the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Gap filling of turbulent heat fluxes over rice–wheat rotation croplands using the random forest model

### Jianbin Zhang

### Zexia Duan

### Shaohui Zhou

### Yubin Li

### Zhiqiu Gao

This study investigated the accuracy of the random forest (RF)
model in gap filling the sensible (*H*) and latent heat (LE) fluxes, by using
the observation data collected at a site over rice–wheat rotation croplands
in Shouxian County of eastern China from 15 July 2015 to 24 April 2019.
Firstly, the variable significance of the machine learning (ML) model's
five input variables, including the net radiation (*R*_{n}), wind speed (WS),
temperature (*T*), relative humidity (RH), and air pressure (*P*), was
examined, and it was found that *R*_{n} accounted for 78 % and 76 % of the
total variable significance in *H* and LE calculating, respectively, showing
that it was the most important input variable. Secondly, the RF model's
accuracy with the five-variable (*R*_{n}, WS, *T*, RH, *P*) input combination was
evaluated, and the results showed that the RF model could reliably gap fill
the *H* and LE with mean absolute errors (MAEs) of 5.88 and 20.97 W m^{−2}, and root mean square errors (RMSEs) of 10.67 and 29.46 W m^{−2}, respectively. Thirdly, four-variable input combinations were tested,
and it was found that the best input combination was (*R*_{n}, WS, *T*, *P*) by
removing RH from the input list, and its MAE values of *H* and LE were reduced
by 12.65 % and 7.12 %, respectively. At last, through the Taylor
diagram, *H* and LE gap-filling accuracies of the RF model, the support vector
machine (SVM) model, the *k* nearest-neighbor (KNN) model, and the gradient
boosting decision tree (GBDT) model were intercompared, and the statistical
metrics showed that RF was the most accurate for both *H* and LE gap filling,
while the LR and KNN model performed the worst for *H* and LE gap filling,
respectively.

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The turbulent fluxes between the atmosphere and the ground play a crucial role in global climate change and atmospheric circulation, and the inaccuracy of long-term observations of surface turbulent fluxes is a major factor in erroneous weather predictions and climate projections. Research on the ecological effects of urban green spaces, agricultural ecosystems, and forests all use surface turbulent fluxes as key indicators. Currently, the eddy covariance (EC) technique can be used to directly measure the turbulent fluxes (Wilson et al., 2001; Jiang et al., 2021; Wang et al., 2021). However, due to sensor failure and adverse meteorological factors (such as rainfall and frost), these high-frequency turbulence data are subject to errors (Khan et al., 2018). As a result, it is difficult to obtain a continuous time series of ground-based turbulent fluxes. Furthermore, quality assurance methods lead to unavailable sections of flux datasets (Nisa et al., 2021). Based on the above reasons, gap filling is in need of retrieving continuous datasets of EC-based fluxes (Alavi et al., 2006). Researchers have developed approaches based on existing meteorological information to fill up the gaps in atmospheric databases, such as interpolation, nonlinear regression, mean diurnal method, and sampling techniques from the marginal distribution (Falge et al., 2001; Hui et al., 2004; Stauch and Jarvis, 2006; Foltýnová et al., 2020). Further, the machine learning (ML) technique has also become an effective method to be used in the calculation of turbulent fluxes (Khan et al., 2021; McCandless et al., 2022).

As a result of recent developments in high computing technology, machine-learning-based algorithms have been developed and successfully used in various areas, such as natural language processing, data mining, biometrics, computer vision, search engines, clinical applications, video games, robots, etc. To address the missing data issue, machine-learning-based models have recently been used to fill data gaps in meteorological elements and turbulent fluxes (Bianco et al., 2019; Yu et al., 2020). As a result of their reliable and repeatable results, these models are now regarded as a standard gap-filling algorithm (Beringer et al., 2017; Isaac et al., 2017). ML algorithms have several deficiencies even if they perform well in some areas. For instance, overfitting is a major concern that can occur when the training window is too short or the training dataset's quality is poor. This is because the present ML approaches are not sufficiently adaptable to work in extreme situations with large values (Kunwor et al., 2017; Moffat et al., 2007). Furthermore, even with the best technique, the model uncertainty of gap filling still plays a role, particularly when the gaps are relatively large. Numerous novel ML and optimization algorithms have been created and put to use in numerous scientific domains since the 2000s, and their superiority has been demonstrated, either singly or as a component of a hybrid or ensemble model (e.g., Gani et al., 2016).

