#### 2.1. Data

This study used datasets which were measured at two different elevations at nine towers in JR-STATION, Siberia Azovo (AZV), Berezorechka (BRZ), Demyanskoe (DEM), Igrim (IGR), Karasevoe (KRS), Noyabrsk (NOY), Savvushka (SVV), Vaganovo (VGN), Yakutsk (YAK) as shown in

Table 1. Although the BRZ tower was equipped for sampling at four elevations, only data from the two upper elevations were selected. The observation towers were distributed over a wide area encompassing different biome types. The BRZ tower is located in the middle of taiga (boreal forest); the DEM, KRS, and NOY towers are located in a forest zone and are surrounded by extensive wetlands; and the IGR tower is situated in the small town of Igrim (population of about 10,000), which is located next to the Ob River and is surrounded by extensive wetlands. Additionally, three towers—AZV, VGN, and SVV, are located in a steppe region. The VGN tower is situated 100 km southeast of the city of Chelyabinsk, while the AZV tower is situated 30 km southwest of the city of Omsk; both cities have a population of over 1 million. The SVV tower is located 1 km south of a small village. The final tower, YAK, is located in East Siberia. The locations of the nine towers are depicted in

Figure 1, which also shows natural emissions of CH

${}_{4}$ (mg/m

${}^{2}$/day) derived from CarbonTracker-CH

${}_{4}$ assimilation system v. 2016 [

15,

16]. Note, JR-STATION tower data are not assimilated by CarbonTracker.

Emissions of CH${}_{4}$ from wetlands have a significant impact on the greenhouse-gas budget of Siberia. As will be shown below, the location of the measurement station relative to the emission zones is the most important factor for determining the temporal pattern of CH${}_{4}$ concentrations.

The detailed description of measurement systems applied for the observation sites is published in [

3,

17]. In the developed CO

${}_{2}$ measurement system the concentration is defined as the mole fraction in dried air using a nondispersive infrared analyzer (model LI-820, LI-COR, USA; a model LI-7000 was used until September 2008 at BRZ). For that purpose, a triple dehumidification system including adiabatic expansion in a glass water trap, a semipermeable membrane dryer (model PD-625–24SS, Permapure, USA), and a magnesium perchlorate trap was employed. With an established standard gas saving system the developed measurement system keeps the analysis precision within 0.3 ppm [

17].

For CH

${}_{4}$ measurements, a tin dioxide sensor (TOS) was used. This instrument is precise, cost-effective, low power, low carrier-gas consumption, and high mobility. However, the TOS detects methane and other flammable gases (carbon monoxide, hydrogen, and alcohols) and is sensitive to temperature and water vapor in ambient air. In the developed measurement system the sensitivity to temperature and water vapor was reduced by implementing temperature-stabilization and dehydration of the atmospheric samples by a heater unit and low-pressure water trap with chemical desiccant made of P

${}_{2}$O

${}_{5}$. To avoid the interference of other combustible gases they are removed by an additional catalyst. The overall performance and stability of the TOS sensor for measurements of CH

${}_{4}$ in ambient air were validated using a gas chromatograph equipped with a flame ionization detector (GC/FID). The precision of the system is within 3 ppb [

3,

18].

In addition to CO${}_{2}$ and CH${}_{4}$ concentrations, wind speed and direction (at the high inlet), air temperature and humidity (at all levels), and solar radiation and precipitation (on top of the container laboratory) were measured at the nine JR-STATION towers.

Initially, we planned to analyze hourly averages of atmospheric CO

${}_{2}$ and CH

${}_{4}$ mixing ratios collected at the nine tower sites between 1 January 2005 and 31 December 2016 (12 years); however, such a long dataset was not available for all towers (

Table 1). Although the equipment was set up to conduct observations every hour, this was not always technically possible, and the datasets therefore contain many gaps. Hourly measurements of CO

${}_{2}$ and CH

${}_{4}$ cover about 50–80% and 40–70% of the 12 year period, respectively. Significantly fewer measurements are available for the following sites: BRZ (CO

${}_{2}$ and CH

${}_{4}$), AZV (CH

${}_{4}$), SVV (CH

${}_{4}$), and YAK (CH

${}_{4}$) (

Table 1). Such extremely low coverage could affect the analysis and distort the results. Therefore, to avoid this, we excluded from consideration the two datasets with the lowest coverage, namely BRZ (CH

${}_{4}$) and SVV (CH

${}_{4}$).

Another issue which could affect the results are the frequent and large fluctuations in concentration due to variations in emissions. The daily mean emissions of CH

${}_{4}$ from Siberian wetlands have been estimated at between 10 and 500 mg/m

${}^{2}$/day [

19,

20,

21,

22]. The daily variation in CH

${}_{4}$ concentration is much larger than the seasonal variation (e.g., for KRS, see

Figure 2e).

#### 2.2. The Prophet Model

The Prophet model was designed for the analysis and forecasting of time-series data based on an additive model with three main model components: trend, seasonality, and holidays [

23]. These are combined in the following equation [

12]:

where

$g\left(t\right)$ is the trend function,

$s\left(t\right)$ represents periodic changes (e.g., weekly and yearly seasonality), and

$h\left(t\right)$ represents the effects of holidays which occur on potentially irregular schedules over one or more days. The error term

$e\left(t\right)$ represents any idiosyncratic changes which are not accommodated by the model. The parametric assumption of [

12] shows that

$e\left(t\right)$ is normally distributed.

Compared to traditional exponential smoothing models, the Prophet model can more easily handle temporal patterns with multiple periods and has no requirements regarding the regularity of measurement spacing. It works best with time-series that have strong seasonal effects and with several seasons of historical data. The Prophet model has a robust performance in the presence of missing data and trend shifts and typically handles outliers well [

12]. The large number of gaps that exist in the JR-STATION measurements make the Prophet model particularly suitable to simultaneously reveal the daily, weekly, and monthly seasonality from the hourly time-series.

Prophet includes two trend models

$g\left(t\right)$ that cover many applications: a saturating growth model, and a piecewise linear model. The logistic growth model in its most basic form is:

where

C is the carrying capacity,

k the growth rate, and

m is an offset parameter.

There are two important aspects of growth that can not be captured in Equation (

2). First, the carrying capacity is not constant. Thus the fixed capacity

C is replaced with a time-varying capacity

$C\left(t\right)$. Second, the growth rate is not constant. The model must be able to incorporate a varying rate in order to fit historical data. The piecewise logistic growth model is used to overcome those issues:

where the rate at any time

t is the base rate

k, plus all of the adjustments up to that point:

$k+a{\left(t\right)}^{T}\delta $. The correct adjustment at changepoint is easily computed as

$a{\left(t\right)}^{T}\gamma $ [

12].

To provide flexibility for periodic effects, the Prophet model uses the Fourier series [

24]:

where

t denotes the time and

P represents the regular period that the time-series is expected to have (seven and 365.25 days for the weekly and yearly periods, respectively). Fitting seasonality requires the estimation of the 2

N parameters

$\beta ={[{a}_{1},{b}_{1},...,{a}_{N},{b}_{N}]}^{T}$. This was done by constructing a matrix of seasonality vectors for each value of

t in the historical data.