Evaluation of Remote Sensing Techniques over the Tropical
Andes for use in Water Resource Management in Ecuador
N.M. Brauders, W. Buytaert
Abstract
As global rain gauge network densities decline institutions are looking
increasingly towards remote sensing techniques to better understand
rainfall distributions. This study evaluates the potential application of the
Tropical Rainfall Measurement Mission (TRMM) 2A25 algorithm for
water resource management in Ecuador. Annual and seasonal long-term
average (LTA) TRMM estimates were compared with LTA gauge
observations.
Ecuador has a highly variable climate with geophysical features, such as
the Andes and Amazon rainforest, which control precipitation patterns.
This study aims to understand the spatial and temporal variations in
TRMM’s performance, in order to highlight any bias and present this in a
manner that allows future studies to correct for such inconsistencies.
The product shows good ability to reproduce rainfall distributions, but
encounters problems quantifying rainfall amounts. It performs well in
seasons and regions of heavy rainfall, however poorer performance is
exposed in low rainfall and orographic scenarios. A general trend of
underestimation is seen in Ecuador, but it is recommended that a separate
bias correction be made over the Amazon. A more severe trend of
underestimation in rainfall less than 300 mm/season is seen between JuneAugust and September-November. Rain gauge spatial interpolation is
recommended to better understand TRMM’s behaviour over the Andes.
N. M. Brauders
Mott MacDonald Ltd.
Demeter House, Station Rd.
Cambridge, CB1 2RS
Neill.brauders@mottmac.com
W. Buytaert
Dept. Civil and Environmental
Engineering,
Imperial College London.
London, SW7 2AZ
Wouter.buytaert@imperial.ac.uk
Introduction
It has been widely documented that the density of rain gauge networks throughout the globe are
predicted to fall in coming years. As the global demand for water and fuel rises with a growing
population, so too does the need for more effective water resource management. However, such
effective management will require better understanding of the spatial and temporal variation of
water as a resource, which will be mired by reducing gauge network densities. As a result, recently
there has been much investment in the study of remote sensing techniques to quantify the spatial
and temporal distribution of precipitation and therefore local water resources.
Ecuador has very dynamic ecology, which comes from some notable geophysical and ecological
features. One such feature is the vast Andean mountain region that ranges from North to South,
splitting the country down the middle. The significance of this is that it subsequently divides the
region into three broad eco-regions, the Andean highlands, the costal lowlands and the Amazon,
also known as the Orient ((de Koning et al, 1998);(Leimbeck et al,2004)). Each region has a very
distinct eco-system, which has a great impact on their subsequent climates. The effect of variation
of both the climate and geophysical features on TRMM’s performance is investigated here.
Data
This study investigates the relationship between the TRMM PR 2A25 satellite rainfall estimates
and observations from the Ecuadorian rain gauge network. The TRMM data was sourced from the
website of the Cloud Systems Research Group, Department of Atmospheric Sciences, University of
Illinois (http://www.atmos.illinois.edu/~snesbitt/data.html) (Nesbit & Anders, 2009). The data
comes in the form of annual and seasonal mean daily rainfall rate estimates (mm/day), over a tenyear period between January 1998 and December 2008 at the newly available higher resolution of
0.05˚. These 0.05˚ pixels provide spatial estimations (mm/day), over a ten-year period (’98-’08),
across Ecuador in a grid format.
The Ecuadorian historical rain gauge dataset contained information for 1046 stations, but this was
reduced to 331 after stringent data quality and confidence checks. It was supplied by the Instituto
Nacional De Meterologia E Hidrologia (INAMHI), Ecuador. Records stretch to as far back as 1922
and hold monthly average rainfall records (mm/month) up as far as 2008. The records for some
stations were intermittent and their lengths varied but only those with greater than two years
continuous records were included.
Both datasets were re-formatted to give an average annual/seasonal rainfall rates (mm/year and
mm/season). The seasons represent the 4 main hydrological seasons of Ecuador, which are the
following: December-February (DJF), March-May (MAM), June-August (JJA) and SeptemberNovember (SON).
Methodology
Trend Analysis
This study aims to assess the performance of the TRMM product by comparing long-term average
(LTA) rainfall estimates. This method was preferred because directly comparing average
annual/seasonal estimates for any particular year would have limited the period of analysis to ’98’08 (the operational period of TRMM) and thus greatly reduced the number of gauging stations
available to the study. However the gauge records, which stretch back to 1922 could only
justifiably be used if stationarity over the period of comparison was proven.
