The use of the Thematic Mapper for the analysis of eutrophic lakes: a case study in the Netherlands

rNT. J. REMoTE sENsrNG, 1993, vol. 14, No. 5,799-821

The use of the Thematic Mapper for the analysis of eutrophic lakes: acase study in the Netherlands.

A. G. DEKKER and S. W. M. PETERSVrije Universiteit-Institute of Earth Sciences, Section Hydrology, De Boelelaan1085, l08l HV Amsterdam, The Netherlands

( Receiued 9 March 1991; in final form 15 Nouember l99l )

Abstract. Landsat TM images were analysed to assess the scope and limitationsof their use for inland water quality detection. The spectral information in the sixvisible to middle infrared bands is discussed. The relatively wide spectral bands, Ito 4, of the TM, in the optical wavelength domain contain a mixture of spectrallyopposing features of absorption and scattering.

Qualitative and quantitative analysis is carried out. The limiting factors in thequantitative determination of water quality parameters are in first instance theradiometric resolution and in second instance the spectral resolution. Combina-tions of spectral bands of the TM are discouraged for analysis purposes as longas a physical explanation of the result is lacking. Under ideal circumstances theTM can be used to assess seston dry weight, sum of chlorophyll a andphaeopigments, Secchi depth transparency with limited accuracy.

1. IntroductionWithin the course of the National Remote Sensing Programme of the Nether-

lands, the Remote Sensing Loosdrecht Lakes project (RSLL) was carried out. Initialobjectives were to determine the possibilities of studying and detecting temporal andspatial variations in water quality of the Loosdrecht Lakes system (Dekker andSeyhan 1988) using remote sensing techniques. use was made of satellite data,reported here, and airborne multi-spectral (CAESAR, Dekker et al 1990a, b) andimaging spectrometry data (PMI/FLI: Dekker et al. l99l). Although airborneremote sensing using high spectral resolution can attain quantitative assessment ofwater quality to a high degree of accuracy (Dekker et al. 1990a, b, 1991), relativelylower spectral and spatial resolution satellite imagery is important for severalreasons. Thanks to their suÍfrcient spatial resolution, the Thematic Mapper (TM)and SPOT satellites are suited for imaging medium sized or smaller inland waters,such as the Loosdrecht lakes. The data is easily available at a moderate acquisitioncost. A continuation of the TM and SPOT satellite programs is foreseen to the endof this decade, assuring continuity of data acquisition.

The TM images discussed here are from the Thematic Mapper instrument whichis mounted on board of the Landsat 5 satellite (launcfued on I March 1984). Theprimary aim of the system is land observation, resulting in specifications which leadto low radiometric sensitivity at low radiance levels, i.e., a small range of digitalnumbers encompasses the water leaving radiances. This small digital number (DN)range leads to a low signal to noise ratio. The maximum number of DNs is 256.Scene location of the Loosdrecht lakes is: Path 198 and Row 24. The overpass timeis l1:06:49 M.E.T. The TM has a 16 day overpass frequency; according to van Der

0143-1161/93 $10.00 @ 1993 Taylor & Francis Ltd

800 A. G. Dekker und S' W' M' Peters

Laan, in Noordzij et at. (1989), this results in I to 3 cloud-free images of the

Netherlands per year over a 14 year period (for Landsat MSS and TM combined).

In these la yèars (1975-1988) the chance to obtain at least one suitable cloud-free

summer "oultug"

from the whole of the Netherlands is 9 in 14, or 65 per cent per

yeaÍ.

2. Spectral signature analysis of Thematic Mapper bands

The spectrJ bands are fositioned to obtain as much information as possible over

a large variety of objects, using seven spectral bands, resulting in the specifications

shown in table 1. To evÁate the spectral information contained within each of the

TM spectral bands, spectral band boundaries were superimposed on spectral

upwelling irradiance .rr*". obtained in situ with handheld spectrometers (figure

1(a)) anà on spectral upwelling radiance obtained with the PMI imaging spectrom-

etàíingure t(i)) rromàn altiiude of 1000m. The figures do not depict the actual

spectiai sensitivíty of TM. They are intended as an illustration of the information

contents available within each band:

band I 450-520 nm. Most of the irradiance penetrating the water is absorbed by

aquatic humus and by chlorophyll 4 and accessory pigments. Towards 500 nm

tË absorption of light by theie parameters decreases. Backscattering becomes

the main spectral feature causing an increase in irradiance reflectance.

band 2 SZó-OOonm. This band shows a mixture of decreasing absorption by

aquatic humus and thus increasing irradiance reflectance caused by the backscat-

teiing by suspended particulate matter. In these eutrophic lakes there is a local

peak in reflectance at 580 nm.

Èanrl3 630-690nm. At 630nm the band cuts the absorption peak of cyanobac-

terial pigments (a biliprotein: phycocyanin) in two. The small irradiance reflec-

tance pát at 645nmls counter-acted by the strong absorption peak at 680nm

due to chlorophyll a and its byproducts (phaeopigments). Band 3 ends at 690nm

where a reflectance peak with a maximum at 706 nm starts to build up' The

reduction of upwelling radiance by the various absorbing agents is counter acted'

by the (back)sóattering. et a spectral resolution of 60 nm no discrimination into

separate features is Possible.UanA I 760-900 nm. The subsurface measurements available to us do not reach

beyond 850nm. From 850 to 900nm absorption by water increases rapidly, so

*. usrrr-e this to be of little significance. At 760 nm band 4 just includes the

Table l. Thematic Mapper specifications.

