Weather conditions during the study period
Temperature, precipitation and humidity are the basic elements of weather that determine the evapotranspiration of a specific area and also affect the state of vegetation and the rate of vegetation. The studied period in terms of thermal conditions in northeastern Poland should be assessed as warm. Monthly and seasonal air temperature anomalies (with respect to the period 1991–2020) based on measurements at the Białystok and Suwałki stations of the Institute of Meteorology and Water Management - National Research Institute (IMWM-NIR) were positive, averaging about + 1°C. Exceptionally warm seasons were summer and autumn in 2018 and winter, spring and autumn in 2019 and 2020, when average monthly and seasonal temperatures at the indicated stations averaged 2–5°C higher than multi-year averages (IMWM-NIR). At the measuring station, the lowest air temperature was observed in January (Fig. 2a), when monthly averages ranged from − 5.3°C (2014) to -0.7°C (2015). It is worth mentioning that during the coldest days the minimum daily temperature was below − 20°C. The highest temperatures were recorded in the months of July and August, with the highest monthly average not exceeding 21°C. The number of days with maximum temperatures > 30°C varied from 1 (in 2020) to 12 (in 2015 and 2021).
The annual course of the temperature determines the seasonal variation of the humidity deficiency (VPD). During the summer months (June to August), monthly average VPD varied in the range of 3.9-9 kPa (Fig. 2b). In the winter season, VPD values were lowest at 0.5 kPa. High values of heat flux and evapotranspiration usually occur at high VPD values. During the study period, in 2018 and 2019, the number of days with VPD values above 15 kPa amounted to 70 and 80, respectively, while in other years such days were less than 60.
The highest wind speed values were recorded in winter or early spring - monthly averages of 2–3 m s− 1. During this period, there were also days with maximum wind speeds above 5 m s− 1 (Fig. 2c). In summer and early autumn, wind speeds were the lowest - monthly averages of 1–2 m s− 1. This season also saw an increase in the likelihood of calm (Fig. 2c).
During the study period, annual precipitation totals in northeastern Poland varied from 480 mm in 2019 to 800 mm in 2017 at the Suwałki station (IMWM-NIR). The highest precipitation was characterized by the summer months when monthly totals exceeded 100 mm, while in the winter season monthly precipitation did not reach 50 mm (Fig. 2d).
From the point of view of assessing the evapotranspiration of the wetlands, it is worth noting the periods characterized by extremely low and high precipitation. The course of monthly precipitation anomalies (with respect to the 1991–2020 period) for the previously mentioned Białystok and Suwałki stations indicate the summer seasons of 2014 and 2015 as those with relatively low precipitation (Fig. 2d). The summer seasons of 2018 and 2019 are similar. On the other hand, the spring, summer and autumn seasons in 2017 can be considered relatively abundant in precipitation and a period of partial restoration of the wetland water resources (Fig. 2d).
Annual variability of energy balance components
The radiation balance (Q*) determines the energy resource, which can then be converted into sensible heat flux (Qh), latent heat flux (Qe) and ground heat flux (Qg). In the subsequent years of the study period, the values of Q* reached a fairly similar level (Fig. 3a). In the winter months, the daily totals of the radiation balance most often took values in the range of -0.5 to 0.5 MJ m− 2 d− 1, causing the monthly totals of Q* to vary in the range of -30 to 30 MJ m− 2 month− 1. During the summer season, the high position of the sun and the relatively long day resulted in daily totals most often taking values in the range of 10–15 MJ m− 2 d− 1 and monthly totals varying in the range of 300–400 MJ m− 2 month− 1 (Fig. 3a).
The aforementioned high dynamics of weather conditions and the development of vegetation in successive years of measurements caused the other components of the heat balance of the wetlands to be characterized by greater variability. For example, in the course of daily sums of sensible heat (Fig. 3b), the summer season in 2015 and 2016, as well as in 2019 and 2020, is clearly marked. At that time, there were recorded a relatively large number of days with daily sum Qh in the range of 4–6 MJ m− 2 d− 1, and monthly sums of Qh exceeded 100 MJ m− 2 month− 1. In other years, the observed sensible heat values were lower during the summer season. Days with daily totals Qh in the range of 2–3 MJ m− 2 d− 1 predominated and monthly totals varied in the range of 40–80 MJ m− 2 month− 1. From December to February, the monthly totals of Qh varied in the range of -40 to 30 MJ m− 2 month− 1 and the lowest daily values reached − 4 MJ m− 2 d− 1.
