RESEARCH ARTICLE

Mumbai 2005, Bihar 2008 Flood Reflected in Mass ChangesSeen by GRACE Satellites

Bramha dutt Vishwakarma & Kamal Jain &

Nico Sneeuw & Balaji Devaraju

Received: 22 June 2012 /Accepted: 23 November 2012# Indian Society of Remote Sensing 2013

Abstract Gravity Recovery And Climate Experiment(GRACE) satellites were launched on March 17 2002to derive with unprecedented accuracy, estimates ofthe global high resolution model of the earth’s gravityfield. Local gravity changes with change in mass ormass redistribution. The mass changes can be due tohydrological events, seismic events or postglacial re-bound, majorly. GRACE is sensitive to changes atlarge spatial scale since the resolution of GRACE is400 km. Hydrological activities over basins providesufficient mass changes to be detected by GRACE. Inthis research paper the discussion would be about twomajor flooding events in India, one being the 2005monsoon flooding in Mumbai and nearby states andother being flood experienced by Bihar in 2008. TheGRACE data is in the form of matrix consisting spher-ical harmonic coefficients. These coefficients are pro-cessed to obtain mass changes in terms of equivalentwater height at a spatial scale of 400 km. The strategyof analysis is also discussed which need to be followeddepending upon limitations of GRACE observation

and requirement of application, here in this case ap-plication is flood induced mass change detection.Time-series and residual plots are generated and theyshow the flooding events for the concerned area asoutliers. Better visualisation is obtained by residualplot, if there is a trend or systematic behaviour intime-series. This work points towards the qualitativecapability of GRACE to detect flooding events at largespatial scale. Quantitative analysis requires in-situ dataover the period of GRACE which is not possible forthe cases discussed here.

Keywords GRACE . Time-series . Residual plot .

EquivalentWater Height (EWH)

Introduction

GRACE is a valuable mission giving Earth’s gravityfield at monthly intervals. It is mapping the globalgravity field with a spatial resolution of 400 km to4,000 km every 30 days. The change in local gravity isdue to redistribution of mass, which can be due tomany nature driven activities. The work done tillnow in hydrology, is basin water cycle study, model-ling of basin, terrestrial Water storage changes and soon. There is a work by (Seitz et al., 2008) whichfocused on detecting European heat waves withGRACE. This motivated to look into other aspects ofhydrology such as floods, whose occurrence producesa large mass change. This work is using GRACE data

J Indian Soc Remote SensDOI 10.1007/s12524-012-0256-x

B. dutt Vishwakarma (*) :K. JainDepartment of Civil Engineering, IIT Roorkee, Geomaticsengineering group,Roorkee, Indiae-mail: bdvknmiet@gmail.com

B. dutt Vishwakarma :N. Sneeuw : B. DevarajuInstitute of Geodesy, Faculty of Aerospace and Geodesy,University of Stuttgart,Stuttgart, Germany

set for the period of 8 years. In this period of 8 yearstwo major flooding events in India which had aGRACE detectable spatial extent and magnitude havebeen observed. Mumbai 2005 floods and Bihar 2008floods affected large areas. In this article, the main aimis to observe floods in Equivalent Water Height(EWH) time-series generated from GRACE data set.Equivalent Water height denotes the mass changesdetected by GRACE in terms of water height change.This terminology is used since most of the masschanges across the globe are due to hydrological massmovement.

Data and Methodology

GRACE release 04 level 02 data sets fromGeoForschungsZentrum (GFZ), Potsdam are used inthis study. The data product consists of monthly sets offully normalized spherical harmonic coefficients of theglobal gravity potential of the Earth complete up todegree and order 120. GRACE satellites revolve roundthe Earth 15 times a day. For better global coverageand good spatial resolution we need to look at aggre-gated monthly data set, since the more are number ofrevolutions in non-repeat orbits better would be spatialresolution. Thus here is a compromise between spatialand temporal resolution which is given by the relation:

S ¼ 20000

n

Where S is the spatial resolution and n is the max-imum degree of the spherical harmonic terms used.For monthly fields we obtain a spatial resolution ofapproximately 400 km, (B. D. Tapley and Bettadpur2004). Data sets used is from August 2002 till May2011 with certain month’s data completely missingand few having repeat orbit problem for which wehave regularized solution. This work sticks to thenormal GFZ gravity solutions instead of its regular-ized solution for this work. The month for which wehave completely missing data we would denote thatmonth by (Not a Number) NaN.

