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Agricultural and Forest Meteorology 200 (2015) 9–20

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Agricultural and Forest Meteorology

j ournal homepage : www.elsevier .com/ locate /agr formet

An improved logistic method for detecting spring vegetation

phenology in grasslands fromMODIS EVI time-series data

Ruyin Caoa, Jin Chenb,c,∗, Miaogen Shend, Yanhong Tang a

a National Institute for Environmental Studies, Onogawa 16-2, Tsukuba, Ibaraki, 305-8506, Japanb State Key Laboratory of Earth Surface Processesand Resource Ecology, Beijing NormalUniversity, Beijing, 100875, Chinac College of Global Changeand Earth SystemScience, Beijing NormalUniversity, Beijing, 100875, Chinad Key Laboratory of Alpine Ecology and Biodiversity, Institute of Tibetan Plateau Research,Chinese Academy of Sciences,Beijing, 100101, China

a r t i c l e i n f o

Article history:

Received 13March 2014

Received in revised form 9 September2014

Accepted 14 September2014

Keywords:

Climate change

Green up

Inner Mongolia

Logistic fitting

Precipitation

Start of the growing season

a b s t r a c t

Satellite-derived greenness vegetation indices provide a valuable data source for characterizing spring

vegetation phenology over regional or global scales. A logistic function has been widely used to fit time

series of vegetation indices to estimate green-update (GUD),which is currently beingused for generating

the global phenological product from the Enhanced Vegetation Index (EVI) time-series data provided

by the Moderate Resolution Imaging Spectroradiometer (MODIS). In this study, we address a violation

of the basic assumption of the logistic fitting method that arises from the fact that vegetation growth

under natural conditions is controlled by multiple environmental factors and often does not follow a

well-definedS-shaped logistic temporal profile.We developed the adaptive local iterative logistic fitting

method (ALILF) to analyze the “local range” (i.e., the range of data points where the values in the time

series begin to increase rapidly) in theMODIS EVI profile inwhichGUD is found. The newmethod adopts

an iterative procedure and an adaptive temporal window to properly simulate the trajectory of EVI time

series in the local range, and can determineGUDmore accurately. GUD estimated by ALILF almostmatch

the date of the onset of the greenness increase well while the traditional logistic fitting method shows

errors of even more than 1 month in the same cases. ALILF is a more general form of the logistic fitting

method that can estimate GUD both fromwell-defined S-shaped time series and from non-logistic ones.Besides, it is resistant to a range of noise levels added on the time-series data (Gaussian noise with a

meanvalueof zero and standard deviations ranging from 0% to 15% of the EVI value). These advantages

mean ALILF may be widely used for monitoring spring vegetation phenology from greenness vegetation

indices.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Spring vegetation phenology refers to the onset of photosyn-

thetic activity, and is controlledbymultipleenvironmental factors.

Spring temperature has been widely accepted as the main factor

driving spring phenology in temperate forests (Piao et al., 2006,

Richardson et al., 2006), and spring precipitation is considered to

be a main driver for deserts and temperate grasslands (Cong et al.,

Abbreviations: ALILF, adaptive local iterative logistic fitting method; AVHRR,

advanced very high resolution radiometer; DOY, day of year; EVI, enhanced

vegetation index; GUD, green-update;MODIS, moderate resolution imaging spec-

troradiometer.∗ Corresponding author at: State Key Laboratory of Earth Surface Processes and

Resource Ecology, Beijing Normal University, Beijing, 100875, China.

Tel.: +86 13522889711.

E-mail addresses: [email protected], [email protected] (J. Chen).

2012;Shenet al., 2011). Other less obvious factors such asphotope-

riod (Partanen et al., 1998) also affect spring phenology. Recent

climate change, particularly spring warming, has greatly altered

spring vegetationphenology (e.g., Menzel et al., 2006; Jeong et al.,

2012). The changes in springphenologyareecologically important

because they strongly affect carbon cycling and energy balance

in terrestrial ecosystems (Chapin et al., 2008; Jeong et al., 2009;

Richardson et al., 2009). For instance,an earlier onset in springwas

found to be one of the main factors to increase the carbon sink

for northern hemisphere terrestrial ecosystems (Piao et al., 2008).

It is thus very significant to monitor spring vegetation phenology

to gain insights into linkage between phenology andclimate at the

largescale,whichis ahottopic inglobalchange research.Currently,

monitoring springphenologywith wall-to-wall spatial coverage is

only available based on satellite remotely sensed data.

Two main types of methods have been developed to determine

thetiming of springphenology from time seriesof satellite-derived

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10 R. Cao et al./ Agricultural andForestMeteorology 200 (2015) 9–20

Fig. 1. A schematic diagram of how the vegetation green-up date (GUD) can be

determined using the logistic fittingmethod,modified afterZhang etal. (2003). The

solid line indicatesthe fitted logistic curve,and thedashed line is therate of change

in curvature of the fitted logistic curve. GUD is defined as the first local maximum

of the dashed curve (i.e., point A), and the second local maximum (i.e., point B) is

identifiedas theonset of vegetationmaturity.The redline indicatesthe Local range

(i.e., the range where the vegetation index begin to increase rapidly) in the time-

series data in which GUD is found. (For interpretation of the references to color in

this figure legend, thereader is referred to theweb version of this article)

vegetation indices. The first type is threshold-based, and defines

spring phenology based on the date when a vegetation index

reaches a predefined threshold (i.e., an absolute threshold; Lloyd,

1990) or a specific percentage (e.g.,20% or50%) of itsannualampli-

tude (i.e., a relative threshold; White et al., 1997; Yu et al., 2010).

