The topic of evaporation estimates is fundamental to
land-surface hydrology. In this study, FAO-56 Penman–Monteith equation
(FAO56–PM), multiple stepwise regression (MLR), and Kohonen self-organising
map (K–SOM) techniques were used for the estimation of daily pan evaporation
(Ep) in three treatments, where C was the standard class A pan with top
water, S was a pan with sediment covered bottom, and SM was class A pan
containing submerged macrophytes (Myriophyllumspicatum, Potamogetonperfoliatus, and Najas marina), at Keszthely, Hungary, in a
six-season experiment, between 2015 and 2020. The modelling approach
included six measured meteorological variables. Average Ep varied from
0.6 to 6.9 mm d-1 for C, 0.7 to 7.9 mm d-1 for S, and from 0.9
to 8.2 mm d-1 for SM during the growing seasons studied. Correlation
analysis and K–SOM visual representation revealed that air temperature and
global radiation had positive correlation, while relative humidity had a
negative correlation with the Ep of C, S, and SM. The results showed
that the MLR method provided close compliance (R2=0.58–0.62) with the
observed pan evaporation values, but the K–SOM method (R2=0.97–0.98)
yielded by far the closest match to observed evaporation estimates for all
three pans.
To our best knowledge, no similar work has been published previously using
the three modelling methods for seeded pan evaporation estimation.
The current study differs from previous evaporation estimates by using
neural networks even with those pans containing sediments and submerged
macrophytes. Their evaporation will be treated directly by K–SOM, in which
the modelling is more than the simple Ep of a class A pan filled with clean
tap water.
Introduction
Open water evaporation is one of the paramount elements of the hydrological
cycle (Brutsaert, 1982). Evaporation losses from various surfaces appear to
be increasing in recent decades (Mbangiwa et al., 2019). Due to climate
change, it is also extremely important to determine evaporation as
accurately as possible (Fournier et al., 2021), for which both direct and
indirect methods are available. As a direct method, the evaporation pans
(primarily the class A pan proposed by the World Meteorological
Organization, WMO, are used extensively throughout the world to measure open
water evaporation and to estimate reference evapotranspiration (Rahimikhoob,
2009; Fuentes et al., 2020). Measurements of pan evaporation may be
spatially and temporally limited (Jensen et el., 1990; Rahimikhoob, 2009),
like in case of maintenance problems which can affect the accuracy of
evaporation measurements, e.g. most often turbidity of water, or watering of
birds or other animals (Tabari et al., 2010).
To indirectly determine evaporation, several methods can be used: empirical
equations are applied that estimate evaporation based on meteorological
variables (air temperature, Ta; relative humidity, RH; global
radiation, Rs), or transfer and water budget methods (Burman, 1976).
The most widely used empirical formula is a FAO-56 Penman–Monteith equation
(FAO56–PM) (Allen et al., 1998), which is the standard method for
computation of daily reference evapotranspiration. However, measuring
meteorological variables requires sophisticated instruments, which can often
be challenging (Arunkumar and Jothiprakash, 2013; Sattari et al., 2020). The
amount of required data and the difficulty of the estimation of the unknown
meteorological elements may be additional problems (Sanikhani et al., 2015;
Khatibi et al., 2020). Therefore, there is a need for alternative methods
that are simple and effective, require fewer inputs, and are also able to
solve problems which are difficult to formalise (Sudheer et al., 2003; Kisi,
2015; Malik et al., 2020a).
A promising tool that can be used to estimate Ep and is a suitable
alternative to the empirical models is different neural networks (Kim et
al., 2015), thus neural networks are increasingly used in evaporation
and evapotranspiration estimation (Kumar et al., 2002; Keskin and Terzi
2006; Rahimikhoob, 2009; Alsumaiei, 2020). The machine learning techniques
can map high-dimensional data to a low-dimensional space and show some
similar properties based on internal data relationships (Pearce et al.,
2011; Zelazny et al., 2011). In recent years, machine learning techniques
have been broadly employed in hydrological and environmental models,
including to forecast evaporation (Wu et al., 2020). Numerous results in the
literature indicate that machine learning algorithms such as artificial
neural network (ANN), M5 model tree (M5T), support vector machines (SVMs),
multivariate adaptive regression splines (MARS), gradient boosting with
categorical features support (CatBoost), and random forest (RF) perform
excellently in predicting pan evaporation as well (Dong et al., 2021).
Of the available methods, self-organising maps (SOMs) are able to handle
noisy, irregular, and multivariate data well (Nakagawa, 2017). As a result,
it has become one of the most popular neural network (NN) methods for data
analysis (Nada et al., 2017). SOMs are used in many disciplines (Nakagawa
2017, 2020), such as agriculture (Li et al., 2019; Kumar et al., 2021a, b),
ecology (Bedoya et al., 2009, Ristić et al., 2020), hydrology (Guntu et
al., 2020; Rivas-Tabares, 2020; Lee and Kim, 2021), meteorology (Nada et
al., 2017; Berkovic et al., 2021, Doan et al., 2021), and water management
(Gu et al., 2019, Gholami et al., 2020; Lee et al., 2021). The unsupervised
NNs, including Kohonen self-organising maps (K–SOMs), have several advantages
(Kohonen, 1982, 2001). The essence of this method is to group the
large-dimensional array of the input layer into a 2-dimensional array in the
output layer, so that all variables of the input vectors can be found in
each node of the output layer (Adeloye et al., 2011). Another advantage of
K–SOM over traditional models is that it also has visualisation abilities
(Hadjisolomou et al., 2018).