Band Spectral resolutionwavelength (nm) Description

TMITM2TM3TM4TM5TM7TM6

450-520520-600630-690760-900

1550-17502080-235010'4-12'51(pm)

visible blue-greenvisible greenvisible red

near infraredinfraredinfrared

thermal infrared

Subsurface Upwelling lrradianceTHEMATIC MAPPER SPECTRAL BANDS 1 TO 4

(Wm-'znmr)0.10

0.08

0.06

0.04

0.02

450 750 800 850

(a)

Upwelling Radiance at 1000 m. AltitudeTHEMATIC MAPPER SPECTHAL BANDS 1 TO 4

450 600 650

wavelength (nm)

(b)

Figure l. (a) Thematic Mapper bands l-2-3-4 (till 850_nm) superimposed on the subsurface- upwelling irradiance scans (Ea" in Vy'm-2qm-1;. lFrom Dekker et al. 1990b). (b)

Upwelling radiance (L.ninWm-2nm-1sr-1) measured at 1000m above lake level byPMI in spectral mode. (From Dekker et al. l99l).7 Breukeleveen, -€- EastLoenderveen, -- Loosdrecht, "" West Loenderveen, -€l- Vuntus, "8" Water-storage,

- V/ijde Blik.

0.00 ffi400 600 650

wavelength(nm)

0.000 -400 750 800 850

\n (W m-'nm-t sr=t;

802 A. G. Dekker and S. W. M. Peters

minimum in solar/sky irradiance caused by the molecular absorption of H2O and

02 (slater 1980). Although many textbooks mention band 4 as the band where

water is totally absorbing and thus black, there is still significant upward

irradiance from the watercolumn in this wavelength interval in turbid waters,

likely to be caused by backscattering from suspended matter.

Bands 1 to 4 of the TM are in the spectral range where light traverses the water

to a suÍficient extent to elicit some information concerning the water quality. The

main effects that could be detected are attenuation of irradiance in band I(absorption by aquatic humus and by chlorophyll a), increase of reflected irradiance

in band 2, and a diÍficult to interpret result of a number of counter-acting processes

in band 3. Band 4 reflectance is the product of rapidly increasing water absorption

and probably suspended matter reflection. Bands 5 and 7 are further in the infrared.

Theàbsorption càefficients of pure water for bands 5 zndT are 700 and 2700m-1respectively (based on data from Palmer and Williams 1974). Therefore no informa-tion can be obtained from these bands concerning the water column. They may have

a purpose as far as presenting a totally absorbing surface. Features such as foam orsurface slicks may be of influence on band 5 reflectance. Band 5 is sometimes

included in algorithms relating water quality parameters such as chlorophyll a,

suspended matter and Secchi-disk depth (DHV 1988, Ortiz Casa and Pena Martinez1989). These algorithms lack a physical explanation. Probably the band 5 data serves

as a constant value (which should then be mentioned). The thermal infrared band 6

makes temperature mapping possible, albeit of the water surface microlayer only.The spatial resolution of 120m makes this band unsuitable for this lake area.

However, for larger lakes, if used, notice should be taken of research by Sódergren

(1984, 1987), who analysed this surface microlayer for lakes in Sweden and foundthe microlayer to be different in composition (physical and chemical) from the

watercolumn. Evaporation heat losses and thermal microgradients in the top few

cms of the watercolumn may influence the thermal signal as well. A thoroughknowledge of these parameters is required to allow interpretation of these results.

Due to the convoluted spectral information in each TM band the use ofcombinations (sum, difference, difference over sum, ratios, etc) of TM spectral bands

to increase correlations with water quality parameters, will produce results whichcannot be explained physically. The amount of information extracted from bands 2

and 3 will not increase by adding or ratioing the two bands. Therefore only aquantitative analysis on single bands for the TM data was performed. Lathrop and

Lillesand (1986) used single bands for reason of the high intercorrelation between

the TM bands 1-4.

3. lmage analysis3.1. Introduction

Of the eight Thematic Mapper images that were available to us, the two images

with least atmospheric influence were selected for further analysis. (The results of ananalysis of the applicability of SFOT images is presented in Dekker et al. 1990b).Figure 2 is a grey-scaled TM band 5 image of the study area.

Figures 3(a) and (ó), and 4(a) and (á) shows Thematic Mapper images on16 June 1986 and 5 July 1987. Figures 3(a) and 4(a) are pseudo natural colourimages (bands l, 2 and 3 as blue, green and red respectively). A supervised linearcontrast stretch was applied in order to increase the image brightness. Figures 3 (á)

A TM study of eutrophic lakes in the Netherlands

Figure 2. The Loosdrecht lakes and northern Vecht lakes area. Based on a ThematicMapper band 5 image.

and 4(b) are standard false colour images of bands 2,3 and 4 (bands 1, 2 and 3 as

green, red and near-infrared respectively). Both types of images show qualitativeinformation such as patterns within and differences between lakes. Quantitativeinformation extraction involves statistical analysis on preprocessed images.

3.1.1. 16 June 1986

On 16 June 1986 the weather was relatively \ilarm with a temperature of 27'C, a

relative humidity of 55 per cent, the wind direction was from NE to ESE with a windspeed of 3ms-1. Horizontal sight was 12km and the air pressure was 1014mbar.

Figure 3 (a) shows the Water-storage Basin, Lake Wijde Blik and Lake Spiegel as

dark blue: these are the deeper clearest lakes in this area. Lake Wijde Gat is also thiscolour: this is contrary to the very eutrophic status of this shallow lake and may be

803

Figure 3.

Figure 4.

A TM study of eutrophic lakes in the Netherlands 805

explained by very high absorption due to high concentrations of aquatic humus andchlorophyll a. Another reason could be a local change in atmospheric conditions.Next Eastern and Western Lakes Loenderveen appear more reddish-brown togetherwith the Lakes Stichts Ankeveen and Hollands Ankeveen and Naardermeer. Thelakes with overall highest reflectance are the Lakes Loosdrecht, Nieuwe Polder,Vuntus and Breukeleveen. These are very eutrophic lakes resulting in high reflec-tances. The feature causing the low reflectance by Lake rWijde Gat apparently doesnot occur in these lakes.