Based on the need for flux dataset gap filling, and the effectivity of the ML technique, this paper aims, firstly, to investigate the performance of the random forest (RF) machine learning algorithm trained from a dataset obtained over rice–wheat rotation croplands in Shouxian County, eastern China, in gap filling the sensible and latent heat fluxes; and, secondly, to analyze the RF model's accuracy with various meteorological input combinations during training; and, thirdly, to compare the performance of RF model with other four typical ML models.

## 2.1 Study area

This observation was conducted at a site in Shouxian County in the eastern
Chinese province of Anhui (32.42^{∘} N, 116.76^{∘} E) (Fig. 1). The altitude of the site is 27 m, and the annual mean air
temperature and annual cumulative precipitation here are 16 ^{∘}C and
1115 mm, respectively. Summer (from June to September) precipitation
accounts for nearly 60 % of the annual precipitation amount, which meets
the high water demand of rice. Drought sometimes occurs due to lack of
precipitation in the growing season of wheat. This observation site is
rather flat, with farmland accounting for more than 90 % of the area.
Winter wheat is grown here from November until late May, while from June to
November the field is flooded, plowed, and harrowed as rice paddies (Duan et
al., 2021a, b) (Fig. 2). The subtropical northern boundary of the monsoon
humid climatic type describes the area's climate.

## 2.2 Data

Over the site described above, EC sensors (EC 150; Campbell Scientific Inc.,
Logan, UT, USA) were installed at 2.5 m above the ground, including a
three-dimensional sonic anemometer (CSAT3; Campbell Scientific Inc., Logan,
UT, USA) and a CO_{2}/H_{2}O open-path infrared gas analyzer. The
sensible and latent heat fluxes were computed half-hourly using EddyPro
software, with time lag compensation, double coordinate rotation, spectrum
correction, and Webb–Pearman–Leuning density correction (Wutzler et al.,
2018; Anapalli et al., 2019). Poor-quality fluxes (Eddypro quality check
flag value of 2) were discarded. And a quality check based on the
relationship between the measured flux and friction velocity was carried out
to remove the biased data (Papale et al., 2006). Then, using the marginal
distribution sampling technique, the flow data were gap filled (Reichstein
et al., 2005). The time series of air temperature, relative humidity, wind
speed, air pressure, friction velocity, and net radiation were also
subjected to quality control. The missing data which need gap filling are *H* and LE, with 7205 and 16 013 missing, accounting for 12.09 % and 26.87 %,
respectively. According to the criteria of $X\left(h\right)<(X-\mathrm{4}\mathit{\sigma})$
or $X\left(h\right)>(X+\mathrm{4}\mathit{\sigma})$, where *X*(*h*) indicates the time
series of the component, *X* is the mean across the averaging interval, and
*σ* is the standard deviation, noisy data were eliminated (Gao et al.,
2003). Data observed from 15 July 2015 to 24 April 2019 are used in this
study, and Fig. 3 shows the daily average data of *R*_{n}: net radiation (W m^{−2}), *u*^{∗}: friction velocity (m s^{−1}), *T*: air temperature (^{∘}), RH:
relative humidity (%), *P*: air pressure (hPa), and WS: wind speed (m s^{−1}).