The study site, Lake Balaton, is the largest shallow freshwater lake in
Central Europe with a surface area of 596 km2 (Fig. 1). The three
most dominant submerged macrophytes in Lake Balaton are Potamogeton perfoliatus, Myriophyllum spicatum, and Najas marina, therefore
it was appropriate to include these three species in the observation. In
Hungary, submerged macrophytes colonise in lakes in the summer season (from
June to September). Evaporation of open water surfaces is usually measured
by means of pans endowed with unrealistic properties. These pans are filled
with clean tap water and the evaporated water is also replaced with tap
water unlike in natural ecosystems. In nature, there may also be submerged
macrophytes living in the open water. The presence of these plants is
essential, and affects the chemical and physical water properties including
its quality (Kimmel and Groeger, 1984; Zhang et al., 2017; Yan et al.,
2019). Furthermore, the species that are rooted in the sediment can
stabilise the sediment by inhibiting its resuspension (Madsen and
Cedergreen, 2002; Vymazal, 2013).
Changes in the heat regime of a water body had been reported to result in
alterations of macrophyte community composition (Barko et al., 1982; Poikane
et al., 2015; Fritz et al., 2017; Kim and Nishihiro, 2020), which may affect
the temporal appearance and spatial distribution of macrophytes in the
future. As a result, due to global climate change, it is important to
examine submerged macrophytes in all aspects, including their effect on
evaporation.
The aim of the study was to investigate the effect of littoral sediment and
macrophytes on lake evaporation, and not an introduction of a new method in
pan evaporation estimation. The previous results in FAO-56 Penman–Monteith
equation (Allen et al., 1998), Kohonen self-organising map techniques
(Kohonen, 1982), and multiple stepwise regression are classic methods,
highlighted widely by citations in the study. They are the tools in
analysing the effect of sediment and macrophytes in pan (lake) evaporation
estimation only. The novelty of the paper is in the way the evaporation
estimation is carried out.
To our best knowledge, there are no studies attempting to project water
bodies' evaporation using traditional A pan measurements, taking the
macrophytes- and sediment-related factors into account under such climate
conditions as our experimental site.
Location map of the study area with agrometeorological research
station (ARS) at Keszthely, Hungary (from https://www.vectorstock.com, last access: 3 November 2021).
Materials and methodsCase study and data description
The climate of the region – see also Fig. 1 – is mild continental (Cfb)
with warm, dry summers and fairly cold winters according to the
Köppen–Geiger classification (Kottek, Grieser, Beck, Rudolf and Rubel,
2006). Months were included in the study (from June to September).
Meteorological variables were recorded by a QLC-50 climate station (Vaisala,
Helsinki, Finland) fitted with a CM-3 pyranometer (Kipp & Zonen Corp.,
Delft, the Netherlands) located at Keszthely agrometeorological research
station (ARS) (latitude: 46∘44′ N, longitude:
17∘14′ E, elevation: 124 m a.s.l.) between 2015–2020. The ARS is
placed on the area of the Hungarian University of Agriculture and Life
Sciences. With the exception of wind speed, meteorological data of Ta,
RH, Rs, daily maximum temperature (Tmax), daily minimum
temperature (Tmin), and precipitation (P) were measured at 2 m above the
ground surface. The height of wind speed (u) measurements was 10.5 m. The
daily mean values of meteorological variables were calculated as average of
10 min observations of a 24 h period.
In this study, class A evaporation pans were used to determine daily
evaporation (Ep). The class A pans were 1.21 m in diameter and 0.25 m
in height located on an elevated (∼0.15 m) wooden grid, with
a water surface area of ∼1.15 m2. The daily rate of
Ep was calculated from the difference in water level for two
consecutive days, considering any precipitation that may have fallen into
the pans. The daily water loss was measured every morning at 07:00 LMT (local mean time).
In the ARS area, three class A pans were placed 5 m apart (Fig. 2). A
class A pan was recommended by the WMO to be used as a standard treatment
(control, C). Two class A pans were covered on the bottom with sediment to a
thickness of 0.002 m (S). The used sediment was psammal/psammopelal (Ø
>6µm–2 mm, sand/sand with mud) with the following
composition: quartz, calcite, aragonite, dolomite, muscovite, chlorite,
feldspar, smectite, kaolinite, and pyrite (Anda et al., 2016). Submerged,
freshwater aquatic macrophytes were planted in third class A pans with
sediment-covered bottom (Anda et al., 2016, 2018). Macrophyte
samples were gathered from Lake Balaton (Keszthely Bay) with similar water
depth (0.6–0.8 m) each year. The amount of crop density was controlled
monthly without variation in the green mass weight of crops between natural
habitat and “seeded” class A pans. In the experimental area, three species
of submerged, freshwater aquatic macrophytes: Potamogeton perfoliatus, Myriophyllum spicatum, and Najas marina were colonised. Due to
the development of submersed macrophytes, class A pans were operational from
June to September in the growing season 2015–2020.
In the last vegetation period, to detect vertical water temperature
(Tw) profiles, four fastened thermistors of Delta Ohm HD-226-1
(accuracy: 0.3 ∘C) collected the temperature data at 0.05, 0.10, and
0.15 m depth from the pan bottom and on the water surface, at 10 min
intervals. Hourly averaged Tw values were used in the analysis. To
present diurnal variation in Tw and stratification, sample days were
selected for clear-sky, calm, and cloudy weather conditions.
Class A pans with different treatments: C, S, and SM denote
“empty”, sediment-covered, and macrophyte-planted class A pans in the
middle of the meteorological garden.
The weather of the studied growing seasons was specified by the monthly
Thornthwaite index (TI) of the World Meteorological Organization (WMO)
report (1975):
TI=1.65PmTam+12.210/9,
where Pm and Tam are the monthly sum of precipitation and the
monthly mean air temperature, respectively.
