Full text of DOI:10.1080/01431160120942

International Journal of Remote Sensing
ISSN: 0143-1161 (Print) 1366-5901 (Online) Journal homepage: http://www.tandfonline.com/loi/tres20
Derivation and validation of the seasonal thermal
structure of Lake Malawi using multi-satellite
AVHRR observations
M. Wooster , G. Patterson , R. Loftie & C. Sear
To cite this article: M. Wooster , G. Patterson , R. Loftie & C. Sear (2001) Derivation and
validation of the seasonal thermal structure of Lake Malawi using multi-satellite AVHRR
observations, International Journal of Remote Sensing, 22:15, 2953-2972
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Date: 21 March 2016, At: 20:30

int. j. remote sensing, 2001, vol. 22, no. 15, 2953–2972
Derivation and validation of the seasonal thermal structure of Lake
Malawi using multi-satellite AVHRR observations
M. WOOSTER
Department of Geography, King’s College London, Strand, London,
WC2R 2LS, England, UK
e-mail: martin.wooster@ kcl.ac.uk
G. PATTERSON, R. LOFTIE and C. SEAR
The Natural Resources Institute, University of Greenwich, Chatham Maritime,
Chatham, Kent, ME4 4TB, England, UK
(Received 19 October 1999; in Ž nal form 15 May 2000)
Abstract. Lake Malawi is the second largest lake in Africa by volume and an
important regional source of food. Seasonal  uctuations in the primary production
of the lake are principally controlled by the lake’s thermal structure, which
modulates the mixing of nutrient-rich deep water with that of the phytoplankton-
rich near-surface layer. Satellites potentially oVer an eYcient, low cost method of
providing information on the lakes thermal structure over the longer term via
remote sensing observations of lake surface temperature. Here we investigate the
accuracy of remotely sensed lake surface temperatures derived using data from
the NOAA-11 AVHRR over a two-year period (1992–1993). Optimised triple
window atmospheric correction algorithms are shown to provide an accuracy of
°
around 0.5 C when compared to in situ water temperatures. The eVect of the
1994 switch in operational night-time satellite from NOAA-11 to NOAA-14 is
assessed using modelling of the transfer of radiation through the Malawian
atmosphere, combined with detail on the diVerences in the satellite spectral
response functions. These simulations indicate that lake surface temperatures
derived from NOAA-14 are warmer than those that would be derived from
NOAA-11 under the same conditions. The magnitude of the temperature diVer-
°±
°
ence is estimated at 0.27 0.07 C, depending on the viewing zenith angle. Finally,
we illustrate the ability of the remotely derived surface temperature maps to
provide information relevant to the lakes 3-D thermal structure. Evaluations of
the annual mixing regime of the lake can be based on this information, this mixing
being directly relevant to the seasonal variations in lake primary production.
1. Introduction
Lake Malawi lies in the western arm of the East African Rift valley (Ž gure 1)
and is the second largest lake in Africa by volume, containing almost 7% of the
Earth’s liquid freshwater. There is strong vertical stratiŽ cation in terms of temper-
ature and nutrients, with nutrients depleted in the upper trophogenic region of the
water column (Eccles 1974, Patterson and Kachinjika 1995). When the epilimnion
temperature approaches that of the metalimnion (22.7–23.5 C) increased mixing
°
occurs and nutrients are supplied to the trophogenic zone, with a resultant increase
International Journal of Remote Sensing
ISSN 0143-1161 print/ISSN 1366-5901 online © 2001 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/01431160010006999