The second type of method commonly used focuses on changing

characteristics in the time series. This group of methods assumes

that vegetation growth follows a relatively well-defined temporal

pattern and can be fitted by a predefined mathematical function,

which isnormally considered tobea sigmoid function. Springphe-

nologicaleventscan then be identifiedfrom thefittedcurve (Fisher

and Mustard, 2007; Zhang et al., 2003, 2006). For example, Zhang

et al. (2003) used a four-parameter logisticmodel to simulate veg-

etation growthanddefined springphenologyas thedate when the

rate of change in curvature for the fitted curve exhibits the firstlocal maximum (Fig. 1).

All thesemethods, in general, adopt different rules todefine the

area-averagedgreennessonsetin spring, andthusremotely-sensed

springphenologyestimatedbydifferentmethods could differ con-

siderably (White et al., 2009). Zhang’s logistic method actually

captures the timingwhen vegetation greenness begins to increase

rapidly,which is represented by the green-up date (GUD) in Fig. 1.

This method has been widely used in regional and global pheno-

logy research (e.g., Shen et al., 2012; Zhang et al., 2004, 2006; Zhu

et al., 2012), and is currently being used for generating the global

phenological product based on the time series of the Enhanced

Vegetation Index (EVI) data provided by theModerate Resolution

Imaging Spectroradiometer (MODIS; Friedl et al., 2010; Ganguly

et al., 2010; MCD12Q2 User Guide; Zhang et al., 2003, 2006).The effectiveness of logistic methods is dependent on the

basic assumption that vegetation growth follows a well-defined

S-shaped temporal profile. In this study, we hypothesized that

determiningGUDfrom time seriesof a greennessvegetationindex,

especially in grasslands, would suffer from uncertainties in logis-

tic curve fitting due to the fact that the time series from spring to

summer does not necessarily follow an ideal sigmoid curve, and

sometimesmay deviate greatly from this curve. Violation from the

ideal S-shaped growth curve occurs quite often, because natural

vegetation does not grow under ideal conditions, but is instead

affected by a range of environmental stresses (e.g., climate, insects

or diseases)at various times. In temperategrasslands, forexample,

grass growth can be greatly interfered by drought events, because

herbaceous plants usually have underdeveloped root system

Fig. 2. Time seriesfor MODIS enhanced vegetation index (EVI)and thedetermined

GUD (the first localmaximum in the rate of change in curvature) in 2007 (A) and

thecorresponding temporal precipitation in 2007 (B). TheMODISEVI time seriesin

2003 and2005 (C), andthe fitted logistic curve(solid line) andthe determined GUD

in 2003 and 2005 (D). Panel (E) shows the mean air temperature and cumulative

precipitation during thegrowingseason (from Juneto August) and in thepreseason

period (fromNovember of the previous year through April of the current year) for

2003 and2005.Note: Alldata representspatially average data for100×100MODIS

pixels around the Xilinhot weather station, Xilin Gol, Inner Mongolia (43.57◦N,

116.07◦E),which is indicatedas thedashed line boxin Fig. 5. Source of climate data:

ChinaMeteorologicalData SharingServiceSystem(CMDSSS,http://cdc.cma.gov.cn).

comparedwith shrubs and forests and are less resistant to the lackof available soil water (Liu et al., 2013; Zhou et al., 2013). Fig. 2A

illustrates this problem: MODIS EVI time-series data collected in

the Xilin Gol grassland exhibited an obvious two-stage greenness

increase inthe springof 2007.Vegetationgrowth stalled inthemid-

dleof this season(fromapproximatelydayofyear (DOY)140 toDOY

180) due to a lack of precipitation during this period (Fig. 2B). Fit-

ting this time series by Zhang’s logisticmethod (hereafter referred

to as the traditional logistic fitting) only tends tomodel theoverall

growth pattern but miss the “local range” (i.e., the range of data

points that occur around the onset of EVI increase) in the time

series (Fig. 2A). Effects of non-ideal logistic vegetation growth on

GUDdeterminationare further illustrated in Fig.2C andD, inwhich

the difference in the determined GUD is asmuch as 23d between

2003 and 2005. For the two years, an almost identical trajectory

http://cdc.cma.gov.cn/

http://cdc.cma.gov.cn/



R. Cao et al./ Agricultural andForestMeteorology 200 (2015) 9–20 11

in the EVI time series in the local range suggests that greenness

onsetwasnearlyconcurrent (Fig. 2C). In this example, theproblem

arises from precipitation-induced variations in greenness during

the later period of vegetation growth (from Jun to Aug; Fig. 2E).

Such summerEVIdifference strongly affects the traditional logistic

fitting and leads to a large difference in the GUD determined from

this fitting. Therefore, we shouldpaymore attention to analyze the

local range in the time series inwhich GUD is found.