Therefore a trend analysis of the data periods 1922-1998 and 1998-2008 was undertaken in order
to investigate the stability of the rainfall regimes in Ecuador. The results of the Investigation into
the stability of the rainfall regimes in Ecuador are graphed below.
Average Monthly Rainfall Trend: 1998-2008 Vs. 1922-1998
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Trend: 1922-1998 (mm/month)
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Station
Line of 100% correlation
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Trend: 1998-2008 (mm/month)
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Figure 1.1: Ecuador rainfall trend analysis between the TRMM operational period and the historical
data for the initial 331 stations.
As can be seen from fig 1.1.the rainfall regimes in the region are not significantly different
between the two periods, apart from a few significant outliers. The LTA’s were calculated by
averaging the TRMM estimations over the ’98-‘08 period, while the same was done for each
gauging station over the available period.
Comparison
The direct comparison was made on a point-pixel scale by comparing 0.5° (4km by 4km) areal
averaged pixel estimations with the relevant point gauge observations within that pixel. Comparing
point with areal averaged estimations has inherent error (Clarke et al, 2011), but for this initial
investigation allowed robust large-scale calculations to assess TRMM’s performance.
The effects of increasing and averaging the number of rain gauges within a pixel were investigated
and allowed conclusions to be drawn about related uncertainty. This was achieved by comparing
multiple point-pixel averages as opposed to simply one point gauge measurement. There were 21
instances for which 2 gauges fell within the same pixel and one other with 3 gauges.
An in depth regression analysis of the relationship between TRMM, Rainfall Observations and
Elevation was carried out. This aimed to highlight any linear relationship between the variables
with a view to incorporating this relationship in future studies
The temporal analysis was conducted on an annual scale along with the 4 main hydrological
seasons DJF, MAM, JJA and SON. The results of this investigation provide vital information on
the ability of the satellite product to successfully reproduce observed measurements at particular
periods throughout the year and how it reacts to certain climatic and rainfall regime variations.
Spatial examination of performance was carried out over the whole of Ecuador and analysed in
relation to 7 sub eco-regions, fig. 2.5. Each sub region having individual characteristics provides
the opportunity to examine the effects of these characteristics on the accuracy of the product.
Investigation into the influence of certain variables was aided by the representation of relationship
qualifiers on a geographical map, which highlighted the spatial extent of their variability. As per
Clarke et al (2011), residuals of regression analysis were plotted spatially. product bias has also
been represented in similar fashion. As the map contains information pertaining to location and
region, the influence of any related variables such as rainfall type, temperature, geophysical
features, gauge density, climatic influences, seasonal rainfall patterns etc can be assessed spatially.
Performance Indicators
The following performance indicators were used in the spatial and temporal analysis:




Correlation coefficient
Bias
Regression Analysis
Graphical Analysis
More information on these can be found in Buytaert et al (2006) & Clarke et al (2011).
Results
The results of the investigation into the ability of TRMM PR 2A25 LTA precipitation estimations
to describe the rainfall regimes in Ecuador, both spatially and temporally are detailed below.
Spatial & Temporal Distribution
As can be seen from fig. 2.1, the overall agreement in terms of distribution is good, as TRMM
shows the same seasonal trend and variation. However TRMM underestimates seasonal totals
consistently by 40-100mm. The regional analysis agrees in that the overall distribution seems to be
reproduced well by the satellite product, but again there are discrepancies in the magnitude of
estimation. It is noted that region 1 (Amazon) shows an overestimation of 7%, which is in contrast
with all other findings.
TRMM does indeed have a pronounced underestimation trend in Ecuador. This is visibly present
in figs. 2.1, 2.2 & 2.3 (a) and (b).
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300
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Gauge:Mean Rainfall Estimation per season (mm/season)
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Gauge Network Estimation (mm/season)
TRMM Estimation (mm/season)
TRMM:Mean Rainfall Estimation per Season (mm/season)
500
DJF
MAM
JJA
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0
SON
DJF
MAM
JJA
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Gauge Network Estimation (mm/year)
TRMM Estimation (mm/year)
TRMM:Mean Annual Rainfall Estimation per Region Gauge:Mean Annual Rainfall Estimation per Region
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Figure 2.1: Seasonal LTA rainfall (mm/season) estimations for TRMM PR and the observed gauge network and
annual LTA regional rainfall estimations for TRMM PR and the gauge network.