2954
M. Wooster et al.
in phytoplankton productivity since this production is normally nutrient limited
(Dengbol and Mapila 1982, Patterson and Kachinjika 1995). A similar increase in
trophogenic zone nutrients is also the expected result of any large-scale upwelling
of lake water, and the resulting increases in phytoplankton productivity have been
shown to correlate with the productivity and survivability of the lake’s pelagic Ž sh
community (Allison et al. 1995).
Because vertical mixing of the water column is so important to productivity, any
study of the lake’s large-scale primary production requires data on the 3-D thermal
structure of the water and it’s seasonal variation. Such data are normally obtained
by interpolating vertical temperature proŽ les made during a series of lake transects.
However, due to the size of Lake Malawi, this is a major and very costly undertaking
that may take up to two weeks from a synoptic cruise to produce data for a single
3-D model. Interpretation of the data derived from such in situ sampling is also
limited by diYculties in separating the eVects of spatial and temporal water temper-
ature variations, which may be highly signiŽ cant within each sampling period.
Satellite remote sensing provides a method of addressing these diYculties since a
single overpass by a US National Oceanic and Atmospheric Administration (NOAA)
polar orbiting satellite will provide Advanced Very High Resolution Radiometer
(AVHRR) data of the entire lake surface (cloud cover permitting). These data can
be used to map the lake surface brightness temperature variation using data from
the AVHRR’s three thermal infrared channels (3.7, 11 and 12 mm) at a spatial
resolution of approximately 1.1 km near nadir. Using variations of the atmospheric
2
correction techniques commonly used to map the surface temperature distribution
of the open ocean (e.g. McClain 1989) these brightness temperatures can theoretically
be related to the true temperature of the lake’s surface water. However, there are a
number of uncertainties that remain to be addressed: (i) how precisely can the
AVHRR brightness temperatures be related to the thermodynamic temperature of
the surface epilimnion layer over the range of an annual cycle?; (ii) how is the
accuracy of the temperature estimates aVected by the changes in operational NOAA
satellite that occur during long-term monitoring campaigns?; and (iii) how do the
derived surface temperatures relate to the lake’s 3-D thermal structure? The purpose
of this paper is to address these questions by (i) calibrating and validating a long-
term set of AVHRR-derived infrared brightness temperatures against a set of contem-
poraneous in situ epilimnion temperatures for Lake Malawi, (ii) using radiative
transfer modelling to evaluate the eVect of diVering AVHRR thermal channel Ž lter
functions on the infrared brightness temperature measurements made under local
conditions, and (iii) comparing maps of remotely-sensed lake surface temperature to
contemporaneous data on the lake’s three-dimensional thermal structure.
2. Remote estimation of surface water temperature using AVHRR
The remote estimation of sea surface temperature (SST) is a well developed
operational application of AVHRR (Kidwell 1995, McClain 1989). The method
generally involves combining infrared brightness temperature measurements from
two or three of the AVHRR thermal channels in order to correct for the absorbing
and emitting eVects of the atmosphere, the so-called ‘split-’ and ‘triple-window’
atmospheric correction approaches Ž rst suggested by Anding and Kauth (1970).
Optimisation of the algorithm coeYcients can provide remote temperature estimates
with a root mean square deviation (RMSD) of around 0.5 C from those taken by
°
in situ  oating buoys on the open ocean (Kidwell 1995). These methods should also

Seasonal thermal structure of L ake Malawi from AVHRR
2955
be applicable to large inland lakes, with some uncertainty regarding the measurement
precision due to potential diVerences between the atmosphere over lakes and that
over open oceans. Such diVerences include the fact that (i) the atmosphere over
inland lakes may not be in thermodynamic equilibrium with the water surface due
to the eVect of the warmer (daytime) or cooler (night-time) surrounding land,
(ii) inland atmospheres may contain markedly increased concentrations of tropo-
spheric aerosols compared to those over open oceans, and (iii) atmospheric thickness
will vary depending on the altitude of the lake surface. These eVects are likely to
be most signiŽ cant in tropical regions and may signiŽ cantly eVect the performance
of AVHRR-based lake surface temperature algorithms. Derivation and testing of
new split and triple window atmospheric correction algorithms for Lake Malawi
allows the accuracy and precision of these optimised remotely sensed temperature
measurements to be determined.
3. Application to Lake Malawi: algorithm derivation and accuracy assessment
3.1. Daytime versus night-time data
Disregarding viewing geometry variations, the AVHRR on each operational
NOAA satellite observes a particular Earth location twice daily, with overpasses
separated by approximately 12 hours (Kidwell 1995). For the period of the initial
algorithm derivation and testing, commencing in 1992, the NOAA-11 satellite was
the operational system. The satellite orbit meant the AVHRR imaged Lake Malawi
within 1 hour of 01:30 (night-time) and 13:30 (daytime) local time each day. Hence
±
it was Ž rst necessary to consider which overpass was the most appropriate for
providing accurate data relevant to lake surface temperature.
Intensively sampled vertical proŽ les of epilimnion temperature were collected at
the Nkhata Bay station (11 36 S, 34 30 E) (Ž gure 1). These were made using a
°
ê
°
ê
purpose-built continuous temperature/depth probe (Plymouth Marine Laboratory,
UK). Figure 2 shows a depth/time plot of a 24 hour study on 6 and 7 April 1992 at
this station. Isotherms were plotted using the Surfer software package (Golden
Software Inc.).
It is clear that after around 10:00h local time, absorption of solar radiation by
the upper water column results in the formation of a diurnal thermocline. The
thermocline strength peaks around 14:00 h, which is close to the 13:30 h daytime
overpass time of NOAA-11. This indicates that lake surface temperatures retrieved
from daytime satellite imagery are representative of only the top few meters of the
water column. The magnitude of the diurnal thermocline eVect would be expected
to increase still further during the hottest months (October–December), especially
during periods of low wind speed. In contrast the night-time satellite overpass around
01:30 h occurs when water temperatures at the near surface (1 m depth) are represent-
ative of the bulk mixed layer, in the case of Ž gure 2 being within 0.1 C of those at
°
25 m depth. This is conŽ rmed by proŽ les made on other dates and, since the mixing
of epilimnion and metalimnion waters is dependent upon the temperature of the
bulk epilimnion layer, these data suggest that the night-time overpass of the NOAA-
11 satellite is most appropriate for hydrodynamic investigations.
An insight into the spatial variation of the diurnal thermocline can be gained
from direct comparison of AVHRR geocoded daytime and night-time imagery
(Ž gure 3). These data were processed using the split window algorithm of McClain
et al. (1985), which was found to give the best performance on Lake Malawi during
the pilot study of Wooster et al. (1994a). A mean surface temperature diVerence of