In this study,we developedan improved logisticmethod,which

we refer to as adaptive local iterative logistic fitting (ALILF), to

improve estimates of GUD from MODIS EVI time-series data. The

ALILF method can address violations of the assumption of sim-

ple S-shaped growth in natural environments, and can determine

GUDmore accurately at the date of the onset of increase inMODIS

EVI. We first present the ALILF method and then provide inter-

comparisons between ALILF and the traditional logistic fitting

method.We didnot evaluate ALILF GUDwith groundobservations

of spring phenological metrics (e.g., bud break or leaf expansion)

because of their different phenological definitions and the incom-

patible spatial scale (i.e., the few plant individuals vs. a pixel

standing for a large area).

2. Methodology

Different from the traditional logistic fitting method, the ALILF

methodmodifies the fitting procedure to closely simulate the tra-

jectory of the MODIS EVI time series in the local range around the

onset ofEVI increase (Fig. 1). Thenewmethodemploys an iterative

technique and an adaptive window and is able to estimate GUD

fromboth logistic andnon-logistic time series. There arefourmain

steps to implement the ALILF method (Fig. 3). We show details of

each step in the Sections 2.1–2.4 and provide the pseudo-code of

the new method in the Appendix A.

2.1. Step1: pre-processing of the MODIS EVI time series

We collected the raw MODIS data, which were used to pro-

duce the Collection 5 MODIS phenological product (MCD12Q2),from the website of the National Aeronautics and Space Admin-

istration (http://reverb.echo.nasa.gov/reverb). First, we generated

raw time-series EVI values from the composited 8-day nadir

bidirectional reflectance distribution function (BRDF)-adjusted

reflectance 500m resolution data (MCD43A4; Schaaf et al., 2002).

We then employed the BRDF-albedo quality product (MCD43A2)

to remove EVI values contaminated by the presence of snowor ice

from the raw time series. Assuming that vegetation is biologically

inactive at low temperatures, we used the land surface tempera-

ture product (MOD11A2; Wan et al., 2002) to remove winter EVI

values forwhich thetemperaturewaslower than 0 ◦C. This process

can account for cases in which the data quality label (MCD43A2)

fails to identify snowor ice.Wefilled the resulting gaps in the time

series by linear interpolation,anduseda three-pointmedian-valuefilter tosmooththe timeseries (MCD12Q2User Guide;Zhanget al.,

2006).

2.2. Step2: modeling the general pattern of the MODIS EVI time

series

Although vegetation growth in natural environments does not

follow an ideal sigmoid curve, it nonetheless exhibits a general

growth pattern in which the vegetation starts to grow in early

spring and reaches its full bloom in summer (Fig. 2). Thus, we used

a logistic model to simulate this general pattern with the goal of

obtaining somepreliminary information about vegetationgrowth.

To simulate vegetation growth, we first determined the time

period in which EVI exhibited a sustained increase, and used this

Fig. 3. Flowchart for the adaptive local iterative logistic fitting (ALILF) method.

NBAR: nadir bidirectional reflectance distribution function (BRDF)-adjusted

reflectance.

period for curve fitting (Ganguly et al., 2010). In practice, the tran-

sition forEVI from increasing todecreasing trendwas identifiedby

a change from positive to negative linear slopeusing thefive-point

movingwindow.Twocriteriawere further adopted toexclude spu-

rious transitions in the EVI time series: the maximum value in the

identified period should exceed 70% of the annual maximum EVI,

and the change in EVI within the identified period exceeded 35%

of the annual amplitude of the change in EVI. We then applied

Zhang’s four-parameter logistic equation to the EVI time series in

the identified period (Zhang et al., 2003):

EVI(t ) =c − d

1+ exp(a+ bt ) + d (1)

where t is the DOY. The parameter c in Eq. (1) is slightly modified

compared to that formulated by Zhang et al. (2003). In the present

equation, c and d indicate the maximum and background EVI val-

ues, respectively, and a and b control the shape of the curve. In the

non-linear least-square curve fitting, we constrained the parame-

ter c to be EVITP (EVI at the transition point, Fig. 4A) plus orminus

10% (i.e., EVITP±0.1EVITP, which we will discuss in Section 4.1).

We did not constrain parameter d in this fitting because of prob-

able contamination of the background EVI observations by noise.

Through the constrained non-linear curve fitting, we first gained

thefitting valuesfor theparameters c and d, hereafterreferredto as

c f and df , which characterizetheannualamplitudeof thechange in

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Fig.4. A schematicdiagramshowing (A)determinationof the localwindowand(B)

the two criteria (cases 1 and 2) for convergence for ALILF, see Sections 2.3 and 2.4

for details.

vegetationgreenness.We thenestimatedGUDfromthefittedcurve

basedonthefirst localmaximum intherateof changein curvature,

andthisGUDestimate isdeemedas theinitialGUD. Theobtainedc f ,

df and the initial GUD provide the basis for refining GUD estimates

in subsequent steps.

2.3. Step3: iterative logistic fitting in the local range

We developed an iterative logistic fitting technique to further

adjust thevegetation growthsimulation. This methodensures that

the fitted curve captures the annual amplitude of the change in

greennesswhile also providing a better simulation of thepoints in

the local range where EVI begins to increase rapidly.

Specifically, we first defined a local window consisting of

nine consecutive EVIobservations (approximately a 2-month time

span), with four points on either side of the initial GUD (Fig. 4A).