MAM has a closer relationship to the 1:1 line with a slope of 0.6, which indicates less of a
tendency to underestimate and more accurate estimations, which is consistent with the results
shown in fig. 2.1.
C=171
M=0.35
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Gauge-TRMM: MAM Estimation (mm/Season)
TRMM Estimation (mm/Season)
TRMM Estimation (mm/Season)
Gauge-TRMM: DJF Estimation (mm/Season)
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ECD Gauge Measurements (mm/Season)
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C=11
M=0.53
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ECD Gauge Measurements (mm/Season)
C=171
M=0.60
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ECD Gauge Measurements (mm/Season)
Gauge-TRMM: SON Estimation (mm/Season)
TRMM Estimation (mm/Season)
TRMM Estimation (mm/Season)
Gauge-TRMM: JJA Estimation (mm/Season)
1500
1500
C=13
M=0.69
1000
500
0
0
500
1000
1500
ECD Gauge Measurements (mm/Season)
Figure 2.2: Linear regression of LTA seasonal rain gauge observations against the LTA TRMM
seasonal estimations for the relevant pixel. The green line indicates the regression line, while the red
line represents 1:1 correlation, the intercept (C) and slope (M) values are also displayed. From top
left to bottom right: DJF, MAM, JJA and SON.
Figure 2.3 (a) exposes that the overestimation alluded to previously in region 1 is not the result of
an overall trend of overestimation and may be the by-product of a few significant outliers. In fact,
more than 80% of the stations in region 1 display a bias of within 10% of the observed rainfall,
which is substantially better than any other region.
The results displayed in fig. 2.2, highlight the consistent regional tendency of TRMM to
underestimate by 15-40%, except for region 1 which actually exhibits a more accurate relationship.
This means regional characteristics such as altitude, rainfall type, climate etc., don’t cause vast
reagonalisation of the product bias in Ecuador. This opens up the possibility of generalising the
bias relationship throughout Regions 2-7.
Residuals Colour Coded per Region
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TRMM Estimation (mm/Year)
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0
0
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ECD Gauge Measurements (mm/Year)
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Figure 2.3 (a): Line plot of the annual LTA bias values per region. The blue line represents an
average bias of 1, which is a perfect average estimation, and the green markers represent the average
bias per region. Region 1 individual station bias is inset.
Figure 2.3 (b): Annual LTA regression analysis for the whole of Ecuador, highlighting each
individual region in separate colours (region: 1 (red), 2 (cyan), 3 (green), 4 (blue), 5 (yellow), 6 (black)
and 7 (purple)). The regression line is in green.
The 2 general trends observed discussed further later seem to average out nicely over the year
leading to a regression line with a slope of 0.61 and an intercept value of 258, which explains quite
well the trend of observed underestimation.
All regions are observed to follow the trend reasonably well at lower rain rates, except region 1
which shows some large overestimations. In general, region 1 has tight scatter about the 1:1
correlation line that signifies good product performance in the region, except for those few
significant overestimations. However regions 2-7 display a markedly different trend and it is this
difference that results in the inability of the regression to explain both areas better.
Factors Affecting Product Performance
TRMM estimated the season with the heaviest rainfall (MAM) the best, with DJF and JJA both
displaying poorer estimations, fig. 2.1. Figure 2.2 shows scatter for MAM to be centred more
generally about the 1:1 line, showing good estimations at both high and low rainfall rates. On the
other hand JJA and SON, show a clearer pattern of underestimation, which is very prominent at
lower rainfall rates of less than 300 mm/season.
Figure 2.2 highlights that two separate trends exist, one for DJF and MAM and another for JJA and
SON. Both trends agree that TRMM underestimates rainfall rates in Ecuador. The most notable
thing about the two trends is the precision of within trend agreement in C, which changes quite
drastically between the two trend types. The large group of low rainfall underestimations close to
the origin in JJA and SON weighs heavily in the regression fitting and subsequently pulls down the
C value. This counter acts the result of the general underestimation, which tends to rotate the trend
line clockwise and increase C, as can be seen in DJF and MAM. In all this exposes the existence of
a more severe trend of underestimation at rain rates less than 300 mm/year in JJA and SON, as
discussed above.