Figure 3 (á) shows the false colour image. Several differences are apparentcompared to figure 3 (a). The Water-storage Basin, Lake Wijde Blik and LakeSpiegel are still lowest in reflectance, but they are also different from each other:removal of band I (and related noise and banding) and inclusion of band 4reflectances cause a differentiation. Lake Wijde Gat now does appear much brighter,especially in the near-infrared (band 4). Lakes Stichts and Hollands Ankeveen andNaardermeer are also bright in the near-infrared. A probable cause is the presence ofsubmerse and emerse macrophytes (a substantial water surface coverage with emerse

macrophytes would result in higher reflectances in band 4 causing these areas to be

classified as land). In spring macrophyte coverage is less than in summer, thereforethe landmask was based on the 23 April 1987 image; this allowed the subsequentrecognition of increasing macrophyte coverage in the summer (and autumn- nottreated here) images. The diagonal line in Lake NaardeÍneer is a linear several

metres wide track of Phragmites which used to be a road. Its influence is mostobvious in the infrared reflectance (compare figures 3 (a) and (á)). Lake EasternLoenderveen is diÍferent from the other lakes, it has a mainly dark blue colour in theimage similar to Lake Wijde Blik in some parts. Which means the red and near-infrared reflectance is low compared to the green reflectance. This could be caused

by different algal species composition or algal concentration, or in a differentcomposition in other suspended matter components.

3.1.2. 5 July 1987On the 5 July 1987 the weather was mildly warm with a temperaturc of 24"C, a

relative humidity of 40 per cent and a wind direction of E to ESE with a wind speed4m'-1. Horizontal sight was 30km, and the air pressure 1025mbar.

The images of figure 2 were created in a similar image processing sequence as the16 June images. Nevertheless the images differ considerably. Changes in lake watercomposition and in atmospheric and weather circumstances are probable. Severalfactors are similar compared to the 16 June image such as the solar height and theDN ranges for bands l,2 and 3 (see legend with figures 5 and 6). Band 4 ranges are

Figure 3. (a) Pseudo natural colour composite of the Thematic Mapper image on 16 June1986; bands 1,2,3 are represented in blue, green and red respectively. (á) Standardfalse colour composite of the Thematic Mapper image on ló June 1986; the green(band 2), red (band 3) and near-infrared band (band 4) are assigned to the coloursblue, green and red. :

Figure 4. (c) Pseudo natural colour composite of the Thematic Mapper image on 5 July1987; bands l, 2 and 3 are represented in blue, green and red respectively. (á) Standardfalse colour composite of the Thematic Mapper image on 5 July 1987; the green (band2), red (band 3) and near infrared band (band 4) are assigned to the colours blue, greenand red.


different. The atmospheric influence on 5 July is much smaller as can be deducedfrom the lowest DN levels and the horizontal sight values (12 versus 30 km).

3.2. Preparatory image analysisTo grid-reference the images a geometrical correction was carried out, ensuring

the same location of the spectral samples of the landmask in the images. For reasonsmentioned earlier, Ihe 23 April 1987 image was chosen as a reference base. Then anearest neighbour correction was applied. The pixel size remained constant. Subse-quently using band 4 a landmask was defined and applied. Band 4 was chosenbecause it represented the band which combined low atmospheric influence withinterpretable spectral knowledge (up to the range of the fieldspectroradiometer of850nm).

TM image quality is influenced by four types of distortions:

l. Random noise due to low radiance levels. The only remedy would be toincrease the radiometric sensitivity of the TM especially at lower radiancevalues.

2. 16line striping caused by inaccurate calibrated Landsat sensor outputs. The16 line noise can be seen clearly in figure 3 (a) and 4 (a), it is most obvious inband l, the blue spectral band.

3. Banding of 16 lines, caused by an unequal response between a forward and abackward scan.

4. Blockshaped noise: Especially at low radiance levels it appears that the sensorbecomes sensitive for antecedent observations and/or calibration errors likerounding. This can result in a random amount of line striping superimposedover the 16 line striping. This type of noise was detected after applying 16 and32 band line destriping algorithms and analysing the residual noise compo-nent. This type of noise is random and on a scale which makes it impossible tocorrect it with local filters.

In the image preprocessing phase the systematic noise component (see noise nr 2)may be reduced. There are a number of ways to reduce the 16 line noise:

1. Decalibrate the image and adjust each of the 16 line sets with respect to thetotal image characteristics and calibrate again (see Grunwald, Mauser andSchneider, 1988). For this method the originally applied system calibrationfactors are necessary.

Figure 5. (a) Colour coded TM band 2 image depicting water quality concentration on the16 June 1986. Concentrations of water quality parameters can be determined bycomparing the DN values in the image with the calculated values in table 7 (a). (b)Colour coded TM band 3 image depicting water quality concentration on the 16 June1986. Concentrations of water quality parameters can be determined by comparing theDN values in the image with the calculated values in table 7 (b).

Figure 6. (a) Colour coded TM band 2 image depicting water quality concentration on the5 July 1987. Concentrations of water quality parameters can be determined bycomparing the DN values in the image with the calculated values in table 7 (c). (ó)Colour coded TM band 2 image depicting water quality concentration on the 5 July1987. Concentrations of water quality parameters can be determined by comparing theDN values in the image with the calculated values in table 7 (d).

807


2. Apply the adjustment algorithm to the calibrated image. This has been done

in this research in order to enhance the qualitative interpretability of the rawimage.

3. Use a local averaging filter with minimal kernel width of 16pixels. Of course

the averaging can only take place over larger surface areas.

Because all these methods change the observed digital numbers it was investi-gated if sampling strategy could compensate for the most serious noise effects.

Final preprocessing products were

1. the geometrical corrected landmasked image2. the line-adjusted version of the geometrical corrected landmasked image

For purposes of quantitative analysis the first type is recommended. For pattern

analysis and qualitative analysis the second type is better suited.