## 2.3 The RF model

RF is a machine learning method that is quick, adaptable, and frequently
used to analyze classification and regression jobs (Breiman, 2001). This
model can successfully evaluate highly dimensional and multicollinear data
and is resistant to overfitting (Belgiu and Dragut, 2016). The RF model provides
a feature selection tool to assist in determining the importance of the
predictor. The contribution of each variable to the model, with important
variables having a higher effect on the results of the model evaluation, is
the definition of feature significance (Liu et al., 2021). Of the data, 90 % collected at the Shouxian observation site throughout the study period
were used to train the RF model, while the remaining 10 % were used to
independently validate the model (hereafter validation dataset). To lessen
the overfitting in this case, a 10-fold cross-validation (CV) procedure was
used (Cai et al., 2020). All training data used here were randomly divided
into 10 subsamples of equal size for the 10-fold CV tests. And 9 out of
the 10 subsamples were used as training data (hereafter training dataset),
while the remaining subsample was used as testing data (hereafter testing
dataset). All 10 of the subsamples were utilized as testing data exactly
once for each of the 10 iterations of the CV procedure. One estimate was
created by averaging the 10 findings from the folds. We modified the four RF
model hyperparameters based on Bayesian optimization to get the optimal
model (Baareh et al., 2021; Frazier, 2018): the maximum number of
features considered to split a node (max features), the maximum number of
trees to build (*n* estimators), the minimum sample number placed in a node
prior to the node being split (min split), and the maximum number of levels
for each decision tree (max depth). Bayesian optimizer is used to tune
parameters, and you can quickly find an acceptable hyperparameter value;
compared with grid search, the advantage is that the number of iterations is
less (time saving), and the granularity can be very small. For example, if we
want to adjust the regularized hyperparameters of linear regression, we set
the black box function to linear regression, the independent variable is a
hyperparameter, the dependent variable is linear regression in the training
set accuracy, then set an acceptable black box function-dependent variable value,
such as 0.95, and the obtained hyperparameter result is a hyperparameter that
can make the linear regression accuracy exceed 0.95. The simulated
performance of the 10-fold CV outcomes was evaluated using four statistical
metrics: the correlation coefficient (*r*), mean absolute error (MAE), root
mean square error (RMSE), and standard deviation (*σ*_{n}). As a
result, the final RF model's parameters were adjusted as follows to have the
best statistical metrics: *n* estimators is 246 min, split is 2, max features is 10, and max depth is 35.

The four statistical metrics are calculated by

where *S* stands for the modeled value, *O* is the observation, $\stackrel{\mathrm{\u203e}}{O}$ is the
mean observed value, and $\stackrel{\mathrm{\u203e}}{S}$ is the mean modeled observation.
*σ*_{n} indicates the standard deviation. The subscript *i* represents
the serial number of samples, and *N* represents the total number of samples.

## 3.1 Driving factors of *H* and LE on a seasonal scale

The possible driving factors of *H* and LE were investigated to determine
their respective contributions by the RF model, as shown in Fig. 4. *R*_{n},
which accounted for 78 % and 76 % of the total variable significance of
*H* and LE, respectively, and was the most crucial variable in regulating the heat
fluxes (Fig. 4a and c). Consistent with the high variable significance
values, *H* and LE also had the highest *r* of 0.79 and 0.75 with *H* and LE,
respectively, as shown in Fig. 4b and d. The other four factors
contributed much less than *R*_{n}, and WS, *T*, RH, and *P* had importance values
of 2 %, 4 %, 7 %, and 5 % (2.2 %, 19 %, 2 %, and 0.6 %) for
*H* (LE), respectively. All these elements such as *R*_{n}, *T*, WS, RH are
normalized before the model starts training. When these elements are
normalized, it ensures uniformity and comparability. In general, all of
these predictors played a role in the *H* and LE calculation, and for *H*, the
sequence of importance was *R*_{n}, RH, *P*, *T*, and WS, while for LE, it was *R*_{n}, *T*,
WS, RH, and *P*. The most significant impact on the change of *H* and LE came
from *R*_{n}, which was the most important energy source of the surface and
modulated the surface temperature directly. RH and *T* had a minor impact on
the *H* and LE changes in terms of climatic parameters, which carried the
information of the light-dependent reactions of *H* and LE fluxes.
Particularly, WS and *P* had minimal impacts on the *H* and LE fluxes. The
WS, *T*, and RH also affected *H* and LE according to the Monin–Obukhov
similarity theory (Monin and Obukhov, 1954), while *P* represented the
contributions from the background weather systems.