Figure 2.4: Shows the spatial distribution of the annual LTA TRMM rainfall bias over Ecuador.
The overestimations in region 1, fig. 2.4, are shown to be located generally on the border of region
1 and 3, which are the lower Andean slopes.
Excluding these inconsistent outliers Region 1 has a consistent trend of more accurate estimation
and therefore, rotates the regression line in fig. 2.3 (b) counter-clockwise away from the general
trend of regions 2-7. This is more evident at higher rainfall rates, as Region 1 exhibits high annual
rainfall and so doesn’t drastically affect the lower levels of the regression. This is why the
regression trend line seems to describe the regions 2-7 more stringently at lower rainfall rates, but
then deviates at higher levels.
Influence of Scale Inconsistency
DJF
MAM
JJA
SON
Unaveraged Averaged Unaveraged Averaged Unaveraged Averaged Unaveraged Averaged
Correlation Coefficients
0.4
0.46
0.57
0.7
0.79
0.86
0.45
0.93
Log Correlation Coefficients
0.53
0.61
0.56
0.68
NA
NA
NA
NA
Coefficient of Determination
0.55
0.98
-0.23
0.83
0.72
0.81
0.58
0.7
Figure 2.5: Displays LTA seasonal regression analysis MAM, for those pixels that contain more than
one gauge, showing the averaged and unaveraged analysis on the normal (blue) scale with regression
equation. The regression lines are shown in black. Related correlation coefficients for the analysis are
also shown.
From analysis of the seasonal plots it is evident that the averaging process greatly reduces the
scatter of the data, as can be seen in fig. 2.5 above. More importantly this reduction in scatter is
centred about the 1:1 line, indicating a marked improvement in estimation accuracy. Visual
inspection of the averaged data is a lot more conclusive than the unaveraged data. Comparing the
unaveraged and averaged values for each season shows improvement in both the correlation
coefficients and the r2 values. Similar results are seen on the annual scale.
It must be noted that this analysis is carried out with a small sample of 22 stations, thus the results
are limited and should only be taken as an indication into the merits of the averaging process.
Elevation
An investigation into the relationship between rainfall and elevation in Ecuador found an almost
horizontal line with a slope of -0.13 and a coefficient of determination of 0.29, which highlights
the non-existence of any linear trend. A similar analysis was carried out for individual
mountainous regions (2, 3, 4 and 6), which expected a more conclusive result but was limited in
some regions by the number of samples.
Table 2.1: LTA correlation coefficients for the TRMM-gauge relationship per region and per season.
Correlation Coefficients
Season
Region
DJF
1
0.51
2
0.42
3
0.26
4
0.19
5
0.53
6
0.01
7
-0.5
Ecuador
0.45
MAM
0.48
0.35
0.46
0.71
0.66
0.76
0.7
0.64
JJA
0.47
0.03
0.74
0.85
0.7
-0.16
0.62
0.7
SON
0.53
0.32
0.72
0.86
0.73
0.13
-0.02
0.68
ANNUAL
0.6
0.29
0.64
0.81
0.83
0.23
0.73
0.69
By examining table 2.1 in conjunction with fig.2.4 a noticeable trend in the correlation of TRMM
with elevation is found. It can be seen that low land regions 4, 5 and 7 exhibit the best correlations
while in the Andean slopes of region 3 the correlation reduces and finally, in the Andean valley
(regions of 2 and 6) it reduces to less than 30%. This clearly highlights increasingly inconsistent
behaviour with increasing elevation over the Ecuadorian Andes.
Performance on Temporal Scales
This study finds that the average seasonal correlations for each region are generally similar to or
improved upon by the annual correlations, as seen in table 2. This result is statistical confirmation
that when the seasonal relationships are combined to form the annual relationship, between
TRMM and the gauge observations the resultant relationship is stronger.
Discussion
One of the main assumptions that have to be made to allow comparison is that ground based rain
gauge data is a “true” observation of rainfall. This is clearly a false assumption because, as pointed
out by Sevruk & Nespor (1998), up to 20% underestimation can be encountered by a rain gauge.
This highlights that the problem of inconsistency does not totally lie with the satellite product,
however the lack of a reasonable alternative in gauge sparse Ecuador makes it plausible.
Both Hughes (2006) and Ebert (2007) highlight poor spatial representation of gauging networks in
mountainous regions, where they are most needed to capture highly spatially varying gradients.