In classifying the weather in each season's months, a 20 % deviation was
assumed from climate norms (1981–2010), above and below the TInorm for
both included meteorological variables (Pm and Tam), allowing the
following weather classes to be distinguished:
warm–dry month (h): TImonth>TInorm×0.8;
cooler–wet month (c): TImonth>TInorm×1.2;
month with normal weather (n): TInorm×0.8≤TImonth≤TInorm×1.2.
By counting the highest number of months within each of these three groups,
the season was considered to be either normal, cool, or warm.
Multiple stepwise regression (MLR)
The regression models are important tools for investigating relations
between dependent and independent data (Razi and Athappilly, 2005), which is a
method that has been used for a long time in the investigation of meteorological
variables. Evaporation can be modelled by multiple linear regressions using
different meteorological variables (e.g. Ta, RH, u) (Almedeij, 2012).
The MLR can be expressed by the following equation:
y=b0+b1x1+…+bkxk+a,
where b0, b1…, and bk are fitting constant,
x1… and xk represent the observed meteorological
variables, and a is a random error term. The a is the remaining effects on
estimated Ep (y) of variables not explicitly included in the model
(Patle et al., 2020). The dependent variable, y, was Ep.
FAO-56 Penman–Monteith (FAO56–PM) method
The Penman–Monteith model is considered as the international standard for
computing potential evapotranspiration and predicting crop water
requirement. FAO56–PM may also be proper method to get pan evaporation with
submerged macrophytes. Wang et al. (2021) reported that actual evaporation
is important for hydrological research due to its direct impact on the
hydrologic processes (water cycle, water resources management). The above
authors concluded that to estimate pan evaporation, it is essential to find
the proper formulation of the Penman–Monteith equation, a special case of
the multiple stepwise regression methods. It may be especially true even in
pans with seeded macrophytes. In accordance with composition of lake
ecosystems, this is the method in evaporation estimation that implies living
organism.
The reference evapotranspiration ET0 was estimated by the WMO
standardised FAO-56 Penman–Monteith method (Allen et al., 1998, 2005) at a daily step for short reference crops (clipped grass of 12 cm) as follows:
ET0=0.408ΔRn-G+γ900Ta+273u(es-ea)Δ+γ(1+0.34u),
where Rn is net radiation (MJ m-2 d-1), G is the soil heat
flux density (MJ m-2 d-1), Ta is the mean daily air
temperature at 2 m height (∘C), u is wind speed (m s-1) at 2 m height, es is the saturation vapour pressure (kPa), ea is the
actual vapour pressure (kPa), Δ is the slope of the vapour pressure
curve (kPa ∘C-1), γ is a psychrometric constant (kPa ∘C-1), and 0.408 is a conversion factor from MJ m-2 d-1 to equivalent evaporation in mm d-1.
Rn was estimated from global radiation, mean daily temperature, the
mean daily vapour pressure, the site latitude, and elevation after Allen et
al. (2005). A fixed value of 0.23 was applied for the albedo. It was assumed
that soil heat flux density was G=0 on a daily basis. Detailed
description of the process can be read in Soós and Anda (2014).
The Tetens equation (Monteith and Unsworth, 2008; Allen et al., 1998;
Tetens, 1930) was used for calculating saturation vapour pressure (es)
as follows:
es=0.6108×exp(17.27Ta/(Ta+237.3)),
where Ta is the air temperature in ∘ C. The actual vapour
pressure, ea, was calculated from the relative humidity (RH):
ea=RH100×es.
Illustration of the winning node and its neighbourhood in the
Kohonen self-organising map (K–SOM).
Kohonen self-organisation map (K–SOM)
The K–SOM is a nonlinear mapping technique, which identifies groups of
similarity in data sets without normal distribution assumption (Kohonen,
1982). SOM is a powerful and effective tool for complex data analyses such
as data mining, estimation, and prediction. Using SOM, informative reference
vectors are obtained via iterative updates under three main successive
procedures: competition with nodes (1), selection of a winner node (2), and
updating of the reference vector (3) (Yu et al., 2018). Every node has its
vector adjusted according to sequential algorithm with the Gaussian
neighbourhood function. The SOM consists of an input layer and an output
layer (Park et al., 2006), where the output layer consists of so-called
neurons, which are usually located in a hexagonal grid and are fully
interconnected (Peeters et al., 2007). A schematic illustration of K–SOM is
presented in Fig. 3. As similar input patterns could have different
outputs, to determine the best output for a given input pattern is to use
the mean output value as the clustered input patterns to the correspondent
neuron, and then the closest (most similar) neuron would be directly used
for the given input pattern (Chang et al., 2010; Kohonen, 1990).
The importance of K–SOM in the field of environmental science lies in the
fact that SOMs can be used for prediction and correlation analysis, mostly
with visual representation (Barreto and Pérez-Uribe, 2007). An
outstanding element of this is that K–SOM finds statistically significant
dependencies among the variables in a multidimensional data sample. In the
case where two variables are highly correlated, K–SOM produces two similar
component planes (Barreto and Pérez-Uribe, 2007).
K–SOM as NN provides a method above the standard estimations of pan
evaporation, which seems necessary to get evaporation of natural ecosystems
including lakes. In other words, applying a method in which the pan
evaporation is estimated from other, easily measurable meteorological
parameters such as sun radiation, air temperature, and relative humidity, has
primary importance. This approach has widely been used for pan evaporation
projection among others by Kisi et al. (2016) and Lin et al. (2013). Kisi et
al. (2016) compared the soft computing model K–SOM and multiple linear
regression (MLR). The authors demonstrated the superiority of K–SOM over MLR
even in the model performance.