## 3.2 RF model evaluation

Figures 5–6 show the comparison between the observed and the RF-estimated *H*
and LE, respectively. In the period of rice, the RF model showed good
performance for both the training dataset (MAE is 8.51 and 17.89 W m^{−2};
RMSE is 14.11 and 29.82 W m^{−2}, for *H* and LE, respectively) and the
testing dataset (MAE is 9.61 and 10.34 W m^{−2}; RMSE is 15.63 and
17.21 W m^{−2}, for *H* and LE, respectively) (Figs. 5a, b, 6a, and b). RF
model also showed high consistency with direct measurements for the
validation dataset (MAE is 5.88 and 20.97 W m^{−2}; RMSE is 10.67 and 29.46 W m^{−2}, for *H* and LE, respectively), (Figs. 5c and 6c). In the period
of wheat, the performance of the RF model for the training, testing, and
validation datasets of *H* and LE was similar to that in the period of rice.
For the training, testing, and validation datasets, respectively, the MAEs
are 7.18, 8.01, and 6.01 W m^{−2} for *H*, and 13.58, 8.82, and 19.93 W m^{−2} for LE; and the RMSEs are 12.27, 13.61, and 9.86 W m^{−2} for *H*,
and 24.92, 15.17, and 28.74 W m^{−2} for LE (Figs. 5d, e, f, 6d, e, f). These results demonstrate that the RF model is capable of
effectively calculating the *H* and LE with input variables of *R*_{n}, WS, *T*, RH,
and *P*.

## 3.3 Examination of input combinations

Meteorological elements may occasionally be unavailable due to the failure
of sensors, so the five-variable input combination derived in Sect. 3.2 is not
always applicable. Therefore, examination of other alternative input
combinations is important to have substitute choices for data gap filling
when the five-variable input combination is unavailable. In this subsection, we
investigated the RF model's performance under the situation of lacking one
element in the five-variable input combination; i.e., we tested the four-variable
input combinations of (WS, *T*, RH, *P*), (*R*_{n}, *T*, RH, *P*), (*R*_{n}, WS, RH, *P*), (*R*_{n},
WS, *T*, *P*), and (*R*_{n}, WS, *T*, RH), by removing *R*_{n}, WS, *T*, RH, and *P* from the
five-variable input combination, respectively. The MAEs and RMSEs for these
combinations are shown in Table 1, and it demonstrates that the RF model's
accuracy may either increase or decrease as a result of the removal of a
meteorological element during the training phase. For instance, it was found
that the model's performance greatly improved once RH was eliminated from
the input combination, with the MAE and RMSE of *H* decreasing from 6.48 and
11.94 W m^{−2} to 5.66 and 11.06 W m^{−2}, respectively, and LE from 19.1
and 39.39 W m^{−2} to 17.74 and 35.27 W m^{−2}. This outcome is logical
given that RH and *H* do not have a strong correlation; as a result,
performance will be enhanced if RH is not included in the gap-filling
processing pipeline. According to our findings, the RF model's performance
may be greatly enhanced by excluding irrelevant meteorological elements from
the study and choosing only those that have a significant impact on the
variable. Our findings imply that in order to attain the best gap-filling
accuracy, it is necessary to take into account both the advantages and
disadvantages of ML-based models and the ideal input components. The
results suggested that RH at a single level was not well correlated to the
fluxes as shown in Sect. 3.1, because the one-level RH was strongly
affected by the irrigation activity which was an external factor of the
weather system. As a result, RF model performance was enhanced when the
irrelevant variable (i.e., RH) was removed from the input list. The same
condition also happened to the removal of WS, as could be seen from Sect. 3.1, WS showed small correlations with the fluxes. WS over this site was
rather small, and frequently below 2 m s^{−1}, and under this light wind
condition, the fluxes were mostly driven by the buoyancy rather than the
wind shear. Figure 7 presents the MAE variation percentage of the four-variable
input combinations from the five-variable input combination. After RH was
removed from the input list, the RF model showed favorable performance for
both *H* and LE, as shown in Fig. 7, with MAE values improvements of 12.65 %
and 7.12 %, respectively. Notably, the removal of *R*_{n} from the input
combination resulted in a considerable decline in the RF model's
performances, with MAE degradation percentage values reaching 16.20 % and
10.73 %, respectively. This outcome makes sense, since *R*_{n} is highly
associated with *H* and LE; hence, performance will be declined if *R*_{n} is left
out of the input training dataset. As a consequence, our findings
demonstrated that choosing strongly associated components could greatly
increase the gap-filling accuracy. According to our findings, the best input
combination is [*R*_{n}, WS, *T*, *P*].