We then used Eq. (1) to fit only EVI data in the local window by

implementing a constrained non-linear optimization algorithm. In

the fitting, parameter c was fixed at the value of c f and parameter

dwas constrained to bewithin the range of df ±0.2(c f −df ). In this

manner, a new GUD is determined from the fitted logistic functionfor the local range. Based on the newly determined GUD, a new

nine-point local window can be defined, and Eq. (1) is used again

to fit EVI data in the new window. This process is repeated. Dur-

ingthis iterativeprocess, it probably encounters theexceptionthat

there are less than four points on one side of the determined GUD

when GUD is determined approximately at either end of the iden-

tified timeperiod. For this case, we require that at least two points

should be found on either sideof the determinedGUD for the local

fitting (i.e., at least seven points in the local window). Otherwise,

we employed all points within the identified time period for the

fitting.

The iterativeprocess is continuing, andgradually, thetrajectory

of the EVI time series in the local window tends to become consis-

tent with the fitted logistic curve around the position of max rate

of change in curvature. In other words, the determined GUD con-

verges on the date of the onset of the increase in EVI. Two possible

conditions indicate that the iteration should end: the determined

GUD stops changing between consecutive iterations (Fig. 4B, case

1);or thesameGUDbeginto reappearafter several iterations, lead-

ing to oscillation between the two values with a certain period

(Fig. 4B, case 2). In practice, the iteration is convergent because

there is a finite total numberof differentnine-point localwindows

for a given growing season. We discuss the influence of the ini-

tial GUD on the iteration as well as the effect of the parameter

constraint further in Section 4.1.

2.4. Step4: determining the final GUD from an adaptive local

window

For the two cases of convergence, we adopted different strate-

gies to determine the final GUD.

When the iteration converges on a final value, we defined the

final GUD as the convergence value, which depends on the fitting

for ninepointsin the localwindow(Fig.4B, case1). This caseis nor-

mally encountered when there is an obvious increase in EVI in the

local range. However, when there is a less obvious increase in EVI

within the local rangedue tonoisy data, this can induce oscillationbetweentwoGUDvaluesduringtheiteration.Inthiscase,wedefine

an adaptive local window that includes the four points below the

minimum GUD, the four points above the maximum GUD, and the

pointsin theoscillation(Fig.4B, case2). ThefinalGUDisthusdeter-

mined by fitting EVI points in this larger window. How to end the

iteration depends on the quality of the EVI time-series data in the

local range. The ALILF method can flexibly adjust the width of the

local windowusing this adaptive technique and is therefore resis-

tant to a range of noise levels, as we will demonstrate in Section

4.1.

Before exporting thefinal GUD, we used an additional criterion

to filter theresults (the decisionpoint labeled “condition” in step 4

of Fig. 3). We assumed that the time interval between GUDand the

timingof vegetationmaturity (i.e.,the time periodbetweenA andBshown inFig. 1) shouldbe at least 1month(i.e., approximately four

EVI observations). If this condition was not met, we employed the

initial GUD as the final output. This constraint was used to ensure

that if the final GUD was determined by fitting the local range of

time series, EVI points after the maturity date cannot be included

in thefitting. Forsiteswith anunusuallyshortgrowing season(e.g.,

alpine desert), this constraint maybemore frequently met.

2.5. Application

We evaluated the ALILF method by applying it to estimate GUD

in the Xilin Gol grassland from MODIS EVI time-series data dur-

ing 2002–2010. The Xilin Gol region is located in Inner Mongolia,

China, and covers an area of 230,000km2, stretching from 41.5◦Nto 46.9◦N and from 111.2◦E to 119.9◦E (Fig. 5). In this region, the

annualmeanair temperature is2.4◦C andtheannualmeanprecipi-

tationrangesfrom250 to350mm,mostofwhichfallsbetweenMay

andSeptember(Zhuoet al., 2007). Precipitation showsawestward

decreasing trend in the spatial distribution, ranging from above

400mm in the eastern region to below 150mm in the western

region. Grasslands dominate Xilin Gol with steppes andmeadows

distributed in the central and eastern areas and desert steppes in

the western region, as is indicated by the 1:1,000,000 vegetation

map of China (Environmental and Ecological Science Data Center

for West China, http://westdc.westgis.ac.cn). Spring phenology of

Xilin Gol grassland was controlled by both temperature and pre-

cipitation (Yu et al., 2003; Liu et al., 2013) and water availability

was shown to have stronger influences (Liu et al., 2013).

http://westdc.westgis.ac.cn/





Fig. 5. Location of the Xilin Gol grassland of China’s Inner Mongolia Autonomous

Region, and distribution of the main vegetation types in Xilin Gol. Source of the

vegetation data: http://westdc.westgis.ac.cn(inChinese), see thetext fordetails.

Before applying the ALILF method, we followed Shen et al.

(2014) and adopted three criteria to exclude some EVI time-series

data in this region due to the lack of vegetation and seasonality.

ALILF was not implemented if any of the following situations was

encountered: (1) the annualmaximum of EVI did not occur within

June–September; (2) the average EVI from July to September was

smaller than0.08,and(3) this averagewassmaller than1.2times of

the background EVI (i.e., the average EVI beforeApril of each year).