3.3. Collection of input data for regression analysisBased on long term records a good assumption about local lake water quality

seemed to be that the intra-lake variability is much smaller than the inter-lakevariability. A number of factors support this assumption such as the compartment-alisation ofthe lakes, different sources ofwater, different usages and so on. Thus an

elaborate (and expensive) sampling campaign was avoided in which spectral samples

are collected exactly on the locations of the field reference data collection sites. Thiswould not have been a sensible approach due to the fact that no reference data were

available for the overpass days. So the water quality data (obtained from routinemeasurements carried out by the Water Pollution Control Authority Amstel- en

Gooiland (ZAG) for the northern Vecht lakes and by the Limnological Institute ofThe Netherlands for the Loosdrecht lakes) was estimated through linear interpola-tion. The interpolated values were subsequently checked against the annual patternsof 1983 to 1988 (Breebaart et al. 1989 for the Loosdrecht Lakes and by the WaterPollution Control Authority Amstel- en Gooiland (ZAG) for the Northern VechtLakes). Any outliers were discarded. Table 2a-b shows the interpolated values ofmain optical water quality parameters per lake on these dates. However, linearinterpolation of data may lead to wrong estimates due to non-linear behaviour ofthe parameters, smoothing of peaks and lows in values and, in general, to not beingable to accurately determine the behaviour of a dynamic ecosystem such as lakes.

Because of the above named reasons Reardon and McGarrigle (1989) declinedusing regression analysis for a research involving 100 lakes in Ireland. Instead theyused clustering algorithms to group their lakes. The method applied here, howeverdoes allow the use of nonsynchronous water quality data (Whitlock, Kuo andLeCroy 1982, specifically recommended research into the area of nonsychronousdata) under the condition that as much attention as possible is given to the reliabilityof the interpolated data. The similar results compared with the study by Lathropand Lillesand (1986) supports this view. It was decided that a reasonable approachwould be to use an interpolated value for each water quality parameter per lake andsubsequently try to relate this to one spectral sample from the lake. The next step

was finding the optimal sample size. In order to assess the potential noise in the TMdata and to assess the impact of potential errors in sample point location Lathrop


and Lillesand (1986) evaluated the comparative response measured by the TM bothof the central pixel and over surrounding local windows which were 3 by 3, 5 by 5,

7 by 7,9 by 9,pixels in size: An analysis of the variance observed over these variousmeasurement areas showed that a 3 by 3 window was adequate for characterising the

Table 2. (a) Lake water quality on 16 June 1986. (Data obtained through linear interpola-tion; ordered by decreasing Pigm levels)

Water quality parameters

Lakes Pigm DW SD P,o,(pg l- t) (mg l- t) (cm) (pg l- t)

809

Wijde GatBreukeleveenLoosdrechtHollands AnkeveenVuntusNieuwe PolderNaardermeer-Bovenste BlikEastern LoenderveenNaardermeer-Groote MeerWestern LoenderveenWijde BlikStichts AnkeveenNaardermeer-SpookgatSpiegelWater-storage

205170l6l161

110

247ll5120209107r80144

5380896449

12653

3l25303l404243395643

1468963

23r27t

444t252929

5

66I8

2I

785548473022t9l04

- : not available

Table 2 (ó). Lake water quality on 5 July 1987. (Data obtained through linear interpolation;ordered by decreasing Pigm levels)

Water quality parameters

Lakes Pigm(pg l- t)

DW(-gl-t)

sD P,o,(cm) (pel-')

V/ijde GatHollands AnkeveenVuntusBreukeleveenNieuwe PolderLoosdrechtNaardermeer-Bovenste BlikEastern LoenderveenWestern LoenderveenStichts AnkeveenWijde BlikNaardermeer-SpookgatSpiegelNaardermeer-Groote MeerWater-storage

28023010560

t2s105244

80777080703l6038

26203030474035558867

16090

254ll3310

4t27422724JJ20l8

8

924J42

258199189162150149118662927221298

5

Mean TM2-DN

oo o o o

xx * * x ' * )<

A.


I37

36

b\'35

34

33

320 100

Standard deviation TM2-DN

200 300Sample size

500

0.8

0.7

(ó) o.o

0.5

0.4

0.3

31

30

(c) 2s

28

27

26

25

Mean TMS-DN32-

o".xx * )1< * x

B+ -G - €r- - -6 - - -EF - - - EJ

200 300Samplê size

Figure 7.

r00


StandaÍd dêviation TM3-DN

0.80

@) o.m

0.60

0.50

0.40

0.30

Sample size

Figure 7. (a) Progression of the mean spectral sample value (in DN) with increasing samplesize for TM band 2 of 16 June 1986. (à) Progression of the standard deviation (inDN) with inoeasing sample size for TM band 2 of 16 June 1986. (c) Progression of themean spectral sample value (in DN) with increasing sample size for TM band 3 of 16

June 1986. (d) Progression of the standard deviation (in DN) with increasing samplesize for TM band 3 of 16 June 1986.

data aÍ each station for their research. This method was carried out for the TMimages in the RSLL project: the results are different (in this research we did notmake use of simultaneous ground-based measurements). For this purpose squaresamples with a cross-section size from I to 2l pixels were taken in the larger lakes.

Graphs (figures 1(a)-(d)) were made which show the change in standard deviationand average DN value with increasing sample size for TM bands 2 and 3. Thegraphs indicated that a 17 by 17 pixel sampling size equal to a 510 by 510 m area was

optimal. If the lake was not large enough for such a sample then the largest possible

sample was taken. The aforementioned 16 line striping and the banding of 16 linesoccurring in all images is probably a prime factor contributing to this value.

