Hydrographic Position Index (HPI)

MNiT@DNRbecause there are nine 1-meter grid cells for every one 3-meter grid cell.Therefore, the 1-meter resolution DEM has the potential for a greater amount ofelevation variability in localized areas of analysis using Focal Statistics. Forexample, LiDAR pulse returns hitting individual large rocks with high profiles indry ephemeral watercourse channels may obscure the ability of the FocalStatistics process to define the channel banks because the surface elevations ofthe rocks may negatively influence the mean value of the neighborhood analysis.4.5 NARROW NEIGHBORHOOD PARAMETERS Tool SettingsBy keeping the neighborhood analysis narrow, contrasting HPI values can occuron sharp planes defining topographic breaks representing banks and edges oflandforms that contain and convey water on Earth’s surface (e.g., channels andlake edges). Focal Statistics neighborhood shapes of circles and rectangles withsmall areas of analysis such as 3-cells by 3-cells proved to produce the mostconsistent and reliable HPI results for much of Minnesota’s landscape.4.6 HPI DEVELOPMENT Description and Loose Work Flow4.6.a FilterSome regions of analysis across Minnesota benefited from a low-passfilter. Although Low-pass filters are recognized as a “smoothing”technique and High-pass filters are recognized as “edge-enhancing”filters, both operate on a 3-by-3 cell window over the DEM. As aresult, a Low-pass filter traversing the detailed elevation values ofthe LiDAR-derived DEM successfully removed extreme neighborhoodelevations (e.g., erratic rocks on the landscape or in a dry channelwith high vertical profile and noise remaining from LiDAR pointclassification algorithms). Filtering techniques were used withcaution and at a minimum because some fidelity of the topographicbreaks beneficial to HPI development can be lost.Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201810of41

MNiT@DNRf ilter dem FILTER(sourceDEM,LOW , DATA)s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e dLOW L o w Pas s F i l erDAT A D AT A — Sp ec if i es t ha t if a N oD at a v a l ue ex is ts wit h i na n ei g hb or h oo d, t h e N oD at a va l ue wi l l b e i g nor e d. O nl yc e lls wi th i n t he n e i gh b or h o o d t h at ha v e d at a v a lu es wi l lbe us e d i n d et er m in i n g th e o ut p ut va l u e. T hi s is t h edef au l t.E q u a t i o n 1 - F I L T E R S yn t a x E x a m p l e ( r e g i o n a l w o r k u n i t s p e c i f i c a p p l i c a t i o n ) .4.6.b MeanElevation values of individual grid cells in the source DEM(dem 3m m) are passed into a unique overlapping neighborhoodkernel-calculation for each individual cell (processing cell) using theFocal Statistics tool with a Mean statistics operator.[ 16] Thisstatistics operation computes an output raster with new valuesrepresenting the arithmetic mean elevation value of all cells in theneighborhood analysis including the processing cell.nbrhd mean FOC ALSTATISTI CS(sourceDEM, {neighborhood}," MEAN","DATA")s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e d{n ei g hb or h oo d} us er d ef i n ed p ar am eter s .M E AN C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.DAT A D AT A — Sp ec if i es t ha t if a N oD at a v a l ue ex is ts wit h i na n ei g hb or h oo d, t h e N oD at a va l ue wi l l b e i g nor e d. O nl yc e lls wi th i n t he n e i gh b or h o o d t h at ha v e d at a v a lu es wi l lbe us e d i n d et er m in i n g th e o ut p ut va l u e. T hi s is t h edef au l t.E q u a t i o n 2 - M E A N N e i g h b o r h o o d F O C A L S T A T I S T I C S S yn t a x E x a m p l e .Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201811of41