Statistics and performance evaluation criteria
The Shapiro–Wilk test was used as a statistical test for normality, with a
chosen alpha value of 0.05 (p<0.05). Two-way analysis of variance
(ANOVA) with Tukey's HSD test was performed to examine the impacts of
treatments C, S, and SM on class A pan Ep. To study the impact of
meteorological elements on Ep of C, S, and SM treatments, Pearson's
correlation analysis was used. This, as well as the MLR, was carried out
with SPSS Statistics software. In this study, the K–SOM algorithm was
executed using MATLAB 2019b software. To train (years: 2015–2017) and test
the models (years: 2018–2020), half of the data were used.
Performance of the proposed models is evaluated by computing statistical
indices, such as root mean square error (RMSE), mean absolute error (MAE),
scatter index (SI), and Nash–Sutcliffe efficiency (NSE) between observed and
estimated values of Ep for the data sets considered. The RMSE range is
zero to infinity (0<RMSE<∞); the lower the RMSE,
the better the model's performance. The RMSE is proportional to the observed
mean, as a result, SI (Shiri and Kişi, 2011) forms a good non-dimensional
error measure. NSE (Nash and Sutcliffe, 1970; ASCE, 1993) compares the
congruence between the observed and predicted data. A high value of NSE (NSE≤1) indicates high efficiency of the model (Duan et al., 2016; Li and
Liu, 2020).
These evaluation criteria calculate as the following equations:
6RMSE=∑i=1n(Epobs,i-Epest,i)2n,7MAE=∑i=1nEpest,i-Epobs,in,8NSE=1-∑i=1n(Epobs,i-Epest,i)2∑i=1n(Epest,i-Epest,m)2,9SI=∑i=1N(Epest,i-Epest,m)-(Epobs,i-Epobs,m)∑i=1NEpobs,i2,
where Epobs,i,
Epest,i is observed and estimated pan
evaporation values on the ith day; and Epobs,m and Epest,m is the mean value of Epobs,i and Epest,i, respectively. The
total number of testing patterns is denoted by n, and i represents the number
of particular instances of the testing pattern.
ResultsMeteorological variables and pan evaporation
The long-term (1971–2000) growing season's average Ta at Keszthely is
18.8 ∘C, the hottest month is July with a mean monthly Ta of
20.5 ∘C, while the coolest month is September (15.7 ∘C). In the study period, the seasonal mean Ta was 5.5 %–15.7 % higher
than the 30-year average. Out of six seasons studied, three warm (2015,
2017, 2019) and three close to normal (2016, 2018, 2020) ones could be
distinguished (Fig. 4). The seasonal mean Ta in warm seasons were
11.5 %–15.7 % higher than that of the climate norms.
The climate of Keszthely is characterised by highly variable and irregular P
with a long-term seasonal total of 274.3 mm from June to September. Monthly
seasonal mean precipitation sums varied from 78.5 mm (June) to 57.1 mm
(September). Warm seasons (2015, 2017, 2019) were characteristically arid
with 4.9 %–21.6 % less seasonal total P, respectively, compared to the
30-year average. In the other study seasons, there were 23.9 %–40.4 % more P
(data not shown) than that of the climate norm.
Figure 4 displays the meteorological variables and observed daily Ep in
different pan treatments determined in a box and whisker plot between
growing season 2015–2020, indicating minimum, first quartile, median, third
quartile, and maximum values. An increasing trend was observed in the
Tmin with an increment of 9.6 %, while the Tmax exhibited an
unchanged trend over the studied growing seasons. In the study location,
there were hardly any differences in seasonal mean RH values (0.6 %–9.2 %)
and daily Rs sums (21.3–24.3 W m-2) between 2015 and 2020. The
highest (1.6 m s-1) and lowest (0.9 m s-1) seasonal mean wind
speeds were measured in 2016 and 2018, respectively.
Box plot of meteorological parameters (Ta – daily mean
temperature (∘C), Tmax – daily maximum temperature
(∘C), Tmin – daily minimum temperature (∘C), RH
– relative humidity (%), Rs – global radiation (MJ m-2 d-1), u – wind speed (m s-1)), and daily evaporation of different
pan treatments (mm d-1) (C – control, S – class A pan with sediment
cover bottom, SM – class A pan with submerged macrophyte) in 2015–2020
growing seasons (June–September). The lower and upper ends of the box
indicate the 25th and 75th percentiles of the variances,
respectively, while the horizontal bar within the box indicates the median.
The two horizontal bars indicate the range that covers 90 % of the
variances. Outliers are indicated with circles.
Daily Ep rates were related to seasonal Ta variations and not to
rainfall patterns. Higher daily mean water losses were registered during the
warm–dry seasons (C: 3.5–3.8 mm d-1, S: 4.2–4.3 mm d-1, SM:
4.5–4.9 mm d-1), while somewhat lower average Ep rates were
measured in the three normal seasons (C: 3.0–3.5 mm d-1, S: 3.4–4.0 mm d-1, SM: 3.6–4.2 mm d-1). As a result of pan seeding,
differences in daily mean Ep rates were more pronounced in warm
summers. In warm seasons, significant deviations of daily mean Ep
between C and S (p<0.001) and S and SM (p<0.001)
were observed. At the same time, significant differences in daily mean
Ep between C and S (p<0.001) and C and SM (p<0.001)
were registered in normal seasons. No significant impact of pan seeding in
all the remaining treatments was detected (p=0.0693–0.0896) (Fig. 4). A
two-way ANOVA was conducted to explore the impact of the studied seasons and
the treatment on Ep rates. There were significant main effects caused
by the growing season (F (5, 211) = 24.241, p=0.001) and the pan
treatment (F (2, 236) = 67.855, p=0.001) in the full dataset. The
interaction between seasons and treatments was not significant (F (10, 29) = 0.085, p=0.503). Tukey HSD post-hoc tests revealed significant
differences among the three pan treatments (p<0.001 for all
pairwise comparisons) for the training, testing phase, and full dataset
(Table 1).
