this result. Open a file to inspect the original evidence.
Input · Document (PDF) ↗application/pdf · 236 KB
Proof 1 · Screenshot ↗image/png · 97 KB
Output file (Markdown) ↗text/markdown · 5 KB
Output file (JSON) ↗application/json · 52 KB
Proof 2 · Screenshot ↗image/png · 6 KB
Proof 3 · Screenshot ↗image/png · 15 KB
Proof 4 · Screenshot ↗image/png · 7 KB
Proof 5 · Screenshot ↗image/png · 15 KB
Proof 6 · Screenshot ↗image/png · 7 KB
Proof 7 · Screenshot ↗image/png · 5 KB
File fingerprints (SHA-256)
A fingerprint identifies the exact file used for this result.
Input · Document (PDF)f3d69b6d9d2191c5806a426fd4ea5e209dcd7cf693ad6abe67a5d18a014b9fd6
Proof 1 · Screenshot35ee74abff15c1c21df2351c5f1710896fcbdfbfab1a31af0197811a08b7a87f
Output file (Markdown)0ae1471f484a259697845a6503610937078eec182ee43a337d6fe8e7d009f6ff
Output file (JSON)429c603563dee6abe6f373bc4567d5e73e5ac848bc404e53aa1b73bc3cb27219
Proof 2 · Screenshotd0e4b094ae6f2f8c6ab0a36ae32893562c580134a8f51601407efc67fff873ab
Proof 3 · Screenshot768a3f54db924894785b7da6142f6d1dd21469eb835efcef7911dc70f4425a32
Proof 4 · Screenshot7164f4da9eb98b10028e6bb48a76bf8271b7e10b118a63631b814d6ffa66422f
Proof 5 · Screenshot3523146f44af8ed742dbbc99be5b38f4f84a9f3f24640dcf3708ae609c5c4fa9
Proof 6 · Screenshot6f988aff9592938804917ea5af1f5fffa27fd2f0ac5c2499d880a0df777d59a1
Proof 7 · Screenshot9e79ce7f1660b2adb331cfcb0490af41188b2b107b30f04356054e95f659a833