MNiT@DNR4.6.3 DEM VarianceThe sample mean and source DEM variance is calculated bysubtracting the Focal Statistics resultant raster (nbrhd mean) fromthe source DEM (dem 3m m) using the MINUS tool.dem var iance MINUS(sourceDEM, nbrhd mean)s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e d{n ei g hb or h oo d} C a lc u l at e d i n eq u at i on #2 .nbr h d m ean C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.E q u a t i o n 3 M I N U S S yn t a x E x a m p l e .4.6.4 Standard Deviation Quantifying Elevation VariationComputing the standard deviation (STD) of the analysis neighborhoodis calculated with the same Focal Statistics neighborhood settings(i.e., {neighborhood}) used in calculating the MEAN (nbrhd mean).nbrhd stdd FOC ALSTATISTI CS( dem 3m m, {neighborhood},"STD","DATA")s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e d{n ei g hb or h oo d} us er d ef i n ed p ar am eter s .ST D C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.DAT A D AT A — Sp ec if i es t ha t if a N oD at a v a l ue ex is ts wit h i na n ei g hb or h oo d, t h e N oD at a va l ue wi l l b e i g nor e d. O nl yc e lls wi th i n t he n e i gh b or h o o d t h at ha v e d at a v a lu es wi l lbe us e d i n d et er m in i n g th e o ut p ut va l u e. T hi s is t h edef au l t.E q u a t i o n 4 - S T A N D A R D D E V I A T AI O N N e i g h b o r h o o d F O C AL S T A T I S T I C S S yn t a xExample.Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201812of41

MNiT@DNR4.6.5 HPI Normalization Data MassagingThe standard deviation values of “nbrhd stdd” can be used toperform a normalization on the source DEM raster (dem 3m m).This statistically teases out the influence of outlier elevation values;essentially dividing by the standard deviation is intended to scale themean towards “0” while maintaining the shape of the originaldistribution of the values.hpi nrmlz (“Sour ceDEM” – “meanDEM”) / (“nbrhd stdd”)orhpi nrmlz (“dem var iance”) / (“nbrhd stdd”)s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e dnbr h d m ean C a lc u l at e d i n eq u at i on #2 .dem va r i a nc enbr h d s t dd C a lc u l at e d i n eq u at i on #3 . C a lc u l at e d i n eq u at i on #4 .E q u a t i o n 5 - H P I N o r m a l i z a t i o n S yn t a x E x a m p l e f o r M a p C a l c u l a t o rCont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201813of41

MNiT@DNR4.6.6 Complete HPI Formulas Calculations SimplifiedThe preceding equations can be synthesized into simplified equationsin Map Calculator.hpi " sourceDEM " – FOC ALSTATISTI CS(sourceDEM,{neighborhood}, " MEAN","DATA")s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e d{n ei g hb or h oo d} us er d ef i n ed p ar am eter s .M E AN C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.DAT A D AT A — Sp ec if i es t ha t if a N oD at a v a l ue ex is ts wit h i na n ei g hb or h oo d, t h e N oD at a va l ue wi l l b e i g nor e d. O n l yc e lls wi th i n t he n e i gh b or h o o d t h at ha v e d at a v a lu es wi l lbe us e d i n d et er m in i n g th e o ut p ut va l u e. T hi s is t h edef au l t.E q u a t i o n 6 - H P I C o m b i n e d S yn t a x E x a m p l e f o r M a p C a l c u l a t o r .hpi nrmlz (“sourceDEM” – FOC ALST ATI STICS(sourceDEM,{neighborhood}, " MEAN","DATA"))/ FOC ALSTATISTI CS(sourceDEM,{neighborhood}, "STD","DATA")s our c e D EMDE M d em 3m m , M in n es ot a ’s p ub l is he d L i DA R - de r i v e d{n ei g hb or h oo d} us er d ef i n ed p ar am eter s .M E AN C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.ST D C a lc u l at es t he m ea n ( a v er ag e va l ue ) of t h e c e l ls i n th ene i g hb or ho o d.DAT A D AT A — Sp ec if i es t ha t if a N oD at a v a l ue ex is ts wit h i na n ei g hb or h oo d, t h e N oD at a va l ue wi l l b e i g nor e d. O nl yc e lls wi th i n t he n e i gh b or h o o d t h at ha v e d at a v a lu es wi l lbe us e d i n d et er m in i n g th e o ut p ut va l u e. T hi s is t h edef au l t.E q u a t i o n 7 - H P I C o m b i n e d S yn t a x E x a m p l e f o r M a p C a l c u l a t o r .Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201814of41