The impact of sediment (S) and submerged aquatic macrophytes (SM)
on evaporation rates (Ep) of class A pan (C) in the full data set
(2015–2020), training (2015–2017), and testing (2018–2020) phase with 95 %
confidence intervals.
Multiple comparisons 95 % Confidence interval (I) Treatment(J) TreatmentMean difference (I–J)Std. errorSig.Lower boundUpper boundFull dataset (2015–2020) CS-0.490∗0.07330.000-0.662-0.318SM-0.845∗0.07350.000-1.017-0.672SC0.490∗0.07330.0000.3180.662SM-0.355∗0.07330.000-0.526-0.183SMC0.845∗0.07350.0000.6721.017S0.355∗0.07330.0000.1830.526Based on observed means. The error term is mean square (error) = 1.741 Training data set (2015–2017) CS-0.712∗0.10660.000-0.962-0.462SM-0.731∗0.10720.000-0.982-0.479SC0.712∗0.10660.0000.4620.962SM-0.019∗0.11240.019-0.2830.245SMC0.731∗0.10720.0000.4790.982S0.019∗0.11240.019-0.2450.283Based on observed means. The error term is mean square (error) = 1.840 Testing data set (2018–2020) CS-0.505∗0.09930.000-0.738-0.272SM-0.716∗0.10010.000-0.951-0.481SC0.505∗0.09930.0000.2720.738SM-0.211∗0.09900.045-0.4430.022SMC0.716∗0.10010.0000.4810.951S0.211∗0.09900.045-0.0220.443
∗ The mean difference is significant at the 0.05 level. The bold mark indicates the significant difference.
The correlation of evaporation of different pan treatments with other
meteorological variables is also given in Table 2. There was a statistically
significant difference in evaporation rates of full datasets and in
the case of training and testing datasets between the seeded and classic
class A pan. The Ta, Tmax, and Rs positively impacted the
Ep, while RH had a negative correlation with Ep. In this study, u
hardly affected the Ep rates irrespective to treatment. The descriptive
statistics of both training and testing datasets showed that most of the
meteorological variables and Ep were similar to the full data set.
Statistics of meteorological variables (Ta – mean air
temperature, Tmax – maximum air temperature, Tmin – minimum air
temperature, RH – relative humidity, Rs – solar radiation, u – wind
speed) and their correlation with evaporation (Ep) of C, S, and SM in
the full time series (2015–2020), training (2015–2017), and testing phases
(2018–2020). C, S, and SM are control class A pan, A pan with sediment
cover–bottom, and A pan with planted freshwater submerged macrophyte,
respectively.
Data setStatisticsTaTmaxTminRHuRsEp of CEp of SEp of SM(∘C)(∘C)(∘C)(%)(m s-1)(MJ m-2 d-1)(mm d-1)(mm d-1)(mm d-1)FullAverage ± SD21.1 ± 3.227.5 ± 4.014.8 ± 3.272.7 ± 8.01.3 ± 0.922.4 ± 6.03.4 ± 1.23.9 ± 1.44.3 ± 1.5(2015–2020)Correlation with Ep of C0.59∗∗0.53∗∗0.42∗∗-0.43∗∗0.010.50∗∗1.00––Correlation with Ep of S0.57∗∗0.51∗∗0.40∗∗-0.42∗∗0.030.53∗∗0.92∗∗1.00–Correlation with Ep of SM0.56∗∗0.50∗∗0.37∗∗-0.44∗∗0.010.52∗∗0.90∗∗0.93∗∗1.00TrainingAverage ± SD20.9 ± 3.427.5 ± 4.414.4 ± 3.371.0 ± 7.51.4 ± 0.923.1 ± 6.13.4 ± 1.24.0 ± 1.44.4 ± 1.6(2015–2017)Correlation with Ep of C0.65∗∗0.59∗∗0.49∗∗-0.48∗∗0.050.51∗∗1.00––Correlation with Ep of S0.63∗∗0.58∗∗0.45∗∗-0.47∗∗0.000.56∗∗0.91∗∗1.00–Correlation with Ep of SM0.63∗∗0.57∗∗0.44∗∗-0.50∗∗0.040.54∗∗0.89∗∗0.93∗∗1.00TestingAverage ± SD21.2 ± 2.927.4 ± 3.515.3 ± 3.074.2 ± 8.21.2 ± 0.921.8 ± 5.73.4 ± 1.23.9 ± 1.44.1 ± 1.4(2018–2020)Correlation with Ep of C0.53∗∗0.46∗∗0.35∗∗-0.41∗∗0.060.51∗∗1.00––Correlation with Ep of S0.51∗∗0.44∗∗0.35∗∗-0.39∗∗0.060.50∗∗0.92∗∗1.00–Correlation with Ep of SM0.49∗∗0.41∗∗0.33∗∗-0.38∗∗0.050.49∗∗0.92∗∗0.95∗∗1.00
∗∗ Correlation is significant at the 0.01 level (two-tailed).