It should be noted that other variables that might have an impact on the *H* and LE were not investigated here. For example, given that our research site
was over farmland and plants were growing, knowledge of the variations of
the leaf area index (LAI) and inclusion of it to the training dataset should
also be useful to increase the accuracy of the RF model in *H* and LE
gap filling. The monsoonal climate here also incurred considerable
precipitation variations, which might as well potentially contribute to the
RF model accuracy improvement. However, due to the lack of LAI and
precipitation observations, the inclusion of the two variables into the RF
model training dataset was not applicable in this study. Additionally, as
shown above, more variables would bring a higher observation demand and
lead to more complexity and potentially decreased results, such as the
adding variable of RH.

## 3.4 Comparison with other four ML methods

### 3.4.1 Comparison in *H* estimation

To further investigate the reliability of the RF model, we used a Taylor
diagram to compare its performance in *H* estimation with the other four ML
models: support vector machine (SVM), *k* nearest-neighbor (KNN), gradient
boosting decision tree (GBDT), and linear regression (LR). SVM is a
data-oriented classification algorithm, and the basic model is to find the
best separation hyperplane on the feature space so that the positive and
negative sample intervals on the training set are maximum. Its advantages
are that the kernel function can be used to map to a high-dimensional space;
the use of the kernel function can solve the nonlinear classification; the
classification idea is very simple, that is, to maximize the interval
between the sample and the decision-making surface; the classification
effect is better; and the nonlinear relationship between data and features
is easy to obtain when the small and medium-sized sample size is large. KNN
is particularly suitable for multi-classification problems. Its advantage is
that it is simple in thought, easy to understand, and easy to implement; there are no
estimation parameters and no training – it is highly accurate and insensitive to
outliers. GBDT can flexibly handle various types of data, including
continuous and discrete values. With relatively few parameter adjustment
times, the prediction preparation rate can also be relatively high. If the
data dimension is high, the computational complexity of the algorithm will
increase. Using some robust loss functions, the robustness to outliers is
very strong. LR is a statistical analysis method that uses regression
analysis in mathematical statistics to determine the quantitative
relationship between two or more variables that depend on each other.The
results have good interpretability, can intuitively express the importance
of each attribute in the prediction, and the calculation of entropy is not
complicated.

All the models were optimized with the same technique described above for
the RF model. The results are shown in Fig. 8. The EC measurements were
used as the benchmark. It can be seen that the RF model generally
outperforms the other four models, with standard deviations (*σ*_{n}) and correlation values of 1.05 and 0.98 during the period of rice
planting and 0.96 and 0.95 during the period of wheat planting,
respectively. The SVM model is the second most accurate model, with a
*σ*_{n} and correlation of 0.92 and 0.98 during the period of rice
planting and 0.91 and 0.93 during the period of wheat planting,
respectively. The LR model performs the worst, with a *σ*_{n} and
correlation of 0.60 and 0.76 during the period of rice planting and 0.80
and 0.72 during the period of wheat planting, respectively. The accuracy of
KNN and the GBDT models is in between the above-discussed models, and the
*σ*_{n} and correlation during the rice and wheat period for KNN is
0.68 and 0.73 and 0.77 and 0.82; for GBDT, it is 0.79 and 0.80 and 0.81
and 0.9, respectively.