Under wetland surface conditions, high substrate moisture content and dense vegetation favor high values of latent heat flux. During the summer period, the observed average daily totals Qe took values in the ranges of 6–10 MJ m− 2 d− 1 which means that in a month the wetland surface consumed from 180 to 280 MJ m− 2 month− 1 for evaporation (Fig. 3c). It is noteworthy that despite the rather high variability of recorded precipitation and a marked decrease in groundwater resources, the monthly flux values in June, July and August in 2018–2021 were the highest in the studied period - at the level of 220–280 MJ m− 2 month− 1. In the winter season, the latent heat flux was very low. The predominant values were in the range of 0–1 MJ m− 2 d− 1 and the monthly totals of Qe varied in the range of 15–35 MJ m− 2 month− 1 (Fig. 3c).
Measurements of heat flux in the ground (Qg) although difficult in the wetlands also showed a clear annual cycle. In the months from April to August, negative values were recorded, which means that the heat flux directed into the wetland soil (Fig. 3d). At the same time, the values of Qg compared to the other components of the heat balance of the wetland surface are very small. In the warm season, the recorded daily totals most often took values in the range of -0.5 to 0 MJ m− 2 d− 1. In the period from late summer (September) to the end of winter (March), the values of Qg were positive (heat flux directed from the deeper layers of the ground to the surface). As in the warm season, the recorded values were small - most often in the range of 0–1 MJ m− 2 d− 1. The monthly totals of Qg varied in the range of 1–20 MJ m− 2 month− 1 in the cold season and in the range of -2 to -30 MJ m− 2 month− 1 in April-August.
Latent heat fluxes and energy partitioning characteristics
The measurement method used and the equipment of the meteorological station allow us to characterize the diurnal dynamics of the sensible heat flux against the diurnal variability of the other components of the thermal balance of the wetland surface. Due to the very low values and low dynamics of latent heat during the winter, the remainder of the paper focuses on discussing the results for the growing season from March to October.
The frequency distribution of hourly Qe values was dominated by low values - less than 50 Wm− 2 (Table 1). Most such cases are observed in the autumn (more than 80%) and spring (60–70%) seasons. In the summer season, the frequency of cases with Qe > 150 Wm− 2 increases (more than 20% of observations). Moreover, in the studied multi-year period, as a result of changing weather conditions and vegetation condition, quite significant differences in the frequency distribution of Qe values were observed. For example, the exceptionally warm summer season in 2018 and 2019 resulted in an increase in the frequency of Qe fluxes with values in the range of 250–350 and above 350 Wm− 2. Also, the recovery and very strong growth of wetland vegetation after the April 2020 fire resulted in an increase in the frequency of high Qe values (in the range of 250–350 and above 350 Wm− 2 ) during the summer and fall seasons in 2020 and also throughout the growing season in 2021 (Table 1).
Table 1
Frequency distribution (%) of 1h Qe values during the observation period.
year | spring | summer | autumn |
< 50 | 50.1–150 | 150.1–250 | 250.1–350 | > 350.1 | < 50 | 50.1–150 | 150.1–250 | 250.1–350 | > 350.1 | < 50 | 50.1–150 | 150.1–250 | 250.1–350 | > 350.1 |
2013 | 67.5 | 24.7 | 6.2 | 1.6 | 0.0 | 51.9 | 43.8 | 18.8 | 14.2 | 3.3 | 84.9 | 12.6 | 2.4 | 0.0 | 0.0 |
2014 | 66.5 | 27.3 | 5.2 | 1.0 | 0.0 | 52.0 | 44.4 | 19.7 | 12.7 | 2.8 | 84.6 | 12.2 | 3.0 | 0.1 | 0.0 |
2015 | 67.0 | 28.8 | 4.1 | 0.1 | 0.0 | 50.0 | 43.5 | 22.9 | 14.4 | 1.3 | 84.2 | 13.8 | 1.8 | 0.2 | 0.0 |
2016 | 68.3 | 24.3 | 7.1 | 0.3 | 0.0 | 52.6 | 45.8 | 19.7 | 13.5 | 2.4 | 83.9 | 11.9 | 4.0 | 0.2 | 0.0 |
2017 | 63.9 | 24.8 | 9.6 | 1.5 | 0.2 | 50.1 | 46.2 | 21.0 | 13.6 | 2.3 | 82.9 | 15.7 | 1.4 | 0.0 | 0.0 |
2018 | 68.8 | 18.2 | 9.7 | 3.0 | 0.3 | 50.3 | 43.4 | 18.5 | 14.6 | 5.7 | 81.5 | 15.4 | 3.0 | 0.1 | 0.0 |
2019 | 68.5 | 27.5 | 3.9 | 0.0 | 0.0 | 49.6 | 41.2 | 20.5 | 16.8 | 2.1 | 80.7 | 17.7 | 1.6 | 0.0 | 0.0 |