3. Results

Fig.6 presents theperformanceoftheALILFmethod forthethree

EVItimeseriesshowninFig.2. Ingeneral,thefittedcurvesshoweda

good ability to simulate thechanging characteristicsof EVIfor localrange inall three years. The GUDwere found tobedetermined reli-

ably at thedateof theonsetofvegetation greennessafterourvisual

inspection of thegraphs (dotted blue lines in Fig. 6A–C). Thediffer-

ence inGUD between 2003and 2005decreased from23d (Fig. 2D)

to 10 d (Fig. 6A and B), which suggests that the ALILF method

was able to account for the influence of inter-annual variations in

greenness on theGUDdetermination. Furthermore, unlike the tra-

ditional logisticmethod, theALILFmethodwas able to address the

precipitation-induced two-stage vegetation growth curve in 2007

(Fig. 6C). To obtain the final GUD, we performed curve-fitting four

times in a nine-point window for the 2003 time series and found

that GUD converged on a fixed value. For EVI curves in 2005 and

2007, however, the iteration showed oscillation without conver-

gence, so the width of the fittingwindowwas adaptively adjustedto include 10 EVI observations.

Fig. 7 compares the regional distribution of GUD determined

using the ALILF method and the corresponding MODIS phenology

product (MCD12Q2). A general spatial trend of increasing GUD

moving from southeast to north and northwest can be seen for

both ALILF and the MCD12Q2 product, which is geographically

consistent with known spring phenological events in theXilin Gol

grassland (Li et al., 2013; Wang et al., 2006). This spatial pattern of

GUD, however, also exhibited some differences between years. It

generally had later GUD in 2006, which was probably due to the

low temperature and the utter lack of precipitation before DOY

120 (Figs. S1 and S2). GUD in 2009 showed less obvious westward

increasing trend and vegetation turned green almost before May,

which might be explained by the abundant precipitation during

March-April across the entire region (Fig. S2). GUD in 2010 were

mainlytakenplacefromlatelyAprilto earlyMay,and thiswasprob-

ably causedby theextremely lowtemperatureduringMarch–April

(Fig. S2)and thegreatest increase in temperature fromApril toMay

for this year (Fig. S3).

Theabsolute difference between ALILFGUDandMCD12Q2 (i.e.,

|difference| in Fig. 7) were usually within 1 month, and there was

no specific spatial pattern for this difference. The largest GUD dif-

ferences occurred in thewest, central part or northeastof XilinGol

for different years. We identified two sub-regions with high val-

ues of |difference| in 2002 and 2007 and further analyzed them

in Figs. 8 and 9, respectively. The comparisons for the sub region

of 2002 showed that ALILF GUD was more continuous in terms of

the spatial distribution; ButMCD12Q2 was quite fragmented with

abrupt changes of GUD within short spatial distances (Fig. 8 A and

B), which is impossible for phenology of natural vegetations. We

additionally visually checked the land cover of this sub region for

the same year by a high-spatial-resolution satellite image (Landsat

TM), and excluded the possibility of cropland in this sub region.

So the discontinuous spatial distributionofMCD12Q2 appeared to

be inconsistent with the reality. The histogram of GUD revealed

the difference between the two methods. A very small number of

pixels turned green before April estimated by the ALILF method,

whereas more than 20% of pixels had GUD inMarch for MCD12Q2

(Fig. 8C).We further calculated the average EVI time series aswell

as theaverage GUDplus thestandarddeviations, for allpixelswith

GUD estimations within the range of DOY [60,90] fromMCD12Q2

but outside this range when using the ALILF method (Fig. 8D). The

investigations showed that ALILF GUD matched the date of the

onset of greenness increase better than MCD12Q2. Similar analy-

ses for another sub region located in the central part of Xilin Gol in

2007 also indicatedtheabilityofALILFtocapturetherealgreenness

onset in regional applications (Fig. 9).

We present the performances of the ALILF method and the tra-

ditional logistic fitting for some representative EVI time series. It

includesa serieswithawell-definedEVItemporal profile(Fig. 10A),

a series with background EVI contamination due to snow and ice

(Fig. 10B), several series with one or more disturbances of EVI inthelatergrowth periodafterGUD(Fig. 10C–E), andserieswith poor

data quality in the local range (Fig. 10F and G). The ALILF method

bettersimulated thetrajectoryof time-seriesdata inthelocalrange

and captured greenness onset effectively in all cases. In contrast,

performancesof the traditional logistic fittingwere unstable and it

lost efficiency in some caseswith non-logisticgrowthornoise con-

taminations. The newmethod appeared to demonstrate an ability

to resist data noise of EVI time series. For instance, for the casesof

noisy time series with a less obvious local range in Fig. 10F and G,

the ALILF method adaptively enlarged the windowwidth and was

also able to estimate a reasonable GUD.

It is also noteworthy that it seems somewhat arbitrary to iden-

tify thesustainedperiodofincreasingEVIforlogisticfittingby using

thefive-point movingwindow technique (Ganguly et al., 2010). Inthe example of vegetation growth with two stages (Fig. 10H), the

transitionpointwouldprobably be identifiedat thelocalmaximum

during the first stage or at its annual maximum (Fig. 6C). As we

expected, thereis nouniversalempiricalcriteriontoperfectly iden-

tify the lengthof thesingle growing seasonparticularly in regional

applications. The identification errors are thus inevitable for some

pixels andprobablyled touncertainties inGUDestimationbasedon

the traditional logistic fitting. However, such errors seemto affect

ALILF less because of the new fitting principle (Figs. 6C and 10H).