The data set contains coefficients up to degree andorder 120, but data set up to degree and order 60 onlyare used, since higher degree and order coefficients areerroneous (John Wahr et al., 2006). The coefficientswith degree and order greater than 15 are itself verynoisy for initial release of GRACE data(Wahr and

Swenson 2004). The release 04 data set is noisy forterms with degree greater than 25. This can be ob-served by the degree variance curve in Fig. 1. TheGRACE data degree variance curve helps us to visu-alize the variation in power of noise and signal withdegree of the coefficients. The green line correspondsto degree value 25 after which the sudden increase inresidual coefficient signal power (against the inversepower law of signal) suggest that the steeply increas-ing error power overtook the residual after that andthus the coefficients are considerably noisy after de-gree 25.

Filtering is a very important tool to suppress noise.Gaussian filter given by (Wahr and Molenaar 1998)for suppressing noise in the spherical harmonic coef-ficients has been used in this work. After filtering, thedata sets contain noise suppressed fully normalizedspherical harmonic coefficients. For getting the masschange the variation in spherical harmonic coefficientsis required. This relation between the mass change andspherical harmonic coefficients is derived by usingpotential theory. The relation is given by:

dVP ¼ GMa

Pn max

n¼0

arp

� �nþ1 Pn

m¼0

ΔCnm cos mlP þΔSnm sin mlP� �

Pnm cos θPð Þ� �

Where δVP is the change in potential, G is theuniversal constant of gravitation, M is the mass ofthe earth, a is the radius of the earth, rp is the distanceof the point of observation from center of the earth, 1is longitude and θ is co-latitude, n is order and m is

degree of spherical harmonic coefficients, Pnm cos θPð Þis Legendre function. To get potential change and then

onwards the mass change, ΔCnm and ΔSnm are re-

quired so we calculated the mean Cnm and Snm,then themonthly spherical harmonic coefficient matrixes weresubtracted by mean spherical harmonic coefficient

matrix to get ΔCnm and ΔSnm. Mean spherical har-monic coefficient matrix was obtained from integernumber of years of GRACE data to avoid the aliasingof seasonal signals (Baur and Sneeuw 2011). Un-modelled phenomenon with over monthly period willalias in to monthly GRACE solution if the number ofyears taken is not integer. Aliasing is inclusion of sea-sonal signals which are not modelled and removed fromGRACE observed gravity variations. The seasonal sig-nal closes every year in form of sine wave and if we

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consider annually then the overall effect for integernumber of years is nullified. The residual spherical

harmonic coefficients (ΔCnm and ΔSnm) thus obtainedwere further converted to mass estimates by the relationmentioned above, in MATLAB. The EWH matrixes forwhole globe for each month were obtained. The statis-tical techniques used for analysis purpose are time-seriesanalysis and residual plot analysis.

Time-series Analysis

A time series is a sequence of data points, measuredtypically at successive time instants spaced at uniformtime intervals. The main objective of time series analysisis to identifying the nature of the phenomenon repre-sented by the sequence of observations. A time seriesmodel will generally reflect the fact that observationsclose together in time will be more closely related thanobservations further apart. The analysis could be carriedout in spectral or temporal domain, here temporal domainis chosen. Time series generation for this study would beto place the EWH obtained from post-processing ofGRACE monthly residual spherical harmonic coeffi-cients as per their chronology. The monthly gaps areconsidered and denote by Not a Number (NaN) inEWH set of matrices. The time series plots generated in

MATLAB have data gaps at these months. The hydro-logical basin shows a good annual signal which is peri-odic in nature like sine waves. The seasonal cycle is veryprominent in time-series. For searching floods in time-series, outliers are observed. These outliers might appeardue to noise or only due to terrestrial water storagechange or due to flooding events. These things are diffi-cult to comment on unless we have some ancillary in-situdata to separate the phenomenon which are seen byGRACE all-together. The time series alone is not enoughbecause for floods at regional scales, the signal due toflood may not appear significant relative to basin extentsignal. Also the systematic behaviour of time-serieswould make the outliers small in magnitude and thusundetectable visually. So there is a need to check resid-uals of the time series generated to make the deviationfrommean behaviour visible by a significant amount andto take care of systematic behaviour of time-series.

Residual Plot Analysis

Residual denote the deviation from the mean behav-iour of time-series. Residual of a time series would tellhow the things have varied with respect to a long termmean. To account for systematic behaviour of time-series data one must identify trend and then de-trend it

Fig. 1 Degree variancecurve

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before calculating mean. The de-trending is necessaryfor improving visualisation of the residual plots. Thede-trend process involves first finding the slope of thetrend in the time-series and then removing the slope.The mean of integer number of years is taken to avoidany seasonal bias. NaN terms in data cannot be in-cluded while computing mean so the time period whenGRACE was healthy and we have continuous datawas opted. The time period from February 2004 toJanuary 2009 is chosen to get the mean of de-trendedtime-series for residual calculation. These residualplots indicate sudden deviation for the time periodwhen these flood events occurred. We have to becareful when we say that whether we can see a flood,and also in deciding how we can see a flood moreefficiently. These things are explained in the followingsections of flood.