2020 | 72.0 | 22.1 | 5.0 | 0.9 | 0.0 | 50.9 | 45.4 | 15.1 | 13.6 | 7.7 | 79.9 | 14.4 | 5.1 | 0.5 | 0.0 |
2021 | 66.4 | 24.8 | 7.7 | 1.0 | 0.0 | 52.1 | 41.2 | 17.1 | 13.7 | 7.0 | 80.5 | 16.4 | 3.0 | 0.0 | 0.0 |
The annual course of solar radiation and temperature as well as the development and condition of vegetation are the main factors responsible for the pronounced change in the contribution of Qe and Qh to the heat balance of the wetland area. In the spring season, the fluxes of latent heat (during midday, 10 am − 2 pm) and sensible heat account for about 20–50% of the energy of the radiation balance (Fig. 4a and Fig. 4b). In contrast, in summer, Qe values dominate the heat balance structure (60–70% of Q* values) while sensible heat flux accounts for only 10–20% of Q* values. A similar trend has been found in studies on the heat balance of wetlands in different climatic zones (e.g. Jacobs et al., 2002; Lafleur et al., 2005; Wu and Shukla, 2014; Zhang et al., 2016; Q. Du et al., 2021). The dominant role of latent heat flux during the growing season is also confirmed by the seasonal variation of Bowen ratio values (Fig. 4c). In summer, the values of the product of Qh/Qe fall below 0.5. The pronounced seasonal cycle of the Bowen ratio is also confirmed by studies conducted in Siberian wetlands (e.g. Alekseychik et al., 2017; Shimoyama et al., 2004), in Florida (Jacobs et al. 2002) or in northern China (e.g. (Zhang et al. 2016).
A comparison of the average monthly values of Qe/Q*, Qh/Q* and Bowen's ratio in the successive years of the study period shows a rather high variability in them depending on the prevailing thermal and precipitation conditions. The aforementioned exceptionally warm period of 2020–2021 showed significantly higher values of Qe/Q* in the summer months. Despite the drought conditions in the 2018–2020 period and the fire in April 2020 (Walesiak et al. 2022), the rapid growth of vegetation led to very high evapotranspiration values and thus high Qe/Q* values. It is also worth noting that in the following year, i.e. 2021, relatively young vegetation (the year after the fire) and fairly productive precipitation led to relatively high Qe/Q* values in the summer as well as in the early autumn of that year. In comparison, the very warm and dry year of 2015 was characterized by relatively low Qe/Q* values (mainly in June and July) and some of the highest Qh/Q* and Bowen ratio values (Fig. 4b and Fig. 4c).
As mentioned earlier, the dynamics of latent heat flux can be affected by both atmospheric conditions and the condition of the ground. In general, the location of the station in the vicinity of typical wetland vegetation allows one to hope that the measured values of latent heat flux, regardless of wind direction, characterize the evapotranspiration process of the wetland surface. However, the dominance of certain vegetation formations and greater soil moisture in the immediate vicinity of the riverbed (eastern and northeastern neighborhoods of the measurement site) may contribute to higher Qe values. Characteristics of wind direction showed that winds from the westerly direction dominated more than 20% of the observations in summer (Fig. 5a), in spring from the northwestern and eastern directions - about 15% each (Fig. 5b), while winds from the southwestern sector dominated in autumn (more than 20%) (Fig. 5c). Characterization of Qe values depending on wind direction (carried out for noon hours (10:00–14:00 UTC), under conditions of best developed turbulence) shows that in summer and spring, higher Qe values are recorded for winds from east and southeast directions (Fig. 6). This is probably due to the dominance in this sector of sedges and rushes overgrowing the channel of the Kopytkova River (Fig. 1). Dense vegetation and relatively highest substrate moisture in the source area may lead to an increase in the recorded values. In autumn, however, the highest Qe values are characteristic of southwesterly winds - from the direction in which the Biebrza wetlands extend.
Daily and monthly evapotranspiration totals
Protecting wetlands or carrying out measures to restore the natural features of wetlands subjected to drainage treatments requires characterizing evapotranspiration on a daily, monthly and seasonal basis.