On the basis of the daily variation of Tw in different depths, two
time periods were distinguished (Fig. 5); daytime (07:00–18:00 LMT)
and nighttime cooling (19:00–06:00 LMT). With clear-sky conditions, the
surface Tw peaked at 14:00, irrespective to treatment. The magnitudes of
surface Tw in daytime (between 07:00 and 14:00) increased from 21.6 to
37.5 ∘C in C, from 23.0 to 37.4 ∘ C in S, and from 19.8
to 38.0 ∘ C in SM. Then, with declining solar radiation, the Tw
slightly decreased during the nighttime cooling to 21.2, 21.8, and
18.7 ∘C in C, S, and SM, respectively, until sunrise. In deeper
water depth, a similar pattern of Tw with slightly smaller magnitudes was
measured with a time lag of 1 to 2 h from the surface Tw. In the classic
A pan, the Tw in deeper depth from the surface did not reduce as rapidly as
Tw in seeded pans. On cloudy days, insignificant Tw differences less than
1 ∘C (p=0.059–0.969) between the neighbouring layers were
observed in every treatment.
Water temperature of different pan treatments (C – class A
pan/control; S – class A pan with sediment covered bottom; SM – class A
pan with submerged macrophyte) in clear-sky and cloudy sample days. The
layers represent the distance from the pan bottom. The lowest sensors' height
was 5 cm.
K–SOM features
Table 3 shows the usual parameter table for K–SOM. The following steps were
required to present Fig. 5: inputs were normalised, the code book was
generated, and the map size complied with the dimensions of the component
planes. The neighbouring function of the pixels was Gaussian, the shapes of
component planes were sheets, and the planes shapes were hexagonal. Two
indicators are most often used to qualitatively evaluate the two main goals
of the K–SOM algorithm: quantisation error (QE) and topographic error (TE)
(Table 3). The QE shows how closely the map vectors match the data vectors,
thereby quantifying map resolution (Kohonen, 1995). The TE, in turn,
determines the extent to which the topology of the input data structure is
preserved on the output map (Kiviluoto, 1996). QE and TE do not have a
default value, but the smaller the QE and TE (if the values tend to be zero),
the better the model is. In this study, the values of QE and TE were equal
to 0.016 and 0.820, respectively, indicating that the K–SOM was
appropriately trained in topology.
Characteristics of trained Kohonen self-organising map (K–SOM) model.
K–SOM can be interpreted using the output map and the individual component
planes, so the relationships between each variable can be explored. The
component planes help to visually illustrate areas in which the intensity of
the relationship of the variables is high, low, or average, and thus helps to
better understand the relationship between the Ep and meteorological
variables. The component planes for each variable of the K–SOM model are
shown in Fig. 6. Superimposed on K–SOM patterns of input meteorological
variables, radiation, air temperatures including minimum and maximum,
relative humidity, and wind speed could be captured revealing their
co-variability with the pan evaporation.
In the map, the similar weight vectors have similar colours, based on the
U matrix according to a naïve contraction model proposed by Himberg
(2000) and Peeters et al. (2007). Among NN features, as the clustering,
classification, prediction, and data mining in large datasets (Kohonen and
Somervuo, 2002; Kalteh et al., 2008), only the prediction and data mining
were applied in the study. As there was no group distinction
(classification), the U matrix has not been presented here.
Kohonen self-organising map (K–SOM) visualisation of pan
evaporation and meteorological variables assessment (Ta – daily mean
temperature (∘C), Tmax – daily maximum temperature
(∘C), Tmin – daily minimum temperature (∘C), RH
– relative humidity (%), Rs – global radiation (MJ m-2 d-1), u – wind speed (m s-1), and Ep – daily evaporation (mm d-1)). The bars indicate the intensity of the variables: the red colour
is high importance and the blue colour is low importance.
A colour was assigned to a node in accordance with the relative value of the
respective component in that node (Li et al., 2018). On the maps, the warm
colours (red, orange) show positive correlation,
and the cool colours (blue) show negative correlation between the study variables.
The darker the colour on the map (both warm and cool colours), the stronger the correlation. Lighter colours indicate lower correlation.
When one variable is red while the
other one is blue on the same place of the heat map, the correlation between
them will be negative. Thus, the correlation between the K–SOM modelled
values of Ep, Ta, Tmin, Tmax, Rs, RH, and u becomes
clearly visible. The colour gradient of Ep was similar to those for
variables related to available energy (Ta, Tmin, Tmax, and
Rs), indicating that these contribute most to the increase of Ep.
The component planes also visually confirm the negative correlation between
RH and Ep, with high values of the RH resulting in low values of the
Ep.
FAO56–PM, MLR, and K–SOM models
Figure 6 depicts the time variation and X–Y scatter plots of the observed
and estimated daily Ep values obtained by C, S, and SM during the
testing period (2018–2020).
Time series and X–Y scatter plot of observed and predicted
daily pan evaporation (Ep) in different pan treatment
(C – control, S – pan with sediment cover bottom, SM – pan with submerged
macrophytes) by daily multiple stepwise regression (MLR), FAO-56
Penman–Monteith (FAO56–PM), and Kohonen self-organisation map (K–SOM) models
during testing period (2018–2020 growing seasons). All probability levels
were equal to p<0.001.
From Fig. 7, it can be observed that most of the estimated daily
Ep values (for MLR and K–SOM) are close to the observed daily Ep
values for all three pan treatments. The possible reason for low R2
values in FAO56–PM might be the role of the variable that is the estimate in
crop potential evapotranspiration and not evaporation in water bodies. The
regression line is above the 1:1 line up to 4 mm, which means that the
FAO56–PM and MLR models slightly overestimated the magnitude of the daily
Ep values in different pan treatments. However, above 4 mm daily
Ep, the FAO56–PM and MLR models already underestimated the observed
Ep values. The daily Ep values of C, S, and SM of the K–SOM model
follow the 1:1 line most accurately. For all three models, R2 values
were highest for SM treatment (FAO56–PM: 0.1393, MLR: 0.6242, K–SOM: 9864).