2956
M. Wooster et al.
Figure 1. Lake Malawi showing the location of the Nkhata Bay and Nkhotakota sampling
stations and the Senga Bay NOAA receiving station.
0.75 C is observed between daytime and night-time conditions, but there is a high
°
degree of spatial variation with a maximum temperature diVerence of 3 C. A propor-
°
tion of this variation will be due to  uctuations in the surface skin eVect (Hepplewhite
1989), but the majority is likely to be due to spatial variations in the magnitude of
the diurnal thermocline, as described above.
3.2. New algorithm derivation: split versus triple window
For routine collection of NOAA-11 night-time data, a PC-based NOAA AVHRR
High Resolution Picture Transmission (HRPT) receiving station was installed at the
lake-shore research station at Senga Bay, Malawi (Wooster et al. 1994b). After HRPT

Seasonal thermal structure of L ake Malawi from AVHRR
2957
Figure 2. Contour plot showing the relationship between water temperature, depth and time
at the Nkhata Bay sampling site on 6–7 April 1992. The daylight period for 7 April
1992 is indicated, as well as the overpass times of the NOAA-11 satellite during the
period of the study (1992–1994). Diamond symbols indicate the location of each
temperature measurement. Local time in Malawi is East Africa Standard, equivalent
+
to GMT 2 hours.
data capture, the AVHRR data are extracted and converted into geocoded maps of
lake surface brightness temperature in the three AVHRR thermal channels, using
the calibration techniques detailed in Wooster et al. (1995). Detection of cloud
contaminated pixels was based on the multi-channel brightness temperature compar-
ison techniques of Saunders and Kriebel (1988), with threshold alterations made to
account for the tropical atmosphere. During an initial eight month period in 1992
in situ surface temperature data were collected from the roving research vessel, R/V
Usipa. These night-time measurements were made every hour between 21:00 h and
06:00 h, and gave a wide coverage of lake surface temperature as they followed the
cruise pattern laid down by the Ž sh acoustic survey (Menz et al. 1995). Water was
sampled using a Khalsico thermometer bucket with a mercury stem thermometer
accurate to 0.1 C. Using these data Wooster et al. (1994a) made a preliminary test
±
°
of the applicability of published SST algorithms for the remote measurement of
tropical lake surface temperature. Though this limited data set did not cover full
seasonal range, results suggested that an accuracy similar to that obtained over the
open ocean could be expected with suitably optimised algorithms. A signiŽ cantly
expanded satellite and in situ data set covering a full two year period (1992–1993)
has now been compiled for the optimisation and testing of new algorithm coeYcients.
The complete data set consists of 65 data pairs of cloud-free AVHRR pixels and
corresponding in situ water temperature measurements taken either during the same
night or on immediately neighbouring nights. This temporal limit was calculated

2958
M. Wooster et al.
from analysis of the maximum change in near surface (1 m) temperature, based on
data from the second Ž xed station (the Nkhotakota station 12 43 S, 34 30 E;
Ž gure 1). This station was visited a total of 29 times in 1992 and 1993 to produce a
°
ê
°
ê
seasonal depth-time plot (Patterson and Kachinjika 1995). From this a maximum
rate of change of 0.15 C day was demonstrated. Half (33) of the data pairs were
Õ1
°
randomly selected as Matchup Set A and used to empirically derive new algorithm
coeYcients optimised for local conditions (equations 1 and 2). The techniques used
for algorithm derivation were the regression-based procedures outlined in Wooster
et al. (1994b), with the relative strength of the satellite versus in situ data relationship
indicated by the correlation coeYcient and RMSD values resulting from the deriva-
tion procedure.
Split Window (r 0.34, RMSD 0.69 C)
°
2=
=
LST 2.1226T
=
1.1226T
271.16
(1)
(2)
-
-
4
5
Triple Window (r 0.92, RMSD 0.39 C)
2=
=
°
LST 0.9115T
=
0.9191T
0.8246T
273.21
-
+
-
3
4
5
where LST is lake surface temperature ( C), T is the AVHRR channel 3 (3.7 mm)
°
brightness temperature (K), T is the AVHRR channel 4 (11 mm) brightness
3
4
temperature (K), T is the AVHRR channel 5 (12 mm) brightness temperature (K).
The most appropriate and robust test of the accuracy and precision of these new
5
equations was to evaluate their performance when applied to an independent satellite
and in situ dataset. For this purpose we utilised the remaining 32 data pairs
(Matchup Set B) not used in the algorithm derivation procedure, with results shown
in Ž gure 4. With this independent dataset the scatter exhibited by the triple window
algorithm is much reduced in comparison to the split window algorithm, with a
consequent reduction in the overall measure of root mean square deviation between
the in situ and satellite-based measurements. The superior performance of the triple
window technique agrees with the pilot study results using previously published split
and triple window SST algorithms (Wooster et al. 1994a).
The reason for the eVectiveness of including AVHRR channel 3 measurements
in the surface temperature derivation can be investigated by comparing the brightness
temperature diVerences between the various AVHRR thermal channels to a measure
of the overall atmospheric eVect on the signal. In this case the atmospheric eVect is
represented by the deŽ cit between the actual in situ temperature measurement and
the brightness temperature recorded in AVHRR channel 4. Figure 5(a) shows that
the brightness temperature diVerence between AVHRR channels 4 and 5 is well
correlated to the magnitude of the atmospheric eVect. This relationship results from
the fact that AVHRR channels 4 and 5 split the 8–14 mm atmospheric window and
are thus diVerentially sensitive to water vapour absorption. This is the basis of
the split window atmospheric correction method originally proposed by Anding
Figure 3. The diVerence in lake surface temperatures retrieved using NOAA-11 AVHRR
data collected at 15:18 h on 26 August 1992 and 02:28 h on 27 August 1992 (all times
±
°
are local). The mean temperature diVerence is 0.75 0.61 C (analysis of 24 932 cloud
free pixels). Bulk water temperatures are not expected to have altered signiŽ cantly
in the 11 hour period between satellite overpasses, thus the observed temperature
diVerence is predominantly due to the formation of a daytime diurnal thermocline.