It appeared that an additional quality criterion was necessary in order to assure

spectral validity of the sample (exclusion of cloudy/hazy aÍeas, emerging macro-phytes, pieces of land etc). The standard deviation of a sample in band 4 proved tobe such a criterion. If this value was belovr l'0 we assumed the spectral signal to be

derived from the watercolumn and a constant water surface and atmosphericcomponent. This caused a decrease in the amount of samples from the original 16

lakes to 9 for the 16 June 1986 image and to l0 for the 5 July 1987 image. Althoughthe amount of samples is less, the spectral quality of the samples has increased. Eachof the samples of bands 2 to 7 taken in the lakes large enough for a 17 by 17 pixelssample (lakes Loosdrecht, Breukeleveen, Spiegel, Eastern Loenderveen and WijdeBlik) also showed a standard deviation smaller than I (see table 3).

The gradient in water quality within this set of lakes, ranging from the clearest tothe most turbid, indicates that sampling of these lakes combined with Landsat TMimages would be suÍficient to map all the other lakes in this area. This could be

applied to other similar water bodies, provided atmospheric circumstances are the

8ll


Table 3. The minimum, maximum and average DN values with the standard deviation ofthe water based pixels in all the lakes measured in the two TM images.

TMl TM2 TM3 TM4 TM5 TM6 TM7

16 June 1986MinMaxAvg meanAvg std

5 July 1987MinMaxAvg meanAvg std

ll5 2123 8

I19.61 4.700'61 0.88

ll3 I120 61t6.75 3.28

0.50 0.96

same or atmospheric correction techniques are available with an accuracy at leastgreater than the standard deviation of the algorithms applied.

3.4. Statistical analysis of Thematic Mapper dataInput data matrices were prepared; each matrix had water quality parameters as

dependent variables and values of TM bands I to 4 as independent variables.Correlation and regression analysis using a linear model was performed.

Based on the selection criteria mentioned above water parameters from thefollowing lakes were used in the analysis of the 16 June data: Breukeleveen -Loosdrecht - East Loenderveen - West Loenderveen - Water-storage - Wijde Blik -Vuntus - Spiegel - Stichts Ankeveen.

On 5 July water parameters from the following lakes were used in the analysis:Breukeleveen - Loosdrecht East Loenderveen - Water-storage - Wijde Blik -Vuntus Spiegel - Wijde Gat - Stichts Ankeveen - Naardermeer-Bovenste Blik.

3.4.1. Linear regression resultsThe results of the bivariate linear regression analyses are given in table 4. All

results with correlation coefficients higher than 0'80 are presented. The statisticallydetermined limit of an interval reliably measurable may be expressed as the standarderror of estimate, S, which is expressed in table 4 as a percentage of the mean of thevalue, (sr,) per cent. But it also holds true that the coeÍficient á in the regressionequation of Y:a-lbxX is equal to the smallest interval of the characteristic to bemeasured between two DNs (or two discrete values of X). This interval is the DNstepsize, and is given in Íable 4 as a percentage of the mean: DN-step %.

(a) Discussion of the 16 June results. The (sr') Yo arc all greater Íhan 23oÁSecchi-disk depth transparency does not have a correlation R>0.80 for thelinear data. Seston dry weight may best be determined using band2, with a(sr,) of 4'88mgl-1. Sum of chlorophyll a and phaeopigments was alsohighest correlated with band 2: a (sn,) of 15.66pg1-1. A water qualityparameter with high correlation with band 2 and band 3 is total phosphate.This is probably due to the intercorrelation between organic matter, both inthe algae and in the seston, with total phosphate. Thus a correlation of band

88100

93.15r.37

647569.01

r.19

3l3834.670.60

2t2925.290.66

25JJ28.600.75

t625r9.680.62

l92622.020.58

92013.450.63

5

13

9.560.94

2ll5'501.00

A TM study of eutophic lakes in the Netherlands 813

2 and band 3 with DW and Pigm reflects itself as a high correlation for totalphosphate. Correlations for DW and Pigm and P,o, with band 2 andband 3

are positive: an increase in DN is proportionate to an increase in the waterquality parameter. This is also true for Pigm which supposedly is correlatedto absorption: apparently backscattering is dominant caused by the algae

and the suspended matter, variables which also tend to covary strongly.Correlations higher than 0.80 for band I as independent variable show

extremely high (sr,) %. Atmospheric path radiance contributions decrease the

correlations. The high aquatic humus and chlorophyll a absorption cause a

low absolute water leaving radiance. The TM has the largest sensor calib-ration errors in band I as well. Equations including band 4 did not reach a

R>0'80 in any of the regression equations.

(b) Discussion of the results of 5 July. Band 1 analysis showed the same result as

for the 16 June image. Similar to the 16 June data TM band 2 correlates

highest with DW and Pigm. TM band 3 correlates highest with SD. The (sr,)oÁ are also all greater than 23 per cent. Except for sD the DN- stepsize is

larger than the (sr,). Secchi-disk depth can only be estimated using band 3 on

5 July 1987 with a standard error of estimate of 65cm. Seston dry weightmay best be determined using band 2 with a (sr) of 4'90mgl-1. Sum ofchlorophyll a and phaeopigments can best be determined using band 2 as

well with a (sr,) of 33'8.

There was a serious drawback attached to using linear regression

analysis: when applying a full range of digital data present in the images tothe regression equations, frequently negative values were calculated (see

table 5). There are several explanations for this, the most obvious being thatthe linear model is not adequate. This was verified by using an exponential

Table 4. Regression equations of the TM data and optical water quality parameters on16 June 1986 (N:9) and 5 July 1987 (N:10).