For example, if the transition is identifiedat the annualmaxima in

Fig. 10H, GUDestimatedbytheALILFmethod variedlittle (DOY120

vs. 119; Fig. 11) but the traditional logistic fitting showed a large

variation (DOY 92 vs. 119), suggesting the advantage of the new

method in being able to resist period identification errors.






Fig. 6. (A–C) The fitted curves (blue solid curve) and final determined GUD (blue dashed vertical lines) by using the ALILF method to analyze the three EVI time series in

Fig. 2. The right columnshowsthe corresponding process of iterations (blue solid polylines) in using theALILF method. (For interpretation of thereferences to color in this

figure legend, thereader is referred to theweb version of this article)

4. Discussion

4.1. Performances and advantages of the ALILF method

We developed and applied the ALILF method to determine

GUD using data for the Xilin Gol grassland of Inner Mongolia.This method is conceptually improved because it compensates

for an invalid assumption used in the traditional logistic fitting

method. As the examples described in the results section show,

the EVI time series is often far from a simple S-shaped pattern

because environmental factors,mainly temperature andprecipita-

tion,control vegetationgrowth undernatural conditions. Although

the air temperature usually follows an S-shaped temporal profile

(Villegas et al., 2001, Zhang et al., 2003), precipitation events are

often temporally unpredictable, which can greatly affect growth

trajectories in a grassland (Fig. 2). To demonstrate the effects of

precipitation on grass growth, we further investigated the rela-

tionshipbetweenvegetationgreennessduring growing season and

concurrent temperature and precipitation around all nine mete-

orological stations in the Xilin Gol grassland (Fig. S1). We found

that precipitation greatly increase EVI and has much stronger

effects on EVI than temperature (Fig. S4), which suggests that the

vegetation growthcanbe strongly affected or even stall when pre-

cipitation is lacking and thus precipitation-driven grassland such

as Xilin Gol is likely to exhibit non-logistic patterns of growth.

To address deviations from the S-shaped growth curve, the ALILF

method adopts an iterative technique and the use of an adaptive

window. Therefore, ALILF is a more general method that has an

improvedabilityto estimateGUDfromboth timeserieswitha well-

defined S-shaped curve and time serieswith non-logistic patterns

(Figs. 6–10).

Since ALILF is based upon logistic fitting of the local range,

one concern might be whether the method is much more sensi-

tive to noisy EVI data. To address this concern, we conducted a

simulation experiment to quantify the effects of different noise

levels on the method’s performance. To do so, we added random

Gaussian-distributednoise,withamean valueof zero andstandard

deviations ranging from 0% to 15% of the EVI value, to an ideal

logistic curve with a true GUD at DOY 120 (Fig. 12A). We consid-

ered twoscenarios in thesimulation experiment. In scenario 1, thetime seriesoutside the local range isperturbedby noise.Weaim to

examine whether the true GUD can be estimated from these noisy

timeseries, byusingboththe traditional logisticfittingandALILF. In

scenario 2, EVIwithin thelocalrangeis perturbedby noise.Because

a highernoise level indicatesa less obvious changing characteristic

for the local range, this scenario is designed to examine how the

width of local window in the ALILF method is related to the noise

level. To obtain a credible result, we repeated the simulation 100

times at each noise level.

In scenario 1, we calculated the absolute difference ( AD)

between GUDestimations and the true GUD, and found increasing

AD with noise levels for both ALILF and traditional logistic fitting

(Fig. 12B). There was no significant difference for AD from both

methods at low noise levels (P >0.01, two independent samples t -

test),whereas at highernoise levelsof 10%and 15%, AD of theALILF

method was significantly smaller than that of traditional logistic

fitting (P <0.01). It suggests that the new method is not more sen-

sitive to noisy data compared with the traditional logistic fitting

method. In scenario 2, the width of the local window in the ALILF

method is found to increase from 9 tomore than 13 points as the

noise level increases from0% to15%,which shows a significant lin-

ear positive correlation (R2 =0.96, P <0.01; Fig. 12C). This confirms

that the width of local window can be adaptively adjusted accord-

ing to the quality of the EVI time-series data in the local range. This

adaptive technique ensures the practicability of the ALILF method

for noisy time series. Without this technique, it would be difficult

toapply thenewmethodto noisy time-seriesdata, especiallywhen

there is high noise in the local range.




Fig. 7. Spatial distributions and statistical histogram of GUD estimations using the ALILF method and those obtained from the MODIS Land Surface Phenology Product

(MCD12Q2) from 2002 to 2010 forthe Xilin Golgrassland of China’s InnerMongolia Autonomous Region. Therightmost columnshows theabsolutedifference (|difference|)

of the two GUDestimations for each year. Twosub regions with large differences in 2002 and2007 areindentified.

Another advantage of the ALILF method is that it is less affected

by period identification errors (Fig. 11). We need to employprede-

fined criteria to identify the timeperiodof increasing EVI for curve

fitting. However, anycriteria aredefinedempirically andcertainly,

they arenotuniversally applicable. TheALILFmethod is tolerant to

this error to someextent because of its fitting in the local range of

time series, which further suggests the robustness of the method

for regional-scale application.




Fig. 8. The spatial distribution of GUD for the sub region of 2002 estimated fromMCD12Q2 (A) and from the ALILF method (B). The statistical histogram for the two GUD

estimations (C), and (D) the average EVI time-series data (circle) and the average GUDplus thestandard deviations, for all pixelswith GUDestimationswithin the range of

[60,90] fromMCD12Q2but outside this rangewhen using theALILFmethod.