Seasonal thermal structure of L ake Malawi from AVHRR
2959

2960
M. Wooster et al.
Figure 4. The new (a) split window, and (b) triple window algorithms, derived with Matchup
Set A and tested with Matchup Set B.
Figure 5. The relationship between the brightness temperatures measured in the AVHRR
thermal channels and the magnitude of the atmospheric eVect, represented by the
temperature deŽ cit between the in situ temperature measurement and the AVHRR
channel 4 brightness temperature. Data are derived from the 65 matchup points used
in the current study. The magnitude of the atmospheric eVect is signiŽ cantly correlated
to the channel 4–5 brightness temperature diVerence (Ž gure 5(a)), but a stronger
correlation is observed with the channel 3–4 brightness temperature diVerence
(Ž gure 5(b)). This highlights the importance of using AVHRR channel 3 measurements
in the tropical atmospheric correction algorithm.

Seasonal thermal structure of L ake Malawi from AVHRR
2961
and Kauth (1970). However, Ž gure 5(b) indicates the relationship is signiŽ cantly
strengthened by replacing the brightness temperature diVerence between AVHRR
channels 4 and 5 with that between channels 3 and 4. This is because measurements
made in AVHRR channel 3 are less aVected by atmospheric water vapour than are
those made at the longer wavelengths of channels 4 and 5 (Hepplewhite 1989). Thus
for high humidity atmospheres the AVHRR channel 3–4 brightness temperature
diVerence will provide a stronger measure of the atmospheric eVect than will the
brightness temperature diVerence recorded in the so-called split window channels.
The tropical nature of the Malawian atmosphere thus necessitates the use of AVHRR
channel 3 data if the performance of the atmospheric correction procedure is to be
maximised. This result also illustrates a further advantage of using night-time
AVHRR data, since re ection of solar radiation from the water surface prevents
quantitative use of daytime 3.7 mm observations.
3.3. Use of angularly varying coeYcients
In addition to incorporating data from AVHRR channel 3, a further method of
algorithm optimisation is to vary the algorithm coeYcients in proportion to the air
mass between the satellite and ground pixel (Llewellyn-Jones et al. 1984, Barton
et al. 1989). The air mass is dependent upon the viewing zenith angle, which in the
case of AVHRR data captured in Malawi was limited to a maximum of 50 in order
°
to avoid near-horizon satellite overpasses. To gauge the eVect of varying view angle
on the retrieved estimates of lake surface temperature, the diVerence between the
in situ and AVHRR-derived lake surface temperatures was plotted as a function of
viewing zenith angle (Ž gure 6). No consistent relationship is apparent, though the
location with the highest air mass also exhibits the largest temperature diVerence.
Figure 6. The diVerence between the in situ and AVHRR-derived lake surface temperatures,
as a function of the air mass between the satellite and the matchup location. The
=
AVHRR LST measurement was made using equation (2) and air mass sec(viewing
zenith angle).