High values of latent heat flux in the summer season result in the highest daily losses of water resources of the Biebrza wetlands to evaporation from June to August. Average daily evapotranspiration totals (ETa_EC) in the following months vary from 2.5 mm to 4 mm (Fig. 7). In June and July, high precipitation and also the strongest development of wetland vegetation bring daily maxima of ETa_EC to reach 5–6 mm.
In spring and autumn, daily evapotranspiration is characterized by greater dynamics. For example, average daily totals increase from 0.5-1 mm in March to 2-3.3 mm in May. In addition, it is noteworthy that in April and May, daily evapotranspiration maxima reach 4-4.5 mm (similar to those in summer). On the other hand, the average daily totals in September fluctuated in the range of 1.4–1.8 mm and in November fell to the level of 0.25–0.5 mm. Comparing the course of the obtained values in the studied multi-year period (daily averages as well as maximum and minimum values of daily evapotranspiration), it can be seen that in the 2018–2021 period evapotranspiration was characterized by slightly higher values (especially in the summer period) compared to those of 2013–2017 (Fig. 7). It is also worth noting the course of the standard deviation of daily ETa_EC values in 2018 and 2020 whose values amounted to1.2-1.3 mm, while in other years they oscillated at 0.8-1 mm. In winter, evapotranspiration reaches the lowest values in the annual course. In 2013–2021 from the wetland area, the average daily evapotranspiration did not exceed 0.5 mm. The results obtained support the thesis that evapotranspiration in this type of environment is one of the highest. The average daily sums of evapotranspiration (3–4 mm in spring/summer and summer) are very close to the results obtained during measurements in wetlands in Canada (Lafleur et al. 2005), Siberia(Shimoyama et al. 2004) or Ireland (Wilson et al. 2022). It is worth noting that these values are higher than those presented from similar measurements in agricultural areas (e.g.Siedlecki et al., 2022) or steppe areas (e.g. Wever et al., 2002; Hao et al., 2007). At the same time, it is also worth noting the results of measurements in temperate zone forest areas. For example, results presented by Kasurinen et al., (2014); Soubie et al., (2016) or Paul-Limoges et al., (2020) indicate higher values of water vapor flux from forested areas compared to those achieved in wetlands.
The high stability of evapotranspiration of the wetlands in the course of daily values is also confirmed by the monthly and annual totals obtained. During the analyzed period, annual losses of water resources to evaporation were in the range of 520–590 mm (Fig. 8). In winter, monthly evapotranspiration totals varied in the range of 5–15 mm. In spring, the loss of water resources to evaporation increased from 20–30 mm in March to 40–50 mm in April. In autumn, on the other hand, the values decreased from 40–50 mm to about 10–15 mm in September and November, respectively. From May to August, monthly evapotranspiration totals reached their highest values in the 60–120 mm range. Moreover, during this season, the values obtained were characterized by relatively low variability compared to the changes in monthly evapotranspiration in spring and autumn (Fig. 8).
The decisive factor responsible for the formation of water resources of wetlands is the relationship of precipitation and evapotranspiration on the scale of months or seasons. The course of cumulative daily values of precipitation and evapotranspiration in successive years shows that in the first half of the year, precipitation exceeds losses due to the rate of evapotranspiration. Usually such a period lasts until mid-May. During this time, monthly precipitation totals are higher than monthly evapotranspiration - by an average of 10 mm. This leads to an increase in the water resources of the wetlands, which is confirmed by the courses of the monthly average soil moisture content (volumetric water content VWC) as well as the ground water level (water table level WTL) (Fig. 8). Then, at the end of May and the beginning of June, the course of the curve of cumulative evapotranspiration exceeds cumulative precipitation, leading to the deterioration of the water resources of the wetland surface. From May to September, monthly evapotranspiration totals are higher than monthly precipitation by an average of 35 mm. This leads to the deterioration of the water resources of the wetland surface. This is particularly evident in 2015 and in 2018–2019 when high evapotranspiration with very low precipitation (described in the section on weather conditions) leads to a decrease in VWC (25–40%) and a decrease in WTL (80–90 cm below surface level) (Fig. 8). In the autumn season, again, monthly precipitation exceeds evapotranspiration - on average by 20–30 mm which, combined with the winter season, led to the restoration of water resources of the wetland environment. However, the aforementioned precipitation deficit in 2018 and 2019, with favorable conditions for high evapotranspiration, led to very severe drying of the wetland surface (Fig. 8). Lowering of groundwater levels during summer as a result of high evapotranspiration was also found in marshes in Canada (Lafleur et al. 2005), wetlands in the vicinity of Lake Huron (Carlson Mazur et al. 2014) or in Sweden (Kellner 2001). Lafleur et al. (2005) indicates that high evapotranspiration when groundwater levels are lowered can be explained by capillary rise in the soil as well as water transport through the root system of wetland vegetation.