MNiT@DNR4.7 HPI DISSEMINATION PRODUCTS Efficiency Techniques4.7.1 Floating Point to IntegerPublication, dissemination and display efficiencies of statewidemosaicked data products can benefit from data massagingtechniques. One method is to scale the values from floating point to8bit-integer values (0 to 255) to make HPI rasters faster and moreresponsive for application.rescaled hpi (source hpi – min value f rom source hpi) * max scalevalue / (max value f rom source hpi – min value f rom source hpi) min scale values our c e D EMan d # 7. H PI r as t er s c a lc u la t ed f r om e qu a ti o n ’s # 6m in va l u e f r om s o ur c e h p i)3. 7 06 1) C a lc u l at e d r as t er s t at is tic ( e. g. ,m ax v al u e f r om s our c e h p i5. 8 55 8) C a lc u l at e d r as t er s t at is tic ( e. g. ,m in s c a l e v a l ue 0m ax s c al e va l u e 255–E q u a t i o n 8 - S yn t a x E x a m p l e f o r r e s c a l i n g f r o m f l o a t i n g p o i n t t o 8 b i t - i n t e g e r va l u e s ( 0 –255).4.7.2 Removing OutliersAnother method of scaling the HPI rasters is to truncate or clipextraneous values from the range of values. HPI values calculatedwith a localized Focal Statistic neighborhood typically fit within anarrow range spanning only several digits / – of zero. However,large HPI assemblages of mosaicked LiDAR-derived DEMs containtheir own unique outlier minimum and maximum values from actualelevation extremes and/or computation noise in the data. Thesevalues can make rendering the products difficult for distributionbundling and display applications. Since realistic HPI values forMinnesota rarely exceed values less than negative ten ( – 10) andgreater than positive ten ( 10), extreme values can be safelyCont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201815of41

MNiT@DNRreclassified without sacrificing HPI signature detail. This techniquefirst multiplies the floating-point data by 100 before scaling, whichtends to retain a majority of the detail of the original data. Next, aSpatial Analyst conditional if/else, evaluation statement (CONstatement) is used on each of the input raster cells.Con(" input hpi" 10, 10, Con(" input hpi " – 10, – 10, " input hpi "))i np ut hp i H PI r as t er s c a lc u la te d f r om eq u a ti o n ’s #6 an d # 7.E q u a t i o n 9 - S yn t a x E x a m p l e f o r r e s c a l i n g / r e c l a s s i f yi n g d a t a va l u e s - 1 0 a n d using a CON statement. 105. HPI COLOR SCHEME5.1 FIRE COLOR SCHEME BackgroundThe HPI color schematic is built on the widely distributed “Fire” symbology suiteof parameters developed by the author (see section 11, Fire Color Scheme Usedto Create the HPI Signatures). Although an abstraction to colors typicallyassociated with the cartography of terrain, this unique symbology relies on thewarm yellow and red hues that trend to black as a means to bring visual order tothe high and low elevations of localized landscapes. Additionally, yellow and redhues are used in the cartographic arena as colors that favor the mind’s eyeability to interpret depth. As a result, colored features ofthe HPI can appear as though they rise off the image. Theperception of depth is enhanced more by draping atransparent HPI over the DEM-derived hillshade.In the HPI, individual raster cells are colored through mapsymbology based on their positive and negative differencesto the surrounding neighboring cells. Dark cells of the HPIindicate localized negative differences defining localneighborhood topographic low elevations, while the yellowcells indicate localized positive differences illustrating highpoints in the terrain (e.g. local hills and road crowns).Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.usImage 2 – Fire ColorScheme Version: 6/1/201816of41

MNiT@DNR5.2 BLENDED HUES Red to Yellow and Red To Dark-red BlendsThese blends of the color spectrum within the Yellow to Dark Red color rampindicate areas of localized-consistent relief forming Local Zones of ElevationSimilarity (LzEs). Using the HPI as an illustration tool for exploitinghydrography features, the sharper contrasting colors of yellow and black tend tobe more valuable than the colors of the LzEs. Dark red to black linearsignatures in the HPI are chains of adjacent localized low cells; visually, thesedarker areas meld to form visible local drainage paths (LDP). Collectively, LDPform watershed-wide local drainage networks (LDN).5.3 YELLOW SIGNATURES Localized High PointsCells trending towards yellow in an HPI raster are zones of higher neighbor reliefthan cells or zones trending towards red, dark red and black, which indicatelower elevations. For example, roads and localized terrain peaks exhibit brighteryellow areas. However, that does not mean a hill with exceptional height existsat every zone of cells trending towards yellow hues. In image-3- right forexample, yellow areas of the HPI in an agricultural field match the lightly shadedareas on a digital orthophoto quadrangle (DOQ). Even at the localized fieldscale, each product is representing slight differences in elevation values that areinfluencing visual signatures from remote sensing technologies.Soil types with less moisture retention in localized relief tend to have lightercolor signatures. Therefore, the beige signatures in the DOQ (see image-3, left)represent areas of higher localized peaks of dryer soils. From the illustrations ofimage-3, we can see the correlation between the DOQ and HPI, validating theeffectiveness of the HPI signatures identifying localized topographic differences.Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201817of41