2962
M. Wooster et al.
A new triple window algorithm which incorporated angularly varying coeYcients
was derived using Matchup Set A.
Angularly varying triple window (r
0.94, RMSD 0.36 C)
= °
2=
LST (1.0650 3.6803A)T
=
(0.7523 2.986A)T
+
-
+
3
(0.7955 0.7090A)T 277.98
4
(3)
-
-
-
5
Where A airmass
1
sec(viewing zenith angle) 1.
=
- =
Accuracy assessment was again carried out using the independent Matchup data
set B. An RMSD of 0.36 C was obtained, which is a small (0.05 C) improvement on
-
°
°
that obtained with non-angularly dependent coeYcients (equation 2). This is insigni-
Ž cant compared to overall algorithm accuracy and, given the viewing geometry
limits set by the data capture system, equation (2) was chosen as most appropriate
for routine LST derivation.
3.4. Aerosol eVects
Under most atmospheric conditions, the AVHRR brightness temperatures
retrieved for the lake surface will decrease with increasing thermal channel wavelength
due to the increasing eVectiveness of atmospheric water vapour absorption over this
region of the electromagnetic spectrum (Llewellyn-Jones et al. 1984). However, as
Ž gure 5(b) illustrates, the retrieved brightness temperatures are sometimes lower in
AVHRR channel 3 than in channel 4. This could potentially result from the eVect
of a strong atmospheric temperature inversion, but in this case the normal channels
4 and 5 brightness temperature relationship would also be reversed (i.e. T
T ),
>
5
4
which is not observed. We therefore suggest that a more likely explanation is the
interaction of the surface emitted radiation with atmospheric aerosols, particularly
dust particles and haze from vegetation Ž res. Hepplewhite (1989) shows that bright-
ness temperature deŽ cits due to atmospheric aerosols are many times more signiŽ cant
for AVHRR channel 3 than for the longer channel 4 or 5 wavelengths. Furthermore,
we only observed depressed channel 3 brightness temperatures at the end of the
1992 and 1993 dry seasons, the period when concentrations of atmospheric dust and
haze is maximised. However, since these anomalous observations were not the ones
to exhibit the largest diVerences between the in situ and AVHRR-derived LST’s, the
eVects of this phenomenon are believed to be relatively minor. Further research to
investigate the potential advantage of deriving aerosol resistant algorithms (e.g.
Walton 1985) would most likely be beneŽ cial.
3.5. Changes in the operational NOAA satellite
The onboard calibration system for the AVHRR thermal channels allows in-
orbit sensor variations to be compensated for during routine data processing (Kidwell
1995). However, since there are diVerences in the spectral response functions of
corresponding thermal channels on diVerent AVHRR instruments, there maybe
residual eVects when switching between data obtained from diVerent satellites
(Kidwell 1995). The Lake Malawi triple window atmospheric correction algorithm
(equation 2) was derived from empirical analysis of NOAA-11 AVHRR data. In
1994 the NOAA-11 AVHRR failed on 13 September and in December the NOAA-
14 satellite was launched as a replacement. An investigation into the eVect of this
satellite change on the accuracy and precision of equation (2) was required if long-
term monitoring of the lake was to be continued using NOAA-14.

Seasonal thermal structure of L ake Malawi from AVHRR
2963
The spectral response functions for the AVHRR instruments on the NOAA-11
and NOAA-14 satellites are shown in Ž gure 7. In general the NOAA-14 AVHRR
channels are shifted to slightly longer wavelengths than the corresponding channels
of NOAA-11. Figure 7 also illustrates that the atmospheric eVect on the water-
leaving thermal radiance, illustrated here by the atmospheric transmission, also varies
considerably across the wavebands. The combination of the inter-satellite spectral
response variations and the wavelength varying atmospheric eVect will cause the
corresponding channels of the two AVHRR instruments to measure slightly diVerent
brightness temperatures for the same emitting temperature of the water surface. Since
equation (2) combines a series of multi-channel brightness temperatures, the lake
Figure 7. The normalised spectral response functions of the NOAA-11 (solid) and NOAA-
14 (dashed) AVHRR thermal channels centred around (a) 3.7 mm, (b) 11 mm, and
(c) 12 mm. These data are taken from Kidwell (1995). Also plotted on the right hand
side y-axis is the atmospheric transmission over these wavebands (dotted line) for
the Lake Malawi atmosphere sampled on 14 November 1992, calculated using the
MODTRAN radiative transfer model.