(R')% (tn')% y DN-step(%)

16 June 1986DW : -1294'57 +14.06*TM1DW : - 399.80+11.97*TM2DW : - 280'38+10'34*TM3

P,o, : - 613'70+19'88*TM2P,o, : - 426'76+17'57*TM3

Pigm : - 4764'54+ 5l'87*TM1Pigm : -1437'54+43'41*Tll2Pigm : -1028'43+38'33*TM35 July 1987SD 1199.93 - 55'90*TM3DW : -207'02+8'96*TM2EW : -165'84+ 9'43*TM3

Pigm : -1137.52 +48.93*TM2Pigm : -913'83+51'52*TM3

95.50 55.916.80 53.516.80 56.2

0.820.960.89

0'860.82

0.830.970.92

0.810.96a.92

72.432.455.2

23.426.s

55.223.138.4

7 5-675.6

67.767.767.7

26.323.2

76.664.156.6

67938l

7567

709585

15.1 93.015.1 79.215. I 68.4

66 64.69t 29.28s 38.6

0.93 87 33.90.90 8l 40.8

99.8599.85

48.951.5


Table 5. An example of concentration intervals of water quality parameters calculatedTM band 2 on 16 June 1986 using the linear regression model.

for

DW (mgl-r) Pigm (pgl-l) P., (pg 1-')

DN32DN33DN34DN35DN36DN37

-23- -ll- I l-l

r*1313-2525-3737-49

-70--21-27-17

l7-6060 104

104-147147,190

t2-3232-52s2-7272-9292-t12

tt2-132

model. The results will be presented further on. Another (partial cause) mightbe a non-linear sensitivity of the TM system for low DNs.

As can be seen from the table the intervals measurable between two DNsis often larger than the (sr,). It is the low radiometric sensitivity of the TMwhich is the limiting factor in an accurate assessment of water qualityparameters.

3.4.2. Discussion of log-transformed data regression resultsLogarithmic transformation of the data enabled the application of an exponen-

tial curve of the form Y: a x Xb using linear regression technique (the equation used

then becomes Ln Y:Ln aIbLn X). This model fits the data much better. There is

physical basis for this as well: firstly negative values (calculated using the linearregression equation) for the parameters do not occur (this could be solved by forcingthe intercept to the lowest DN encountered over water in the entire image- resultingin lower correlations); secondly most of the correlation between radiance values and

the water quality parameters is based on the (back)scattering properties of the waterconstituents. An increase in scattering will also increase the multiple scattering, thisis likely to give the increase an exponential character. Thirdly the spread in the datafrom highly eutrophic lakes varies more in time than data from oligotrophic ormesotrophic lakes,

Lathrop and Lillesand (1986) arrived at the same best fit for their TM data ofGreen Bay and Lake Michigan, making use of in sítu sampling techniques carriedout within l'5 hours of the TM pass. This is an indication that the non-simultaneoussampling technique used in this research is appropriate (given the lack of simul-taneous data). They found highest correlations:

N:9. R:0'99 for SD and TM band 2 forN:6, R:0'95 for SD and TM band 2 forN:13, R:0'99 for chlorophyll a and TMl'04 pg l- L

.

N:7, R:0.98 for chlorophyll a and TM band.2 for Lake Michigan, with a (sr,) ofl'05 pg l-

3.4.2.1 Log-tranformed data regression results for the 16 June and 5 July images.In contrast to the result from the non-transformed data, the log-transformed

data had a higher correlation of SD, DW and Pigm with band 3 than with band 2.

The values are given in table 6.

Green Bay, with a (sn) of l05cm.Lake Michigan, with (sr.) of ll2cm.band 2 for Green Bay, with a (sn,) of


The log-transformation caused calculated dimensions of the dependent variablesbased on the bivariate linear regression results to be more realistic, especially at lowdigital numbers for the DW and Pigm concentrations and at high DNs for SDtransparencies. At the other end of the scale, however, the values become unrealisti-cally high for DW and Pigm. Therefore the lowest and highest DN values in table7 (a-d) which lead to the calculation of unrealistic values are marked with a lowerthan (<) or greater than (>) sign instead of an estimated parameter value.

A drawback of using log-transformed data is that at high DN (low DN for SD)levels the interval of water quality parameter estimation between two DNs increases

exponentially as illustrated in table 7. (Lathrop and Lillesand (1986) also calculatedexponentially increasing intervals for colour coded TM band2 images of chlorophylla and SD). The SD values calculated for TM band 3 at low DNs are unrealistic:probably from DN 25 or less SD should be given as greater than 390cm. These

regression equations are based on a small set of interpolated data. More data valueswill increase the reliability of the results. Another possibility could be to use anexponential relation for the lower DN range and a linear relation for the upper DNrange. In that case non-linear regression should be applied to see if one regressionequation can cover the entire range of water quality parameters and associationDNs. A larger and better data set is needed to actually prove if this is a goodapproach.

3.5. DiscussionExcept for the (sn,) as a limiting factor for accuracy of determination, the

absolute amount of DN levels is also limiting. The amount of concentration levelsmaximally discernible expressed as DNs, with a minimum threshold of at leastl0pixels per levels, is:

Table 6. Regression equations using the log-transformed data for 16 June, 1986 and5 July 1987. (The regression formula: Y:aXb; the coefficients are determined using theformula: ln Í:ln a+bln X).

R @\(%)

16 June 1986ln SD

ln DWln l)W

ln Pigmln Pigm

5 July 1987ln SDln SD

+ 54'97 - 15'13 ln TM3

-112'74+32'34In TM2- 82.16+25.08 ln TM3

- 88'32+25'95 ln TM2

- 63.65+20.08 ln TM3

+ 42'75- ll'95 ln TM2+ 37.36- ll'15 ln TM3

- 49'39+16'07lnTll42- 40.87+14.56ln TM3

- 55'37+18'39In TM2- 43'54+ 15.97In TM3

-0.90 81

-0.82- 0.93

0'850.93

0.870.91

0'880.90

0.830.85

7882

7072

6886

7386

7783

ln DWln DW

ln Pigmln Pigm


Table 7 (a). Concentration intervals of water quality parameters on 16 June 1986 calculatedfor TM2 DN values using the log-transformed regression equations from table 6(figure 5(a)).