Flood Visibility in GRACE Data Set, Analysis Strategy

Flood is defined as overflow or inundation of water thatcomes from a river or other body of water and causes orthreatens damage. Flood occurs when certain hydrolog-ical conditions exist at same time such as saturation insoil moisture, increased and continuous precipitation,groundwater saturation and high humidity. The precip-itation alone is not responsible for floods. Hydrology isgoverned by the water balance equation:

P ¼ Qþ E þ $S

Where P is precipitation, Q is run-off, E is theevapotranspiration and ΔS is change in mass storedwhich is a representative of soil moisture change andgroundwater storage change. GRACE is sensitive tothe mass change, which in case of hydrology would beeither due to ground water change, surface waterchange, or soil moisture content change.

The different phenomenon due to which the totalmass varies can be separated if we can get access tothe in-situ data and generate/simulate models to esti-mate mass changes due to individual phenomenon.Since here aim is to do the qualitative analysis ofGRACE observations we are not discussing the sepa-ration of layers (phenomenon) to validate or quantifythe GRACE observations.

While preparing time series for flood analysis anddeciding which flood could be seen by GRACE, thethings which should be taken care of are as follows:

1. Floods occur not at the basin scale rather they arelocalized generally in a location nearby river only.So if we select whole of the basin the strong signallimited to certain spatial extent would be averagedout with whole basin area signal. So the strengthof signal would diminish and even might get lost,hence while analysing floods one should take careof the area for which the time series and residualplots are generated.

2. Secondly, the floods are not events that last formonths or even few weeks in general. Floods areshort -lived, lasting hours to days. Only large scalefloods can last weeks or months and such floodsare rare. Since the GRACE solutions are monthlyso if we have a flooding event for a week it wouldbe averaged over month so in that case also get-ting strong signal for flood is tough job. Thus onlylarge scale floods can be seen in GRACE data set.

3. The occurrence of floods during time when al-ready there is high value of EWH normally wouldprovide distinguished peak while if a flood occursduring the time of year when we observe a lowvalue of EWH then for that particular time/in-stance the value of EWH would be relatively lessnegative/low.

The detailed methodology is illustrated in Fig. 2. Thedata initially in the form of fully normalised sphericalharmonic coefficients up to degree and order 120. Theyare truncated to terms up to degree and order 60. The setof spherical harmonic coefficients are filtered usingGaussian 500 km spatial filter by John Wahr to reducenoise. Then the residual spherical harmonic coefficientsare computed by subtracting mean spherical harmoniccoefficients computed from integer number of yearsfrom each month spherical harmonic coefficients.Then the residual spherical harmonic coefficient areconverted to first mass change and then to EWH.Finally the time-series and residual plots for EWH aregenerated and flood occurrence is analysed.

Results and Analysis

The analysis of the 2005 monsoon flooding inMumbai and neighbouring region of Karnataka is dis-cussed in this section. The flooding event was listed asone of the deadliest in the last decade. There washeavy rainfall in July and many part of the city were

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severely hit by water logging. The condition of floodwas observed in Karnataka also. Large numbers ofpeople were stranded on the road, lost their homes,and many walked for long distances back home fromwork that evening. The floods were caused by theeighth heaviest ever recorded 24-hour rainfall figureof 943 mm (37.1 in.) which lashed the metropolis on26 July 2005, and intermittently continued for the nextday. Torrential rainfall continued for the next week. Ittook 987 lives and affected neighbouring state

Karnataka, Andhra Pradesh and Goa also (Dartmouthflood observatory flood archive 2005). The spatialresolution of monthly solutions of GRACE is400 km so an area more than 400 km is selected.The area selected for analysis with GRACE observa-tions is shown in Fig. 3.

Then time-series plot is generated from GRACE datawith the values in the time-series data point as the meanof EWH of the area shown in Fig. 1. The values on Yaxis are the values of EWH in meters and on X axis the

Fig. 2 Flowchart for themethodology

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year is denoted where every point denotes the starting ofcorresponding years. Since the flood was observed inJuly thus we must look at the mid of the year 2005. TheSignal in July of every year is normally negative but in2005 it appears strongly positive, it has been encircledblack in the Fig. 4. The EWH showed a peak in middleof 2005. But still the peak is dubious to be recognised asa representative of floods occurred there. The time-series plot is shown in Fig. 4.

