312gao_ea_2021gao_ea_2021.xmlLong-term, medium spatial resolution annual land surface phenology with a Bayesian hierarchical modelReference20218Xiaojie GaoRemote Sensing of Environmenthttps://doi.org/10.1016/j.rse.2021.112484Backlinks314ocs-0006ocs-0006.xmlDouble Logistic Greendown ModelNote2025320Logistic sigmoid function for modeling Phenology detailed in Elmore et. al 2011 & Gao et al. 2011. The function combines spring and autumn seasons into a single equation to account for the greendown phenomena by allowing for a gradual reduction of VI values in mid-summer. Typically the model is fit to all VI observations within a single year using maximum likelihood methods. where is the modeled VI value at time in terms of day of year (DOY) is a parameter vector controlling the shape of the double-logistic function. represents the mean VI value in the dormant period; represents the difference between VI value at time and the dormant mean; and are the inflection points that are commonly used to represent start-of-season (SOS) and end-of-season (EOS) dates in terms of DOY in the spring and autumn; and are the corresponding slopes of the VI trajectories in spring and autumn; is the “greendown” parameter that accounts for the VI greendown phenomenon in the mid-summer time.Given the set and , a single years phenology would be estimated by the following curve. {} m m}{ \path coordinate (#1nw) ++(#2,-#3) coordinate (#1se) coordinate (#1sw) at (#1se -| #1nw) coordinate (#1ne) at (#1nw -| #1se) ; \path[spath/save = #1north] (#1nw) to (#1ne); \path[spath/save = #1west] (#1nw) to (#1sw); \path[spath/save = #1east] (#1ne) to (#1se); \path[spath/save = #1south] (#1sw) to (#1se); } \usepackage{tikz, tikz-cd, mathtools, amssymb, stmaryrd} \usepackage{pgfplots} \usepackage{amsmath} \usetikzlibrary{matrix,arrows, patterns} \usetikzlibrary{backgrounds,fit,positioning,calc,shapes} \usetikzlibrary{decorations.pathreplacing} \usetikzlibrary{decorations.pathmorphing} \usetikzlibrary{decorations.markings} \tikzset{ desc/.style={sloped, fill=white,inner sep=2pt}, upright desc/.style={fill=white,inner sep=2pt}, pullback/.style = { append after command={ \pgfextra{ \draw ($(\tikzlastnode) + (.2cm,-.5cm)$) -- ++(0.3cm,0) -- ++(0,0.3cm); } } }, pullback 45/.style = { append after command={ \pgfextra{ \draw[rotate = 45] ($(\tikzlastnode) + (.2cm,-.5cm)$) -- ++(0.3cm,0) -- ++(0,0.3cm); } } }, ne pullback/.style = { append after command={ \pgfextra{ \draw ($(\tikzlastnode) + (-.2cm,-.5cm)$) -- ++(-0.3cm,0) -- ++(0,0.3cm); } } }, sw pullback/.style = { append after command={ \pgfextra{ \draw ($(\tikzlastnode) + (.2cm,.5cm)$) -- ++(0.3cm,0) -- ++(0,-0.3cm); } } }, dotted pullback/.style = { append after command={ \pgfextra{ \draw [densely dotted] ($(\tikzlastnode) + (.2cm,-.5cm)$) -- ++(0.3cm,0) -- ++(0,0.3cm); } } }, muted pullback/.style = { append after command={ \pgfextra{ \draw [gray] ($(\tikzlastnode) + (.2cm,-.5cm)$) -- ++(0.3cm,0) -- ++(0,0.3cm); } } }, pushout/.style = { append after command={ \pgfextra{ \draw ($(\tikzlastnode) + (-.2cm,.5cm)$) -- ++(-0.3cm,0) -- ++(0,-0.3cm); } } }, between/.style args={#1 and #2}{ at = ($(#1)!0.5!(#2)$) }, diagram/.style = { on grid, node distance=2cm, commutative diagrams/every diagram, line width = .5pt, every node/.append style = { commutative diagrams/every cell, } }, fibration/.style = { -{Triangle[open]} }, etale/.style = { -{Triangle[open]} }, etale cover/.style= { >={Triangle[open]},->.> }, opfibration/.style = { -{Triangle} }, lies over/.style = { |-{Triangle[open]} }, op lies over/.style = { |-{Triangle} }, embedding/.style = { {right hook}-> }, open immersion/.style = { {right hook}-{Triangle[open]} }, closed immersion/.style = { {right hook}-{Triangle} }, closed immersion*/.style = { {left hook}-{Triangle} }, embedding*/.style = { {left hook}-> }, open immersion*/.style = { {left hook}-{Triangle[open]} }, exists/.style = { densely dashed }, } \newlength{\dontworryaboutit} \tikzset{ inline diagram/.style = { commutative diagrams/every diagram, commutative diagrams/cramped, line width = .5pt, every node/.append style = { commutative diagrams/every cell, anchor = base, inner sep = 0pt }, every path/.append style = { outer xsep = 2pt } } } \tikzset{ square/nw/.style = {}, square/ne/.style = {}, square/se/.style = {}, square/sw/.style = {}, square/north/.style = {->}, square/south/.style = {->}, square/west/.style = {->}, square/east/.style = {->}, square/north/node/.style = {above}, square/south/node/.style = {below}, square/west/node/.style = {left}, square/east/node/.style = {right}, } \ExplSyntaxOn \bool_new:N \l_jon_glue_west \keys_define:nn { jon-tikz/diagram } { nw .tl_set:N = \l_jon_tikz_diagram_nw, sw .tl_set:N = \l_jon_tikz_diagram_sw, ne .tl_set:N = \l_jon_tikz_diagram_ne, se .tl_set:N = \l_jon_tikz_diagram_se, width .tl_set:N = \l_jon_tikz_diagram_width, height .tl_set:N = \l_jon_tikz_diagram_height, north .tl_set:N = \l_jon_tikz_diagram_north, south .tl_set:N = \l_jon_tikz_diagram_south, west .tl_set:N = \l_jon_tikz_diagram_west, east .tl_set:N = \l_jon_tikz_diagram_east, nw/style .code:n = {\tikzset{square/nw/.style = {#1}}}, sw/style .code:n = {\tikzset{square/sw/.style = {#1}}}, ne/style .code:n = {\tikzset{square/ne/.style = {#1}}}, se/style .code:n = {\tikzset{square/se/.style = {#1}}}, glue .choice:, glue / west .code:n = {\bool_set:Nn \l_jon_glue_west \c_true_bool}, glue~target .tl_set:N = \l_jon_tikz_glue_target, north/style .code:n = {\tikzset{square/north/.style = {#1}}}, north/node/style .code:n = {\tikzset{square/north/node/.style = {#1}}}, south/style .code:n = {\tikzset{square/south/.style = {#1}}}, south/node/style .code:n = {\tikzset{square/south/node/.style = {#1}}}, west/style .code:n = {\tikzset{square/west/.style = {#1}}}, west/node/style .code:n = {\tikzset{square/west/node/.style = {#1}}}, east/style .code:n = {\tikzset{square/east/.style = {#1}}}, east/node/style .code:n = {\tikzset{square/east/node/.style = {#1}}}, draft .meta:n = { nw = {\__jon_tikz_diagram_fmt_placeholder:n {nw}}, sw = {\__jon_tikz_diagram_fmt_placeholder:n {sw}}, se = {\__jon_tikz_diagram_fmt_placeholder:n {se}}, ne = {\__jon_tikz_diagram_fmt_placeholder:n {ne}}, north = {\__jon_tikz_diagram_fmt_placeholder:n {north}}, south = {\__jon_tikz_diagram_fmt_placeholder:n {south}}, west = {\__jon_tikz_diagram_fmt_placeholder:n {west}}, east = {\__jon_tikz_diagram_fmt_placeholder:n {east}}, } } \tl_set:Nn \l_jon_tikz_diagram_width { 2cm } \tl_set:Nn \l_jon_tikz_diagram_height { 2cm } \cs_new:Npn \__jon_tikz_diagram_fmt_placeholder:n #1 { \texttt{\textcolor{red}{#1}} } \keys_set:nn { jon-tikz/diagram } { glue~target = {}, } \cs_new:Nn \__jon_tikz_render_square:nn { \group_begin: \keys_set:nn {jon-tikz/diagram} {#2} \bool_if:nTF \l_jon_glue_west { \node (#1ne) [right = \l_jon_tikz_diagram_width~of~\l_jon_tikz_glue_target ne,square/ne] {$\l_jon_tikz_diagram_ne$}; \node (#1se) [below = \l_jon_tikz_diagram_height~of~#1ne,square/se] {$\l_jon_tikz_diagram_se$}; \draw[square/north] (\l_jon_tikz_glue_target ne) to node [square/north/node] {$\l_jon_tikz_diagram_north$} (#1ne); \draw[square/east] (#1ne) to node [square/east/node] {$\l_jon_tikz_diagram_east$} (#1se); \draw[square/south] (\l_jon_tikz_glue_target se) to node [square/south/node] {$\l_jon_tikz_diagram_south$} (#1se); } { \node (#1nw) [square/nw] {$\l_jon_tikz_diagram_nw$}; \node (#1sw) [below = \l_jon_tikz_diagram_height~of~#1nw,square/sw] {$\l_jon_tikz_diagram_sw$}; \draw[square/west] (#1nw) to node [square/west/node] {$\l_jon_tikz_diagram_west$} (#1sw); \node (#1ne) [right = \l_jon_tikz_diagram_width~of~#1nw,square/ne] {$\l_jon_tikz_diagram_ne$}; \node (#1se) [below = \l_jon_tikz_diagram_height~of~#1ne,square/se] {$\l_jon_tikz_diagram_se$}; \draw[square/north] (#1nw) to node [square/north/node] {$\l_jon_tikz_diagram_north$} (#1ne); \draw[square/east] (#1ne) to node [square/east/node] {$\l_jon_tikz_diagram_east$} (#1se); \draw[square/south] (#1sw) to node [square/south/node] {$\l_jon_tikz_diagram_south$} (#1se); } \group_end: } \NewDocumentCommand\SpliceDiagramSquare{D<>{}m}{ \__jon_tikz_render_square:nn {#1} {#2} } \NewDocumentCommand\DiagramSquare{D<>{}O{}m}{ \begin{tikzpicture}[diagram,#2,baseline=(#1sw.base)] \__jon_tikz_render_square:nn {#1} {#3} \end{tikzpicture} } \ExplSyntaxOff ]]>