TM2 DW (mg1-r) Pigm (pg l-1) colour code

DN32DN33DN34DN35DN36DN37

0-lt-22-66- l5

I 5-36>36

3-t'l-16

l6-3535-7373-ls0

> 150

bluedark green

greenyelloworange

red

TableT (ó). Concentration intervals of water quality parameters on l6 June 1986 calculated

for TM3 DN values using the log-transformed regression equations from table 6.

(fieure 5(á)).

TM3 DW (mel-r) Pigm (pgl-1) SD (cm) colour code

DN23 0-0DN24 0-0DN25 0-0DN26 0-1DN27 1-3DN28 3-6DN29 6-15DN30 l5-35DN31 35-77

0-lt-22-44-99- l8

I 8-3737,7575-146

146-278

> 390> 390> 390

390-21 8

218-124124-7272-4343-2626-t6

dark blueblue

dark greengreen

green-yellowyelloworangesalmon

red

Table 7 (c). Concentration intervals of water quality parameters on 5 July 1987 calculatedfor TM2 DN values using the log-transformed regression equations from table 6,

(figure 5(c)).

TM2 DrW (mgl-l) Pigm (pgl-1) SD (cm) colour code

DN22 l-2DN23 2-4DN24 4-7DN25 7-14DN26 t4-26DN27 26-47DN28 > 47DN29 > 47

3-77-t5t5-3232-6666-133> 133> 133> 133

439-25525s-lsll5l-9292-s7s7-3636-2323-15<15

bluelight bluedark greenlight green

green-yellowyelloworangesalmon

.Table 7 (/) Concentration intervals of water quality parameters on 5 July 1987 calculatedfor TM3 DN values using the log-transformed regression equations from table 6(figure s(d)).

TM3 DW (mg 1- 1) Pigm (pgl-1) SD (cm) colour code

DNIT 1-2DNt8 2-5DNlg 5-l IDN20 fi-23DN2l 23-45DN22 > 45

3-99-21

2t-4949-l l0

l 10-235>235

445-231231-124t24-6969-4040-2323-14

bluelight bluedark greenlight green

green-yellowyellow

A TM study of eutophic lakes in the Netherlands 817

16 June 1986

band 2: 8 DN; band 2--{estriped and averaged: 6 DNband 3: 9 DN; band 3--destriped and averaged: 9 DN

5 July 1987

band 2: 8 DN; band 2--{estriped and averaged: 6 DNband 3: 9 DN; band 3--{estriped and averaged: 9 DN

if a threshold of l0Opixels per DN level is applied the maximum range woulddecrease to 6 levels. The two images discussed here are centred around maximumsolar elevations (approximately 58") at the overpass time at this geographical

location. The gradient in water quality parameters covered is large and is foundwithin a relatively small area. The aforementioned arguments imply that LandsatTM images are likely to be of lirnited value for surface water quality determinationpurposes.

4. Interpretation of the colour coded images of water qualityThe algorithms developed through statistical anlyses are based on the assump-

tion that a 17 by 17 pixel area is a representative sample for the average waterquality measured there. If each lake were homogeneous (i.e., well mixed) the

concentration maps on basis of these algorithms would show no variation at allwithin the lakes. In reality gradients and patterns may be observed (see flgures

3 (a b) and 4(a á)). There is enough variability between the lakes for the calculatedregression line to be valid. So the hypothesis for this method: that the optimizedspectral sample is representative for the average measured parameters is not rejected.

To recapitulate the process used to obtain the images showing the water qualityparameter estimates as colour codes:

(a) Determine the averages of the most valid lake-based sampling measurements(in this research through interpolation).

(á) Determine the most reliable spectral sampling size (: 17 xl7).(c) Perform optimal sampling.(d) Perform regression analysis; obtain regression equations.(e) Apply regression equations to the image, thus estimating concentration from

the images.(f) Ensure that the regression equations do not produce nonsense results such as

negative or extremely high concentrations or values (sensitivity and sensi-

bility analysis).

The Thematic Mapper band 2 and band 3 images are presented in figures 5 (a-b)for 16 June 1986, and in figure 6(a-b) for 5 July 1987. Each DN level coincides withone colour of the colour bar. The lowest DN value, always shown as dark blue,varies. The difference between band 2 and band 3 is caused by a decreasingatmospheric path radiance contribution. The difference between the same band DNson the two different dates is caused by differing atmospheric circumstances resultingin a much lower atmospheric path radiance contribution in the image of 5 July 1987

(DN 32 on 16 June and DN 22 on 5 July for the lowest band 2 values). Theconcentration intervals are dependent on the factors named above in the discussionon linear regression results. Table 6 presents the regression equations based on thelog-transformed data. Table 7 (a-d) presents the calculated water quality parameters.parameters.


Although the statistical results show the estimates of SD, D'W, Ptol and Pigm notto be very exact, the concentration maps based on these regression equations appear

to be consistent with the general overall picture of the water quality status of thelakes based on prior knowledge. It must be emphasised that the imagery was trainedbut not tested.

(a) 16 June 1986. Figures 5 (a-b) are bands 2 and 3 after image corrections witha linear colour look up table applied: each colour is a DN. The results of the

statistical analysis can directly be transferred to these DNs. Thus band 2 isthe most accurate map of DW, Ptot and Pigm. Band 3 is not as accurate,

although atmospheric influence is less at longer wavelengths. This is due tothe complexity of the opposing spectral features as mentioned in the

discussion of the spectral features in the optical wavelength range. Althoughthe colours and ranges are slightly different, the overall pattern in the lakes

remains similar. Compared to the pseudo natural colour and false colourcomposites, the colour coded images show quantified information whichmakes visual interpretation more accurate. In lakes Spiegel, Water-storage

Basin, Wijde Blik and Stichts Ankeveen the two lowest DNs in band 2 arcencountered: this means their green reflectance is lowest. Lakes Eastern and

Western Loenderveen and Naardermeer show the two following DN levels,

Lakes Hollands Ankeveen and Wijde Gat are intermediate between these

levels and the levels of the very eutrophic Lakes Loosdrecht, Nieuwe Polder,

Breukeleveen and Vuntus. Gradients are visible but no consistent direction is

present. Lake Loosdrecht has increasing reflectance from south to north,whereas the

.Water-storage Basin and Lake Loenderveen show a decreasing

reflectance from south to north. Lake Wijde Blik shows an east to westgradient. The other lakes do not show any gradients. The procedures used,

remove noise without affecting large-scale patterns such as gradients. No newpatterns are introduced, so it is safe to qualitatively interpret the images.