In the case of K–SOM, it can also be observed that low Ep values are
overestimated, while higher Ep values are underestimated, although the
estimated “middle” Ep values (which occur most frequently in a growing
season) were close to the observed Ep values regardless of pan
treatment. A greater degree of underestimation is observed for SM treatment
for K–SOM.
In this study, we developed Ep models based on three different
approaches (FAO56–PM, MLR, and K–SOM) with daily meteorological variables,
and tested the performance of the models by four commonly used statistical
indicators (MAE (Ideal = 0, (0,+∞)), RMSE (Ideal = 0,
(0,+∞)), NSE (Ideal = 1, (-∞,1)), and SI (Ideal = 0,
(0,+∞))). Figure 8 shows the overall performance of the three
predicted methods at the three pan treatments.
The K–SOM models (RMSE = 0.222–0.253; NSE = 0.761–0.951; SI = 0.065–0.074) performed the best in the testing period, their RMSE and
MAE were lower, and their NSE was higher than those of FAO56–PM and MLR
models regardless of pan treatment (C: 0.951; S: 0.906; SM: 0.761).
Additionally, the MAE value for treatments C and S was the lowest in the
K–SOM models (MAE = 0.164 and MAE = 0.338, respectively); in contrast,
the FAO56-PM had the best MAE value for SM treatment (MAE = 0.601).
Overall, the MLR (RMSE = 0.834; MAE = 0.660; S = 0.217) was slightly
superior to FAO56–PM (RMSE = 0.877; MAE = 0.675; SI = 0.220) in the S,
and there was only a small difference in the value of NSE between the two
models (MLR: 0.572; FAO56-PM: 0.580). In the C treatment, RMSE (0.796) and
SI (0.200) were lower for FAO56–PM, while MAE (0.648) and NSE (0.531) values
were more favourable for the MLR model. Nevertheless, both the K–SOM model
and MLR model were better than the FAO56–PM model during the testing period
for “non-empty” treatments (S and SM).
Discussion
To date, there is little information about the impact of submerged aquatic
macrophytes on Ep rate. According to a previous study in India (Kota,
Rajasthan), water hyacinth evapotranspirated 26 % more water than free
water surface in a 9-month experiment (Brezny et al., 1973). In the same
place as this study, Anda et al. (2016, 2018) have shown that the presence
of sediment increases the evaporation of the class A pans by an average of
12.7 %, and the submerged aquatic macrophytes by an average of 21.3 %,
between 2014 and 2016. Jiménez-Rodríguez et al. (2019) reported
that the observed Ep were higher for aquatic plants than the open water
cover in Palo Verde National Park, Costa Rica, between December 2012 and
January 2013 (45 d). Concerning the relationship between pan treatments
and meteorological variables, it can be concluded that positive correlation
was observed with most meteorological variables, while a negative
correlation was observed with RH. This result was supported by other studies
in the literature (Sheffield et al., 2017). In this study, u hardly affected
the Ep rates of each treatment. This does not confirm the conclusions
made by earlier studies (McVicar et al., 2012). This may be due to the fact
that Keszthely is sheltered by surrounding mountains causing lower wind
speeds (Anda et al., 2016).
Daily mean Tw increases were 5.4 and 4.5 ∘C in S and SM,
respectively, compared to C during clear-sky conditions. Despite the less
intense stratification on overcast days, Tw of seeded pans was
5.4 ∘C higher than that of daily mean Tw of C.
In accordance with shallow lake stratification results of Jacobs et al. (1998), increased stratification was evident in daytime, but the number of
layers strongly depended on macrophyte presence. More moderate Tw layer
differences were also present at night. The stratification was the most
intense with three significantly different layers (p<0.001) in seeded
pans, during clear-sky daytime. At the same time, the number of layers with
varied Tw was only two (p<0.001-p=0.012) in classic A and
sediment covered pans. Results in the study were confirmed by Andersen et
al. (2017) concluding that shallow lakes colonised by submerged macrophytes
strongly stratify the water body, mainly during the daytime. The reason for
this stratification is the dissipating turbulent kinetic energy and
absorbing heat (Vilas et al., 2018). The plants may act as a barrier to
seeded pans water mixing, attenuating underwater light, thereby enhancing
the thermal stratification inside the pan's water column.
The strength of stratification, the daily mean Tw differences between
the surface and bottom water were 2.5 (p=0.005), 3.0 (p<0.001),
and 6.5 ∘C (p<0.001) in C, S, and SM, respectively, on
cloudless days. At night-time cooling, variation in Tw between
different layers was less pronounced, remaining below 1 ∘C
(p<0.001–p=0.005).
In addition to stratification, the macrophytes have strengthened the daily
variation of Tw in different depth. A 0.3 ∘C increase in
daily mean surface Tw of seeded pans related to C was obtained during
daytime, with a variation (Tmax–Tmin) of 18.4 and
19.3 ∘C in C and SM, respectively. On the bottom, an opposite
trend in daytime mean Tw was detected; the seeded pans Tw in 0.05 m depth was 3.1 ∘C (p=0.040) cooler than that of the Tw of
C. Probably the macrophyte presence resulted in insufficient downward heat
transport, maintaining the more stratified water body of seeded pans. Herb
and Stefan (2004) also found reduced turbulent mixing in shallow Otter Lake,
Minnesota, with rooted macrophytes. The authors observed that Tw
fluctuations at 20 cm depth were 3 ∘C in open water and
4.5 ∘C in lake water with macrophyte cover. Evapotranspiration
functions of SM fitted to surface Tw evolution; the higher the surface
Tw, the more intense the Ep rate was measured in SM related to
Ep of classic A pan.