2964
M. Wooster et al.
surface temperature output may diVer signiŽ cantly when using data from the two
diVerent AVHRR instruments. Unfortunately a direct comparison of contemporan-
eous NOAA-11 and NOAA-14 AVHRR data was not possible since the satellites
did not operate simultaneously. Nor were high precision in situ temperature data
available for comparison with NOAA-14 imagery since, after the derivation and
testing of equation (2), routine monitoring of the lake temperature is conducted
using remote sensing methods only. Instead the magnitude of the NOAA 11 to
NOAA 14 switch was gauged using simulated NOAA-11 and NOAA-14 brightness
temperature measurements, constructed using a radiative transfer code parameterised
with data of the Malawian atmosphere. Using these simulated measurements in
equation (2), it is possible to predict the diVerences in remotely sensed lake temper-
ature that would be obtained by the two satellites when observing the lake under
identical viewing conditions.
The MODTRAN radiative transfer code (Berk et al., 1989) was parameterised
with historical atmospheric proŽ le data taken by the Malawi Meteorological
Department in Lilongwe during March, September and December 1977. Using the
techniques of Byrnes and Schott (1986) the lower section of these proŽ les were
adjusted to represent conditions over the lake surface using contemporaneous data
from the lake-shore meteorological station at Salima. These historical data were also
supplemented with data from two more recent radiosonde ascents, collected directly
over the lake in November 1992 (Brown 1995). The MODTRAN code was para-
meterised with each atmospheric proŽ le in turn and used to simulate the path of
thermal radiation from the lake surface to the satellite and to predict the top-of-
atmosphere (TOA) spectral radiance over the entire wavelength range covered by
the AVHRR thermal channels shown in Ž gure 7. For each proŽ le the emitting surface
water temperature was varied in 2 C intervals between 20 C and 30 C, encompassing
°
the full range of lake surface temperatures, and the viewing zenith angle was varied
°
°
between 0 and 50 . The spectrally varying fresh water emissivities given by Masuda
°
°
et al. (1988) were assumed. The TOA radiance data resulting from each model run
were convolved with each AVHRR channel spectral response function to provide a
prediction of the measured spectral radiance over each AVHRR waveband. Following
the description of Cracknell (1997), the corresponding AVHRR channel brightness
temperatures were then calculated using iteration of equation (4), given in the
NESS107 supplement to Kidwell (1995), until the assumed brightness temperature
value reproduced the calculated channel spectral radiance.
n
B(l , T )DlR (l )
æ
i
i i
Spectral Radiance (Wm sr mm
Õ2 Õ1
)
i=1
(4)
Õ1 =
DlR (l )
i
i
where T is the channel brightness temperature, B is the Plank Function spectral
radiance (Wm sr mm ), n is the number of measurements comprising the
Õ2 Õ1 Õ1
channel spectral response function, Dl is the wavelength increment between the
measurements of spectral response (mm), R is the normalised spectral response
function at location i (unitless) l is the wavelength at spectral response function
location i (mm)
i
i
The calculated channel brightness temperatures were then used within equation
(2) to reproduce the lake surface temperatures that would be obtained by the two
satellite instruments when observing the lake under the same viewing conditions.

Seasonal thermal structure of L ake Malawi from AVHRR
2965
As an example Ž gure 8 shows the radiosonde proŽ le data taken on 14 November,
1992, and Ž gure 9 shows the diVerence in the NOAA-11 and NOAA14 derived lake
surface temperature estimates, calculated using these radiosonde data within the
MODTRAN code and simulating observations at the two stated viewing conditions
and six surface temperatures. These data indicate that there is a diVerence in the
Figure 8. The temperature and water vapour proŽ le of the atmosphere over Lake Malawi,
sampled by radiosonde on 14 November 1992.
Figure 9. The diVerence in the estimates of lake surface temperature (LST) calculated using
simulated NOAA-14 and NOAA-11 AVHRR brightness temperatures within equation
(2) for nadir (lower line) and far oV-nadir (upper line) conditions. Brightness temper-
ature values were simulated using the radiosonde data of Ž gure 8 within the
= °
MODTRAN code, with zenith angle 0 for nadir, and zenith angle 50 for far-oV
nadir observations. Dotted lines indicate the best linear Ž t to each set of data points.
= °

2966
M. Wooster et al.
lake surface temperatures calculated using the NOAA-11 and NOAA-14 AVHRR
instruments under these atmospheric conditions, and that this diVerence increases
with the surface temperature of the lake and with the zenith angle used to make the
observation. However, the data indicate that the magnitude of the eVect is relatively
small, with values of 0.21 0.8 C for the nadir observations, and 0.25 0.8 C for the
±
°
±
°
far oV-nadir observations. Analysing the diVerence in the individual channel bright-
ness temperatures indicates that the AVHRR channel 3 measurements are negligibly
aVected by the change in satellite, with a maximum brightness temperature diVerence
of 0.02 C, whilst the AVHRR channel 5 measurements are most signiŽ cantly aVected,
°
with a maximum brightness temperature diVerence of 0.6 C. This re ects both the
°
varying nature of the spectral response function diVerences between channels shown
in Ž gure 7, and the fact that the atmospheric eVect generally increases with increasing
channel wavelength.
Figure 10 shows the lake surface temperatures retrieved from the NOAA-11 and
NOAA-14 AVHRR simulations, using all sampled atmospheres and all simulated
viewing conditions. It can be seen that the temperature estimates made using the
two satellites are very highly correlated (r 0.99), with estimates made using simu-
2>
lated NOAA-14 AVHRR data 0.27 0.07 C higher than the corresponding estimates
±
made with simulated NOAA-11 AVHRR data. This positive bias will counteract the
°
negative ( 0.17 C) bias originally exhibited by equation (2) when tested with NOAA-
-
11 AVHRR and in situ data (Ž gure 4(b)). In this way it is predicted that a bias of
°
only around 0.1 C should result between in situ LST measurements and the corres-
°
ponding estimates produced from application of equation (2) to NOAA-14 AVHRR
data. The magnitude of this predicted bias is lower than the noise level of the
AVHRR sensor (Kidwell, 1995) and of the same order as the 0.1 C precision of the
°
Figure 10. Modelled NOAA-14 and NOAA-11 lake surface temperature (LST) measurements
for a range of actual surface temperature and view angle conditions. LST measure-
ments were calculated using NOAA-11 and NOAA-14 AVHRR brightness temp-
eratures simulated using the MODTRAN code with a seasonal range of Lake Malawi
atmospheric proŽ le data. The 1:1 line is indicated.