This increase in spatial sampling error, along with undercatch errors associated with snow and
wind at high altitudes contribute in a more than trivial way to the inconsistent behaviour noted in
the Ecuadorian Andes.
Trends
It is worth noting that the negative correlations arise, as the sample sizes of the respective regions
are too small to average out individual gauge errors. Region 7 has only 5 stations in its sample and
experiences such problems. It is proposed that region 7 is joined with region 5, as region 5 has 110
stations and would be able to average out any error observed in region 7. This is plausible not only
because region 7 is located within region 5 but also both regions exhibit the same TRMM-gauge
relationship and bias of estimation.
Two main bias relationships were outlined on the annual scale, one in the Amazon and another in
regions 2-7. The underestimation is generally between 15-40% in the Pacific Coast and Andean
Highlands, which then significantly improves to a more accurate slight underestimation in the
Amazon. Thus it is recommended that separate correction factors be applied to both regions. A
global correction for all regions would not allow for the trend difference and subsequently be more
erroneous.
Furthermore, it is proposed that either the correction within the Amazon itself is made in two parts
or the borders of region 3 are extended to include the overestimating stations. The highlighted
overestimations in the Amazon region are affected by their location on the border of region 3, a
region of inconsistent behaviour proposed for further study. These stations of overestimation
follow a similar trend to that of region 3.
Annual correlation coefficients in the region of 0.65-0.85 are generally observed but a marked
reduction in these values is seen with increasing elevation towards the Andean Highlands.
Dinku et al (2007) completed a comprehensive study of satellite products over complex
topography in East Africa. The study revealed that TRMM performed well with correlation
coefficients of around 0.5, comparable with those for lower regions in this study. Similar
correlation coefficients are observed in the tropical Andes of Columbia by Dinku et al (2010),
revealing underestimations in both the Pacific Coast and Andean Highlands, ranging between 1025%. In contrast with our findings good correlation was observed over the complex topography of
the Andes. It is important to note that kriging was used to interpolate the gauge data, but these
studies show similar results to the point-pixel method in areas of relative topographical
homogeneity.
Factors influencing performance
It is found that the relationship between rainfall and elevation in the Ecuadorian Andes is simply
too complex to be characterised by a basic linear relationship, as also noted by Bookhagen and
Strecker (2008)
Satellite products find it difficult to detect light orographic rainfall, which is very prominent in
such regions as the Outer Andean Slopes ((Kidd, 2001); (Bookhagen & Strecker, 2008); (Kubota
et al, 2009)), especially considering the topographic barrier effect it provides in Ecuador. It is also
know that TRMM performs worst in cooler conditions and encounters large errors in snow capped
mountainous areas (Ebert et al, 2007), thus the higher altitudes of the Inter Andean Valleys are
expected to observe unstable behaviour. TRMM’s increasingly poor performance with altitude in
Ecuador can be attributed to these two points and because steep spatial rainfall gradients,
characteristic of mountainous regions, are difficult to reproduce because of the course nature of the
satellite observations. These results are seen in table 1.8, which shows a reduction in regional
correlation coefficient with altitude.
As described previously MAM is the season of heaviest rainfall as the equatorial current dominates
all but the southern, arid regions of the coast and so this is the season with the most accurate
rainfall rate estimation. It was highlighted in the results that the seasonal analysis estimated the
season with the most rainfall the best, while the regional analysis severely underestimated the
region with the heaviest rainfall, region 4 in the lower Andean slopes. As the reasons for poor
performance in region 4 have now been outlined, it is exposed that the region with the next
heaviest rainfall the Amazon provides the most accurate estimation. Thus, both seasonal and
regional best estimates are of the heaviest season and region, which is consistent with the current
literature.
TRMM tends to perform best in heavy convective conditions, backed up by Kubota et al (2009).
This trend in performance can be confirmed here, as the most consistently accurate region in terms
of bias is region 1 with an annual estimation of within 7%, despite the heavy overestimation in
some stations. The Amazon is an area of year round heavy convectional rainfall, due to the tropical
heating of the large river basin. This year round heavy convectional rainfall is the reason for the
year round consistency in correlation coefficient and accurate annual estimation.
The opposite is true for light rainfall and as discussed previously TRMM’s poor performance in
the Andean slopes of Ecuador confirm this.