TheALILFmethodadoptsa constrainednon-linear least-squares

fitting in its implementation (Fig. 3). It is reasonable to constrain

the parameter c in Eq. (1) to obtain an ecologically meaningful

maximum EVI. However, an accurate c value is not necessary in

the ALILF method because the method focuses on the changing

characteristics of EVI in the local range, so its estimates of GUD

are less sensitive to the c value. Therefore, we constrained c to be

within 10% of the EVI value at the transition point in step 2, and

fixed the estimated c f in step 3. In a similar manner, the ALILF

method constrains parameter d to be df (the fitted initial value

of d produced in step 2), plus a variation of 20% in (c f −df ) inthe fitting. This guarantees that the curve-fitting from the ALILF

method captures the annual amplitude of the change in greenness

while also accounting for some noise values in thebackground EVI

(Fig. 10B). However, the ALILF method does not make efforts to

improve thepre-processingonnoiseEVI, such as thesnow/ice con-

tamination in thebackgroundEVI andcloudcontaminationleading

to gaps in the time-series data. Although a number of methods

have been developed to filter noise and to reconstruct vegeta-

tion indices (e.g., Jönsson and Eklundh, 2002; Chen et al., 2004),

we used the simplest linear interpolation to fill gaps in the EVI

time series. Our investigations showed that in grasslands, tempo-

ral profile of EVI could inherently exhibit various shapes including

the two-stage increase in greenness. So we should take caution

when using a predefined filter (e.g., Gaussian filter; Jönsson and

Eklundh, 2002) to construct time series data. Without a prioriknowledge of vegetation growth, we recommend using the lin-

ear interpolation to fill gaps. Nevertheless, large errors could be

expectedoncenumbersofconsecutiveEVIaremissing (Zhangetal.,

2009).

Fig. 9. (A–C) Similar to Fig.8 butfor thesub regionof 2007. (D)The average EVItime-series data (circle) andthe average GUDplus thestandard deviations, forall pixelswith

GUD estimationswithinthe range of [60,75] fromMCD12Q2 butoutside this rangewhen using theALILFmethod.




Fig. 10. Applying theALILFmethodand thetraditional logistic fitting to some representativeMODIS EVI time series to estimate GUD. Each panel includes an enlargedview

of the local range aroundthe determined GUD. WW:thewidthof local windowused by ALILF.

Finally, we suggest that the accuracy of GUD estimation using

ALILF would be less affected by the initial GUD because of the iter-

ative procedure and the parameter constraints used in the fitting.To support this belief, we conducted a simulation experiment.We

first assumed that the initial GUD varied within 1 month before

or after the final determined GUD for the three EVI time series

in Fig. 6. We then used the ALILF method to estimate GUD. The

results confirm that the final determined GUD is independent of

the initial GUD despite the use of different numbers of iterations

(Fig. 13). Thenumberof iterations usually increases (e.g. from four

to eight in 2007), with an increasing difference between the initial

and final determined GUD. Therefore, a more accurate initial GUD

could improve thecomputational efficiency. Atpresent,we recom-

mendgenerating the initial GUD in the way described in this paper

for estimation of regional GUD using the ALILF method.

4.2. Applicability of the ALILF method

We used the ALILF method to analyze MODIS EVI time-series

data. This source of data is considered tobeof highquality because

theeffects of clouds, viewingangles, andatmosphericaerosolshave

been greatly minimized (Huete et al., 2002; Schaaf et al., 2002). In

practice, the ALILFmethod canbe also applicable to other satellite

time series, such as the longer recordof thenormalized-difference

vegetation index (NDVI) time series provided by the Advanced

VeryHighResolutionRadiometer (AVHRR).However,AVHRRNDVI

time series may suffer from low data quality due to the fact that

the AVHRR sensors were not originally designed for vegetation

monitoring and their near-infrared bands cover an atmospheric

water vapor absorption feature (Cihlar et al., 2001; Yuet al., 2013).

Recent studies found that low dataquality of AVHRR NDVI leads to

Fig. 11. Applying the ALILF method and the traditional logistic fitting to the time

series in Fig. 10Hwhen thefitting periodis determined to be from thebeginning to

theannual maximum EVI.

detection of a false decadal trend in GUD in the Tibetan grassland

(Yu et al., 2010; Zhang et al., 2013). Therefore, we recommend

applying the ALILF method to the more advanced MODIS EVI

data and potentially its heritage provided by Visible/Infrared

Imager/Radiometer Suit (VIIRS) instrument onboard the S-NPP

satellite (Vargas et al., 2013), which enable monitoring of vege-

tationphenology continuously at the global scale.

Although MODIS EVI products have improved the spatial res-

olution to 500m, a MODIS pixel potentially represents a mixture

of plant species that might have substantially different phenology,

and this variation poses a challenge to defining a representative

GUDwithinagivenpixel.A fewstudieshavesuggestedthatin some




Fig.12. (A)An ideal logistic curve(thefittedcurve in Fig. 6A) with a true GUDat DOY120 used forthenoisesimulationexperiment.Noise wasapplied tothe time-seriesdata

outside the localrange (scenario 1) or only to the local range (scenario 2). (B) In scenario 1, the absolute error between GUD estimation and the trueGUD (themean value

plus the standard deviation for 100 random iterations) at different noise levels. * indicates a significant difference of the absolute error between ALILF and the traditional

logistic fitting (P <0.01, two independent samples t -test). (C) In the scenario 2, the relationship between the width of the local window used in the ALILF method and the

noise level.

forests, theremight bea large phenologicaldifference between the

understory shrubs and grasses, and the overstory canopy (Badeck

et al., 2004; Richardson and O’Keefe, 2009), and this can confuse

remotelysensedsignalsandaffectGUDdeterminations.At present,

none of theexistingmethods (including ALILF) cansolve this issue.