Error statistics (root mean square error – RMSE, mean
absolute error – MAE, scatter index – SI and Nash–Sutcliffe efficiency –
NSE) for the multiple stepwise regression (MLR), FAO-56 Penman–Monteith
reference crop evapotranspiration (FAO56–PM), and Kohonen self-organisation
map (K–SOM) models during the testing period for different pan treatments (C
is standard class A pan with clean water, S is class A pan with sediment
cover bottom, and SM is class A pan containing submerged macrophyte).
Many researchers have conducted research with neural networks aimed at the
estimation of Ep as a function of meteorological variables (Keskin and
Terzi, 2006). Several of these researchers found better results in Ep
estimation with neural network approach than those obtained from the
Priestley–Taylor and the Penman methods (Rahimikhoob, 2009; Malik et al.,
2020b). Consistent with other studies, this study demonstrated that
modelling of Ep is possible through the use of K–SOM technique in
addition to the FAO56–PM and MLR methods. The comparison results indicated
that, in general, the K–SOM model was superior to the FAO56–PM and MLR
methods. Chang et al. (2010) used different methods to estimate pan
evaporation, including also the K–SOM and the FAO56–PM. According to the
results of Chang et al. (2010), K–SOM was the best of the studied methods,
and it was found that the Penman–Monteith method is also likely to
underestimate evaporation. Malik et al. (2017) used four heuristic
approaches and two climate-based models to approximate monthly pan
evaporation, where the K–SOM model performed better than the climate-based
models. The regression line in scatter plots has R2 as 0.937 for K–SOM
model at Pantnagar and Ranichauri (India). In the study of Malik et al. (2017), RMSE values were 0.685 and 1.126 for K–SOM, when 50 % of the total
available data was used in the testing of models in two stations.
Conclusions
The Ep of a class A pan with submerged aquatic macrophytes and with a
sediment-covered bottom was observed at Keszthely, over six consecutive
(2015–2020) growing seasons. In this study, it was attempted to model
Ep by employing models consisting of FAO56–PM, MLR, and K–SOM, using
daily pan evaporation values in different class A pan treatments (C, S, SM).
The Ep rate of SM and S was always significantly higher than that of
the “empty” class A pan each growing season. The presence of submerged
macrophyte resulted in a higher Ep than in the sediment-covered class A
pan.
Macrophyte-induced thermal stratification in water bodies (lakes/evaporation
pans) emerges only in the vegetation period, during macrophyte development.
One less layer in classic A pan compared to macrophyte seeded pans was
probably due to modified Tw stratification causing changed water column
stability. Wider Tw values-induced dynamics presented in the
macrophyte seeded pans demonstrated the possibility of developing a more
heterogenous environment for aquatic ecosystems. Macrophyte-induced modified
thermal stratification with higher surface Tw could explain the
increased Ep in seeded pans. Modified Ep of seeded pans made those
values closer to the Ep of natural lakes with submerged macrophytes.
While the Tw stratification trend in SM was similar to that of natural
shallow lakes, it may also provide a new consideration for routine
hydrometeorological management. Tw distribution in macrophyte-covered
lakes impacts other physical properties such as nutrient cycling, dissolved
oxygen, etc. When treating Ep from a pan to that from a vegetated
surface including lakes or other aquatic habitats, to improve evaporation
estimation, multidimensional approximation is necessary, offering simple
methods for end-users including hydrologists, meteorologists, or any other
specialists.
Daily Ep rates for all pan treatments were related to seasonal Ta
variations. Correlation analysis revealed that Ta, Tmax, Tmin,
and Rs had a positive correlation with pan evaporation, whereas RH had
a negative correlation (-0.42 to -0.44) with Ep of C, S, and SM in the full
dataset. Among all, the R (correlation coefficient) of Ta (ranging from
0.56–0.59) had a stronger positive correlation followed by R of Tmax
(ranging from 0.50–0.53) and R of Rs (ranging from 0.50–0.53). The
relationship with u was low for the Ep of the three treatments, which
can be explained by the low u of Keszthely in the growing seasons. Using the
visualisation capability of the K–SOM, it was clearly confirmed that the
Ep was more closely correlated with the variables related to available
energy than the RH.
The performance accuracy of the different applied models was evaluated with
RMSE, MAE, NSE, and SI statistics. Results showed that the K–SOM model has
accuracy in prediction precision over the FAO56–PM and MLR models. Comparing
the FAO56–PM and MLR models, MLR performed better in this study in S and SM
treatments.
Since the Ep of one sample place was included in the study, the
“generic” impact of submerged macrophytes on Ep was not fully
discussed; maybe for different reasons, our results in other sites became
variable. More surveys are needed to reveal the applicability of planted
standard A pan Ep for different geographical and climatic conditions.
A possible application value of the study is in validating the presence of
littoral sediments and macrophytes in evaporation estimation; the amount of
lost water by wetlands that can easily be accounted in the prediction of
their performance. Results from the study may also contribute to the
protection of aquatic plants and to environmental management of wetlands
also in other regions of the world. Management strategies aiming to estimate
accurate water budget terms including evaporation can be a realistic aim for
preventing further inaccurate water loss projections.
Data availability
The meteorological datasets are downloaded from
https://odp.met.hu/climate/station_data_series/daily/ (last access: 12 February 2021).
The supplement related to this article is available online at: https://doi.org/10.5194/hess-26-4741-2022-supplement.
Author contributions
BSG and AA designed the experiments. BSG and SG carried them out. BSG
produced all figures and tables and formatted the article. BSG and AA
prepared the article. BSG, SG, and AA reviewed, revised, and supervised
the progress of the paper.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Financial support
This research has been supported by the Ministry for Innovation and
Technology from the National Research, Development and Innovation Fund (grant no. PD 138660).
Review statement
This paper was edited by Daniel Green and reviewed by Meine van Noordwijk and four anonymous referees.
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