Seasonal thermal structure of L ake Malawi from AVHRR
2967
in situ measurements used in the original algorithm derivation and testing. As
previously mentioned, due to the logistics involved in making extended high precision
in situ temperature measurements from the research vessel, no long-term in situ data
of a similar precision are available for direct comparison with temperature estimates
provided by NOAA-14. However, for periods interspersed throughout 1997–98 night-
time in situ temperatures are available from two thermistors/data loggers that were
anchored at around 1 m depth at 13 26 S, 34 45 E and 13 52 S, 34 52 E (Ž gure 1).
°
ê
°
ê
°
ê
°
ê
Due to the diVering methodology, the precision of these measurements is lower than
the 0.1 C quoted for the original bucket temperature measurements, but they provide
°
an empirical method of testing for any gross errors in the temperature estimates
derived using equation (2) with NOAA-14 data. Matchups were made between these
thermistor data and NOAA-14 AVHRR images taken within 1 hour of the thermistor
measurement on twenty occasions in 1997–98, spaced approximately evenly through-
out the less-cloudy May–November period. Two bucket temperature measurements
made from the research vessel over this period were also matched to cloud free
imagery. Figure 11 shows the results of this matchup study, with a positive bias of
0.06 C between the satellite and in situ data. This compares with the negative bias
°
originally obtained when using NOAA-11 data (Ž gure 4(b)) and helps conŽ rm the
suggestion that, viewed through the same atmosphere, water surface temperatures
derived via NOAA-14 observations are slightly warmer than those derived via
NOAA-11. The scatter of the data shown in Ž gure 11 is a little higher than that
obtained during original testing of the new triple window algorithm (Ž gure 4(b)),
which probably re ects the lower precision of the thermistor measurements compared
to those made using the bucket measurement technique. Overall the results from
the empirical study conŽ rm the hypothesis developed using the radiative transfer
Figure 11. The matchup data set for empirical testing the accuracy of the NOAA-14-derived
lake temperature estimates. The AVHRR estimated temperatures were derived using
triple window equation (2) with NOAA-14 AVHRR data, whilst the in situ data set
consists of thermistor and bucket temperature measurements made within one hour
of the corresponding satellite overpass.

2968
M. Wooster et al.
modelling, in that the NOAA-14 derived LST measurements possess a negligible
temperature bias in comparison to the measurement precision. They indicate that
when using NOAA-14 AVHRR data to estimate the surface temperature of the lake
with equation (2), an RMSD accuracy is obtained that is comparable to that achieved
using the NOAA-11 AVHRR data for which the algorithm was originally designed,
i.e. around 0.05 C.
°
4. Seasonal monitoring of lake thermal structure
In order to validate their use in limnological and hydrological studies, the images
of lake temperature retrieved using remote sensing must be compared to three-
dimensional data on the lake water structure, derived using the standard methods
of direct in situ sampling and data interpolation. For this purpose our in situ data
consisted of vertical temperature proŽ les collected during a series of research cruises
in 1992 and 1993. Temperature measurements were made using a hydrographic
probe and were taken along the central north–south axis of the lake to around 320 m
depth (or close to the bottom if shallower). Satellite-derived LST maps were produced
from the application of equation (2) to night-time NOAA-11 AVHRR data acquired
on a near-daily basis from May 1993 to September 1994. This period partly over-
lapped with the in situ cruise sampling period carried out between January 1992 and
January 1994. Useful comparisons between these data sets were not possible for the
mid- to late-wet season (January–March 1994) due to excessive cloud cover.
However, this is the hottest period of the year and it was shown for previous years
to be a period when thermal stratiŽ cation of the lake water was strongest and thus
mixing was at a minimum (Patterson and Kachinjika 1995). Outside of this period
there is good agreement between all the in situ and satellite-derived datasets. Figure 12
shows a good example from July 1993, with the water temperature structure derived
from interpolation of a series of lake-wide in situ temperature proŽ les compared to
the AVHRR-derived lake surface temperature map of the same period. This LST
map is derived from maximum value compositing of four separate July 1993 LST
images, each of which had part of the lake obscured by cloud. A 3 3 smoothing
×
algorithm was applied to reduce the eVect of AVHRR sensor noise (Llewellyn-Jones
et al. 1984) and the land has been masked using a GIS data Ž le of the lake shoreline.
The major thermal feature in July 1993 (Ž gure 12) is the presence of a signiŽ cant
cold water plume located around the position of the second vertical proŽ le (midway
across the lake at a latitude of around 10 11 S). On the proŽ le data the plume is
°
ê
apparent at this location as a set of near vertical contours, with colder water
apparently rising to the surface from the metalimnion layer at around 100 m depth.
Such a vertically rising cold water plume is expected to have signiŽ cantly increased
the photic-zone nutrient concentration in this region of the lake. On the satellite-
derived lake surface temperature map the plumes presence at the stated location is
indicated by a colder patch of surface water of around 30 km , exhibiting temper-
2
atures around 1 C cooler (24.25–24.75 C, green on the LST map) than the immediate
°
°
surrounding surface water (yellow-orange-red on the LST map). A few months after
the July 1993 upwelling a similar cold water event was again noted on LST maps
of the northern lake region, and Patterson et al. (1995) describe how these 1993
upwellings were correlated with higher levels of zooplankton and Ž sh larvae produc-
tion when compared to the latter part of 1992, when no such upwellings were noted.
These comparisons conŽ rm that real, large-scale limnological events having direct
relevance to lake productivity are observable using the remote sensing technique.