For such complex scenes, it would be more meaningful to find

ways to discriminate among different spring phenological events

for different species by decomposing the time-series data. Such ananalysis is beyond the scope of this study, and will be explored in

our future phenological research.

Our study highlighted the importance of carefully considering

characteristics of vegetation growth when estimating phenology

from time-series data by logistic fitting. Several recent studies also

noticed this issue andhave improved simulations of time-series of

vegetation indices to better estimate phenology (Che et al., 2014;

Elmore et al., 2012). As satellite-derived vegetation phenology has

been increasinglyused by theresearchcommunities of globalecol-

ogyandclimate change,wecall formoreattentiontothe phenology

detection for various ecosystems to provide reliable data basis for

ecological applications.

4.3. Conclusions

Non-ideal growth trajectories are probably most common in

certain typesof ecosystems, particularlygrasslands.The traditional

logistic fitting method actually does not account for these varia-

tions in that it does not model the EVI trajectories accurately. The

ALILF method, however, appears to yield GUD dates that are less

Fig. 13. ThedeterminedGUDandnumber of iterations when different initial GUDvalues areused in theALILFmethod forthe three EVI time seriesin Fig.6. The initial GUD

values were assumed to vary within1 month before or after thefinal determined GUD. Thedottedarrowsindicate theinitial GUDthat is generatedby theALILFmethod.




influenced by the variations and are closer to the actual time that

the land surface began to green up. The new method is resistant

to a range of noise levels because of an adaptive window, which

enable ALILF to enlarge the windowwidth used for logistic fitting

when noise level increases. In addition, the ALILF method is less

affected by the definition of the maximum EVI and the identifica-

tion of thefittingperiod. These advantages suggest that this simple

newmethodmaybewidely used formonitoring springvegetation

phenologybased on satellite time-series data.

Acknowledgments

We thank three anonymous reviewers and the associate editor

Wagner-Riddle for their detailed and constructive comments that

helpedus to improve themanuscript. This studywas supportedby

the project of early detection and prediction of climate warming

based on the long-term monitoring of fragile ecosystems in East

Asia funded by the Ministry of Environment, Japan, and a grant to

M.S. from the National Natural Science Foundation of China No.

41201459.

Appendix A. Appendix A:

The followingpseudo-code describes the ALILFmethod

// Input parameters:

evi= time series data with time resolution of 8-d

ts,tp = thesequential number for the start (land surface temperature> 0) and

transition of the evi time-series, respectively

// Outputs:

gud=green-up onset date

// the equal-weighted logistic fitting for the first estimate

wts[all]← 1.0

gud=Getgud (evi, wts, 1)

GUD result[1]← gud

// the iterative logistic fitting

iternum=2

WHILE (iternum≥ 2) {

centerpoint=Round(( gud-1)/8) +1 // determine thecenter point of thewindow

wts=Getwts (centerpoint, centerpoint )

gud=Getgud(evi, wts, iternum) // call the functions

GUD result[iternum]← gud

FOR i =1 to iternum-1 {

IF (GUD result[i]= GUD result[iternum]) THEN {

IF i = 1 THEN {

gud← GUD result[1]

iternum← 0

Break

ELSE

maxgud←Max (GUD result[i to iternum])

mingud←Min (GUD result[i to iternum])

maxpoint ← Round ((maxgud -1)/8)+1

minpoint ← Round ((mingud-1)/8)+1

wts=Getwts (minpoint, maxpoint )

gud=Getgud (evi, wts, iternum)

gud= (gud-maturity date>30) ? gud: GUD result[1] // the additional

// constraint in step 4; thematurity date is calculated based on

// thefour fitting parameters

iternum← 0Break

} //end if

} //endif

} // end for

Iternum+ +

}// endwhile

//two functions

Functionwts=Getwts(centerpoint, centerpoint )

Global tstp //global variables

// theintersection of thetwo vectors

intersect= [centerpoint -4 to centerpoint+ 4]∩[ts to tp]

IF Length(intersect ) ≥ 7 THEN {

// at least seven pointsare included in thefittingduring iteration

wts[all]← 0.0

wts[intersect]← 1.0

ELSE

Appendix A: (Continued)

wts[all]← 1.0

}

Function gud=Getgud (evi, wts, iternum)

Global tp c f df // global variables

IF iternum= 1 THEN {

Limits c : evi[tp]±10%evi[tp]

[c f , df , gud]= Logistic fitting (evi, wts,c )

ELSE

Fixes c : c f AND Limitsd: df ±20%(c f −df )gud= Logistic fitting (evi,wts, c,d) // forthe non-linear least-square

// fitting procedure, refer to http://purl.com/net/mptif

}

Appendix B. Supplementary data

Supplementary material related to this article can be found,

in the online version, at http://dx.doi.org/10.1016/j.agrformet.

2014.09.009.

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