Previous studies have revealed that TRMM tends to underestimate in low rainfall and this is
consistent with the findings of this study for the JJA and SON seasons. The results point out a very
prominent underestimation trend at lower levels of rainfall, but more specifically at levels less than
300 mm/season. A further analysis was carried out to show the difference between the higher level
and lower level rainfall trends and for both seasons the rates less than 300 mm/season displayed a
markedly increased trend of underestimation.
It is recommended that the more severe underestimating relationship observed at low levels of
rainfall, less than 300 mm/season, in JJA and SON should be corrected for independently of higher
rainfall amounts.
Another interesting discussion point is the poor correlation coefficient for the coast in DJF in
relation to other seasons. As TRMM performs better in warmer conditions (Ebert et al, 2007) it is
contrary to expectation that the DJF coastal correlation coefficient is less than the colder JJA, SON
seasons. This strange behaviour is suspected to be due to the arid region located in the south of the
coastal region during DJF. Its existence produces a heterogeneous climate throughout the region
and reduces the strength of the TRMM-gauge relationship trend. The effect of this arid region is
clearly visible in fig. 2.4, which shows a cluster of overestimations on the annual scale, directly
related to the position of the arid region along the coastline. This is expected as Ebert et all (2007)
highlights TRMM’s tendency to overestimate in dry, arid conditions.
Interpolation and Elevation
Clarke et al (2011) proposes that for accurate verification of satellite estimates over land, there is a need for
careful interpolation of the ground-based observations to allow consistent areal comparison (Clarke et al,
2011). The influence of scale analysis shows that there are indeed benefits to be gained by improving the
areal sampling.
This study found no evidence of any significant linear relationship between elevation and rainfall either in
the coastal mountainous area or the Andean region of Ecuador. This is in contrast to the findings of Singh &
Kumar (1997) in the West Himalayas where rainfall is observed to increases linearly on the outer slopes, as
no such relationship was exposed on the outer slopes of the Andes in this study. As noted before, this is due
to the complex non-linear nature of the relationship in the Andes.
Analysing with gauge interpolation comes inherent problems in areas with poorly distributed gauge
networks such as the Amazon and in highly variable mountainous regions such as the Andes (Hughes,
2006). So this study recommends that the complex rain relationship with elevation be further studied, in an
attempt to include it in the interpolation model in order to give a better account of ‘true’ rainfall.
Despite the advantages of interpolation the direct point-pixel method shows relevance for investigative
studies such as this also.
Scale of analysis
On the seasonal scale there is more observed variance in the regional relationships between
TRMM and gauge observations, and as such any attempts to correct these relationships should be
made with prudence.
Conclusion
The performance of the 0.5˚ resolution TRMM PR 2A25 algorithm was evaluated with uninterpolated point gauge observations over Ecuador. The general conclusions are as follows:
1. This study’s finds that TRMM has good ability to reproduce rainfall distributions in
Ecuador but encounters problems with estimating rainfall totals accurately. The product is
found to consistently underestimate in Ecuador, however 2 separate bias corrections are
recommended. The Amazon displays a more accurate trend of underestimation to the rest
of the region and so requires unique correction. No significant rationalisation occurs
throughout the rest of the Ecuador and thus a general bias correction can be applied.
2. The product is found to be most accurate in heavy convective conditions, such as in the
Amazon and Pacific Coast regions and in the season of MAM. TRMM displays significant
underestimating tendencies in seasons of low rainfall at rainfall rates below 300
mm/season. It also encounters significant problems detecting orographic rainfall on the
Andean slopes and exhibits notable unstable behaviour in the Andean Highlands.
3. It is found that the implementation of a rain gauge interpolation method, such as kriging
would address the point-pixel areal sampling discrepancy. However, co-kriging with
elevation as a co-variable would not present any significant benefit, due to the lack of
linear relationship between rainfall and elevation found here in the Ecuadorian Andes.
Thus, ordinary kriging is recommended, as per Demaria et al, 2011. If this method is found
not to be fruitful then the interpolation model is recommended incorporate the complex
relationship between rainfall and elevation, highlighted in the Andes by Bookhagen &
Strecker, 2008.
4. Finally, temporal analysis on the product revealed more stable behaviour on the annual
scale, with much less noise than on the seasonal 3-monthly scale. It is thought that the
averaging out of sampling errors over a 12-month period is most likely to be the reason for
this.
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