### 3.4.2 Comparison in LE estimation

Figure 9 illustrates a comparison of the estimated LE by all five models
during the period of rice and wheat planting. The results are similar to
those in the *H* estimation, and the RF model is found to perform better than
the other four models, with *σ*_{n} and correlation values of
0.95 and 0.97 during the period of rice planting and 0.97 and 0.96 during
the period of wheat planting, respectively. Nonetheless, the KNN model
performs the worst for LE estimating, and it has *σ*_{n} and
correlation values of 0.68 and 0.82 during the period of rice planting and
0.62 and 0.79 during the period of wheat planting, respectively. Overall, as
shown by the Taylor diagram of Figs. 8 and 9, in this study, the RF model
has the best accuracy in either *H* or LE estimation for data gap filling.

To assess the RF model's capacity for gap filling the sensible and latent
heat flux measurements over rice–wheat rotation croplands, 90 % of the
total observation data gathered at Shouxian were utilized for training and
testing, and the remaining 10 % of data were used for independent validation. Our findings
demonstrate that *R*_{n} is the most important variable in regulating *H* and LE,
and it accounts for 78 % and 76 % of the total variable significance in
the RF model construction for *H* and LE calculation, respectively. The least
important variables are WS and *P*, and their total variable significance is
2 % and 0.6 %, respectively. During the periods of rice and wheat
planting, the RF model with a five-variable input combination shows reliable
performance, with MAE values of 5.88 and 20.97 W m^{−2} and RMSE
values of 10.67 and 29.46 W m^{−2}, respectively. However,
further analysis of the RF model with four-variable input combinations
indicates that the performance of the model is improved when RH is removed
from the input list, and the MAE values decrease by 12.65 % and 7.12 %
for *H* and LE, respectively. Nonetheless, the four-variable input combination
without *R*_{n} causes an increase in the MAE values of the model, by 16.20 %
and 10.73 % for *H* and LE, respectively. Therefore, the best input
combination found in this study for heat flux gap filling is [*R*_{n}, WS, *T*,
*P*]. Statistical comparison of RF and other four typical ML models (LR, KNN,
SVN, and GBDT) by Taylor diagram further shows that RF is the most accurate,
with the standard deviations and correlation values of 0.95 and 0.97 during
the period of rice planting and 0.97 and 0.96 during the period of wheat
planting, respectively. On the other hand, the LR and KNN models perform the worst for *H* and LE gap filling, respectively, according to the statistical metrics of
the Taylor diagram.

This study is based on only the data collected over rice–wheat rotation
croplands, but the method presented above to find a reliable gap-filling ML
model can also be used over other types of underlying surfaces and in
other climate zones. It should be noted that over different types of
underlying surfaces and climates, the variable significance can vary, and a
careful check of the input combinations is needed. For example, over polar
oceans with strong winds, *R*_{n} probably is not the most important driving
factor, while the winds which cause mostly the turbulence may take the first
place. On the other hand, over areas without human irrigation activity, RH
will possibly be strongly related to the latent heat flux, and hence the
inclusion of it in the input list may increase the ML model performance.
Besides the examination of the input combinations, the choice of an ML model
and the method to optimize its parameters are also important.

Overall, this study shows the potential to use the RF model to produce
trustworthy gap-filling data of *H* and LE over rice–wheat rotation
croplands, and the ML methods are suggested to be used to derive the fluxes'
estimations when direct EC observations are not available.

The data used in this paper are archived in Zenodo at https://doi.org/10.5281/zenodo.7765608 (Zhang et al., 2023).

JZ: methodology, data analysis, and writing (original draft). ZD and SZ: methodology and data analysis. YL and ZG: conceptualization and writing (review and editing).

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are grateful to the anonymous reviewers for their incisive comments. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Nanjing University of Information Science & Technology.

This study is supported by the National Natural Science Foundation of China (41875013).

This paper was edited by Simone Lolli and reviewed by three anonymous referees.

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