So we went for residual plot analysis. Residual plothelps us to distinguish the events denoted by outliersin a better manner. Now normally there is a risingsignal in later half of every year, turning into a peakrelative to the whole year by the end of every year. Instart of 2005, 2006 and 2007 there are peak. Thisanalysis highlights the flooding event as distinguishedpeak in mid of July. The residual plot generated isshown in Fig. 5. In the figure the exceptionally

Fig. 3 Area selected for Mumbai 2005 flood analysis

Fig. 4 Time-series plot ofEWH for area selected forMumbai 2005 flood analysis

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positive signal with respect to the normally low signalin July appears to be strongly positive, the residualvalue is greater than 0.06 m of EWH which is verysignificant deviation from mean behaviour. The peakin residuals corresponding to flood is encircled blackin the Fig. 5.

Bihar is usually struck by floods which originatefrom river Koshi. On 18 August 2008, one of the man-made embankments failed. The river reverted from theprescribed western channel to an old channel near the

centre of its alluvial fan. The river spread out widelyand inundated towns, villages, and cultivated fields onthe densely populated alluvial fan. The flood killedaround 900 people and forced nearly 3 million peoplefrom their homes in Bihar. More than 300,000 houseswere destroyed and at least 340,000 ha (840,000 acres)of crops were damaged (Dartmouth flood observatoryflood archive 2008). The extent of flood was 163700square km and it lasted for 38 days. We would checkwhether GRACE is able to see the Bihar flooding. The

Fig. 5 Residual plot ofEWH for area selected forMumbai 2005 flood analysis

Fig. 6 Area selected for Bihar flood analysis

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area of more than 400 km is selected for analysis. Thearea selected is shown below in Fig. 6:

The time-series plotted shows no significant sign offloods in 2008 at first look, but on observing carefullythe latter half of year struck by floods is shown as aless low value of EWH than that from other years atthe same time. The search for peak in time-serieswould not provide the visualisation to comment onpresence of flood. The less depth attained (encircledblack) by the hydrological signal in time-series ofEWH indicate some activity leading to mass change.Still it is difficult to attribute such behaviour as floodcompared to previous case, since in case of Mumbaifloods the EWH value for flood affected month waspositive while for the same time of year the value forother years was negative. Here the value remainsnegative but the value is significantly low comparedto other years for same month. Also the presence oftrend supresses the outlier induced behaviour in time-series so now move to the residual plot analysis. Thetime-series is shown in Fig. 7:

The residual plot in Fig. 8 shows a clear anomalousbehaviour in year 2008, initially value of EWH

residual is low and later it rises and attains peak afterAugust, Since the flood was of large magnitude andthe water introduced during August remains least af-fected during coming winter months of December,January and February, we obtain a consistent peakthroughout starting of 2009. Please, note that residualplot shows the deviation from mean so we are gettingpeak till March of 2009 since the EWH value isexceptional with respect to other years for same monthat start of a year. Thus we can observe the mass changeintroduced due to Bihar flood in the year 2008.

Conclusions and Future Scope

The GRACE mission has been used to study the groundwater storage changes in India (Rodell et al. 2009) andeven people use it for hydrological modelling of basinsto know the storage change and use it as an input forvarious studies, because the GRACE mission senses themass change. For flood analysis the basic idea was tolook for outliers and check through the available infor-mation on occurrence of flood during that time. The

Fig. 7 Time-series plot ofEWH for area selected forBihar 2008 flood analysis

Fig. 8 Residual plot ofEWH for area selected forBihar 2008 flood analysis

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residual plot alone or time-series alone cannot providesubstantial analysis for occurrence of floods. There is aneed to consider both of them simultaneously withintelligent interpretation. Studying peak for flood inEWH time-series is not the correct way if the floodoccurred during relatively dry season of the year and itcan be seen in both the cases where the occurrence offloods is during seasons with low EWH. In this studythe source of validation was news and media whichconfirmed of a flood occurrence at that place and at thattime. Large mass change because of the floods can beobserved. Further in the study the constraints areexplained, that short-lived floods and floods on smallspatial extent cannot be seen by GRACE, this announ-ces why other floods in the time period of GRACE arenot observed and thus not discussed in this work. Alsothe work illustrates that the time-series plot only is notsufficient for flood analysis from GRACE data, ratherresidual plot together with time-series is a potential toolfor making a comment.

The GRACE mission observes the mass changethat has took place due to all possible phenomenonat every layer responsible for mass redistribution sowe need to separate layers and use models to quantifythe changes for validation. The next step in the workwould be to generate hydrological models, use in-situdata and illustrate how efficiently can GRACE be usedin flood analysis and generating the models whichwould predict the amount of rainfall required, alongwith other inputs to comment on possibility of flood in

a particular area. Thus the work which we can expectin future could be flood forecasting with GRACEobservations and climatological forecasting in collab-oration in a model.

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