MNiT@DNRI m a g e 3 – L o c a l i z e d t o p o g r a p h i c h i g h e l e va t i o n s w i t h d r i e r s o i l s r e p r e s e n t e d i n t h e D O Qimage (left) as white signatures (colors) in the agriculture fields. The HPI represents thes a m e f e a t u r e s a s ye l l o w s i g n a t u r e s ( r i g h t ) .5.4 BLACK SIGNATURES Localized Low PointsAs the color blend signatures trend toward black in the HPI, the more anindividual cell’s elevation values are less than their neighborhood mean cellelevation values. Therefore, the blackest signatures indicate cells with valuessharply less than their neighborhood cells, which define localized elevationdepressions.Concentrations of cells with black symbology forming organized linear striationsindicate localized linear depressions (LLD). These LLD features form strongsignatures within the HPI raster representing incised topographic landforms onEarth’s surface that convey concentrated flow. From these signatures, we havegreater success identifying the head or start of concentrated flow on thelandscape (i.e. formation of channels, erosion headcut/knickpoints,). This visualpattern based on statistical neighborhood raster analysis enhances the ability todefine LDN.5.4.1 Key Topics for Consideration Related to HPI Black SignaturesLiDAR data captures the detail of Earth’s surface, how a technicianrepresents that detail in a derived DEM is influenced by theresolution of the DEM and symbology settings utilized for displayingthe data. For example, the black HPI signatures are independent ofmap scale and watershed scale; however, these signatures are DEMresolution dependent (i.e., 1-meter and 3-meter horizontaldimensions).Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201818of41

MNiT@DNRBlack signatures are helpful for identifying water conveyancelandforms that could be lost in techniques such as flow accumulationthreshold development and stream order classification.The black signatures give equal hydrologic significance to alltopographic landforms that convey water; there is no intention tocategorize watercourse features into perennial, intermittent, seasonalor ephemeral classifications from the HPI.Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201819of41

MNiT@DNRImage 4 - HPI Draped on a hillshaded DEM6. LOCALIZED WATERSHED INTERPRETATIONThe HPI allows the user to visualize the hydrology, and geomorphologyrelationships of Earth’s surface as a system of sub-watersheds and waterconveyance features, without having to conduct detailed hydrological analysis.For example, the localized highpoints on the HPI surface represented by colorstrending towards yellow allow the interpreters’ eye to visualize local drainagewatershed (LDW ) boundaries by visually connecting the high points of the HPIsurface (see Image-5). The HPI can also serve as visual backdrop for validationof hydro-terrain analysis derived watersheds.Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201820of41

MNiT@DNRImage 5 - Localized Watershed Interpretation7. CAST SHADOWS7.1 Hill-SHADED DEM DESCRIPTIONThe hill-shaded DEM [1] is the standard derived product used to bring asimulated 3-D visual perspective to the viewing environment. The hill-shadedDEM is a synthetic illumination of a surface based on the elevation value, slopeand aspect for each cell in a raster. This surface illumination is obtained bysetting a position for a hypothetical light source (modeled position of the sun)and calculating the illumination values of each cell in relation to its neighboringcells. The hypothetical light source is dependent on an azimuth and altitude toproject the simulated light source across the DEM landscape (see Image-6).Cont act: Sean Vaughn, MNiT @ MN DNR, sean. vaughn@state.mn.us Version: 6/1/201821of41

MNiT@DNRI m a g e 6 - E x a m p l e o f a 3 - m e t e r L i D A R - d e r i ve d H i l l - s h a d e d D E M .This derived hillshade DEM becomes the foundation for creating visuallyappealing relief maps that are benefi

Hydrographic Position Index (HPI): Description and Symbolization . Hydrographic Position Index (HPI) SEARCH TAGS. . topographic/terrain ruggedness index (TRI) [12] and topographic position index (TPI), [13][14]] the HPI is a special terrain ras ter dataset and color scheme developed by the author.