Large scale sensor-based distortion or atmospheric path radiance differencesmay influence the image.

(ó) 5 July 1987. Figure 6(a) (TM band 2) Lake Nieuwe Polder, Wijde Gat andHollands Ankeveen are now similar. Lake Vuntus is now separate (up to twoDNs higher) from Lakes Loosdrecht and Breukeleveen. Lake Vuntus has aconcentration of blue-green algal trichomes of 210000perml with a Pigm ofl89pgl* 1, Lake Loosdrecht trichomes of 140000perml with a Pigm ofl43pgl- 1 and Lake Breukeleveen trichomes of 140000 perml with a Pigmof 1621tgl- r. In the pseudo natural colour image (figure a@) Lake Vuntusseems to be more yellowish: this is caused by higher green and slightly higherred reflectance, possibly caused by the high amount of trichomes. Otherexceptions are Lake Naardermeer and the south eastern Lake Naardermeer-Bovenste Blik, which differ now by two DNs. Lakes Stichts Ankeveen andHollands Ankeveen are almost invisible because they disappear into thelandmask.

5. Conclusions and recommendationsAs far as water quality detection is concerned the advantages of current TM and

similar satellite images are: the synoptical view combined with an acceptable


resolution; the repetitive coverage of large areas reducing the cost per image and per

surface; the availability of customised digital image processing systems; the world-wide application of analysis methods, and due to repetitive coverage, the possibility

of an archive or library may be created of water quality status. The continuity indata gathering with new satellites being launched to replace existing satellites is also

important.Disadvantages are that the research, design, manufacturing and launching costs

of the systems often leads to compromises. Complexity of system design and

construction, leads to a time lag as far as technical state of the art in research is

concerned. These factors and the fact that the TM was primarily designed for land

application led to the relatively low spectral and radiometric resolution of these

systems. Once launched the systems are not versatile, they follow fixed paths. The

effective temporal resolution of Landsat is low under mid-latitude temperate climate

conditions.Spatial atmospheric distortions influence the interpretation of images: the only

way to prevent this is by a pixel by pixel calculation of the atmospheric distortionfactor, allowing correction of atmospheric gradients across the image.

At low concentrations of water constituents a log-transformed data set is better

suited for carrying out bivariate linear regression analyses. An exponential relation

aXb describes the relationships best, except at the highest digital numbers orradiance values (measured from water surfaces in this research). The exponentialrelationship may lead to unrealistically high concentrations. It is recommended thata calculation using radiative transfer theory is carried out to determine the

theoretical shape of the relationship between any optically active water qualityparameter and radiance reflectance from a water body in the spectral bands of the

remote sensing systems used. It is possible that the best fit is exponential at low tointermediate concentrations and may approach a linear relationship at higher

concentrations. It is recommended to use non-linear regression analysis in future, forthis is probably a good method for statistical analysis (it does not presume a specific

function).For the regression equations using the linear data the Digital Number step-size is

most often more limiting in the resolution of the determination of the water qualityparameter than the standard error of estimate. It is the radiometric resolution of the

Thematic Mapper which limits determination possibilities.

A predictive modelling (using a radiative transfer approach) should be carriedout in order to estimate the range of reflectance values to be expected and tounderstand the influence of size, type and concentration of the main optically active

water quality parameters (such as algae, suspended matter and aquatic humus) on

the spectral signature of the waters under consideration.It is recommended that previous research and ongoing research in the Nether-

lands using satellite remote sensing for surface water quality determination performa regression analysis on their data sets using a log-transformation of the data or anon-linear regression with a forced zero intercept. This will prevent results such as

negative values when applying the full range of digital numbers present in the image

to the regression equation.The result shown here are in accordance with the results by Lathrop and

Lillesand (1986) over Green Bay and Lake Michigan. The range of the water qualityparameters used in this research is twice as high for chlorophyll a and half the values

for SD. The TM digital number data for each band are equivalent in the two studies.


Recommendations are to carry out the following activities, either at a regional,national, continental or global scale:

1. Construct a database for inland surface water satellite observations.2. Develop atmospheric correction procedures to make comparison of all images

possible.3. Incorporate model knowledge and field observations.4. Construct a Surface Water Expert System.

list of symbolsDN : digital numberDN-step : digital number step sizeDW : seston dry weight (mgl t)Pigm : sum of chlorophyll-a and phaeopigments (pgl-1)P,o, : total phosphate (pgl t)R : correlation coeÍficientSD : Secchi depth or Secchi disk transparency (cm)(Rt)% : coefficient of determinationEu" : subsurface upwelling irradiance (Wm-2nm 1)

Lui, : airborne measured upwelling radiance (Wm-2nm 1sr 1)

(sr,)oÁ : standard error of estimate expressed as a percentage of the mean value of thedependent variable

(sr,) : standard error of estimate, : mean value of the dependent variableln : natural logarithm (e-based)

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Basic data 1983-1988 (in Dutch), WOL-Report nrl989-5, Limnological Institute,Nieuwersluis, The Netherlands.

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The use of the Thematic Mapper for the analysis of eutrophic lakes: a case study in the Netherlands

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