Seasonal thermal structure of L ake Malawi from AVHRR
2969

2970
M. Wooster et al.
Using the extended satellite time-series, the overall seasonal pattern of water
temperature variation within the bulk epilimnion layer can be deduced. Figure 13
shows the mean and standard deviation of the whole lake surface temperature for
the 17 month period of initial satellite data collection. Each point on the Ž gure
corresponds to a low cloud cover ( 10%) image of the lake and is calculated from
<
all cloud-free lake pixels (n 20 000). The results indicate that mean lake epilimnion
>
temperature reaches a minimum in August, when vertical mixing is assumed to be
at a maximum. September 1993 and 1994 sees an upturn in mean lake epilimnion
temperature, related to atmospheric warming and a reduction in evaporative cooling
caused by reduced winds. Such near-continuous temperature data are useful for the
calculation of water density and can be applied to the calculation of parameters
(such as the Wedderburn number) which deŽ ne the dominant tendency of a water
body i.e. mixing or stratiŽ cation (Talling and Lemoalle 1998). Patterson et al. (1995)
indicate how Wedderburn numbers calculated using remote sensing data of this type
for Lake Malawi can reliably reproduce those calculated from in situ measurements,
thus allowing the mixing regime to be quantitatively assessed from remote sensing
and meteorological data alone (assuming some knowledge of metalimnion density).
5. Conclusion
This study has indicated that night-time NOAA-11 AVHRR observations com-
bining data from all three AVHRR thermal channels can provide estimates of the
near-surface (1 m depth) water temperature of Lake Malawi to a RMSD accuracy
of around 0.5 C when compared to in situ water temperature measurements. A new
°
triple window atmospheric correction algorithm is presented for this purpose. The
eVect of the switch in operational night-time satellite from NOAA-11 to NOAA-14
at the end of 1994 has been assessed and it has been shown that accurate lake surface
temperatures can continue to be derived from these new NOAA-14 data without the
need for major algorithm alteration. Comparison with vertical temperature proŽ les
±
Figure 13. The mean 1 standard deviation of Lake Malawi surface temperature calculated
from cloud-cleared AVHRR data taken between May 1993 and September 1994.
Images with 10% cloud cover or less were used in this analysis.

Seasonal thermal structure of L ake Malawi from AVHRR
2971
indicate that the near-surface temperature estimates derived via remote sensing are
representative of the bulk mixed epilimnetic layer, which represents the thermal
barrier to lake water mixing. AVHRR-derived lake temperature maps are shown to
portray information related to the 3-D thermal structure of the water, in particular
on the horizontal and vertical displacement of lake isotherms and on large-scale
upwelling events that are also observed via detailed in situ sampling. Analysis of 17
months of AVHRR data indicates that the mean surface (epilimnion) temperature
most closely approaches that of the metalimnion in August, which is inferred to be
the period of maximised mixing of these waters. During this period there will be
increased nutrient loading from deeper waters into the trophogenic zone, with a
corresponding increase in primary production. Ideally the use of AVHRR data for
monitoring of lake surface temperatures into the future will continue to be supple-
mented by the input of in situ temperature measurements. These will be used to
routinely check the continued validity of the AVHRR-based atmospheric correction
algorithms and to prepare for further changes in operational satellite.
Acknowledgments
We thank the staV of the Lake Malawi Pelagic Fish Resource Assessment Project
for their support and assistance with in situ and satellite data collection during this
work. We also thank Dr Harvey Bootsma and colleagues of the GEF Lake Malawi/
Nyasa Biodiversity Conservation Project for continuing to support the study and
for provision of in situ lake temperatures for 1997–98. We are grateful to Hanscom
Airforce Base Geophysics Laboratory for provision of the MODTRAN code, to
Roma Beaumont of King’s College London for detailed redrawing of certain Ž gures,
and to Mr Danduala and Mr Kamdonyo of the Malawi Meteorological Department
for supplying radiosonde and surface meteorological data for the year 1977. Dr
Simon Brown of the UK Meteorological OYce generously supplied additional
radiosonde data for 1992. This work was funded by the UK Department for
International Development (formally the Overseas Development Administration),
and M Wooster is supported by the NERC Earth Observation Science Initiative.
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