It is also worth noting that the consequence of continued high evapotranspiration under conditions of rainfall deficiency, leading to lower groundwater levels, is responsible for slowing methanogenesis conditions. Many studies show a linear relationship (e.g. Jungkunst et al., 2012;Strachan et al. 2016) between methane emissions from the wetland surface and the depth of the water table. This was also observed at the study site when CH4 fluxes were lowest in 2015 and 2018 (Fortuniak et al. 2021). At the same time, changes in carbon dioxide fluxes were found in these years and the wetland surface became a source of CO2 (Fortuniak et al. 2021). The indicated changes in the water balance of the wetland environment also lead to the transformation of vegetation. This is confirmed by the research ofGrygoruk et al. (2014), showing the encroachment of shrub and forest vegetation under the conditions of changes in the groundwater level of wetlands.
Wetland evapotranspirations in relations to weather conditions
Analyzing the course of daily sums of evapotranspiration of wetlands against selected weather conditions, it should be noted that the highest values of evapotranspiration (ETa_EC > 5 mm/day) occur when the daily value of Q* is in the range of 15–18 MJ m d− 2 −1, the average daily temperature exceeds 18°C and the moisture deficit varies in the range of 6–12 hPa. Evaluating the relationship of selected weather conditions by season, the dynamics of daily ETa_EC values are most strongly influenced by radiation balance values during the growing season (spring, summer and autumn seasons). The coefficient of determination (R2 ) varies in the range of 0.65–0.7 (Fig. 9). A similar relationship was found in studies of evapotranspiration over marshes in Russia(Kurbatova et al. 2002) or the US (Burba et al. 1999). Slightly less influence is exerted by temperature and moisture deficit values. While in the spring and autumn seasons the mentioned weather elements quite significantly affect evaporation dynamics (R2 values are in the range of 0.46–0.66), in summer ETa_EC dynamics is explained by only 19% of the observed temperature values (Fig. 9). At a similar level, the relationship of daily evapotranspiration with temperature and humidity is shown by studies in different regions of China (Q. Du et al., 2021; Zhang et al., 2016; Wang et al., 2023). Wind speed has the least influence on ETa_EC values, during spring, summer and autumn. The dynamics of daily evaporation values is explained by less than 1% of observations. In contrast, the relationship becomes much stronger during the winter season. For observations from December to February, the values of R2 increase to 0.44. At the same time, it should be noted that in this season the relationship with other meteorological conditions is very weak. R2 values are in the range of 0.001–0.33.
In the next step of evaluating the relationship between the dynamics of daily ETa_EC values and weather conditions, multiple regression (MLR) was used to examine the combined relationship of selected meteorological conditions on evapotranspiration. In the course of the ongoing research, a series of equations were proposed for different combinations of meteorological conditions (Table 2). The best results were obtained for a model considering 4 parameters (MLR1), i.e. radiation balance, temperature, moisture deficit and wind speed. Similar proposals were put forward in the studies of Du et al. (2021) or Wang et al. (2023). In the summer and autumn seasons for such a formula, the coefficient of determination reached 0.8 and the mean error (MAE) and root mean square error (RMSE) are in the range of 0.2–0.4 mm/day. The evapotranspiration results obtained from the subsequent proposed formulas (MLR2 and MLR3) are characterized by greater discrepancies from the measured results. The value of the coefficient of determination varies in the range of 0.5–0.6 and the values of MAE and RMSE are in the range of 0.3–0.7 mm/day.
Table 2
The multiple linear regression equations used in this work and the corresponding indices of performance
Model | seasons | MLR equations | R2 | MAE | RMSE |
MLR1 (Q*, T, VPD, V (Wind speed)) | Spring | ET0 = -0.52–0.04 * T + 0.01 * VPD + 0.14 * Q* + 0.3 * V | 0.76 | 0.36 | 0.47 |
Summer | ET0 = -0.54–0.04 * T + 0.03 * VPD + 0.18 * Q* + 0.34 * V | 0.79 | 0.31 | 0.43 |
Autumn | ET0 = -0.26–0.02 * T + 0.05 * VPD + 0.16 * Q* + 0.23 * V | 0.82 | 0.22 | 0.29 |
Winter | ET0 = -0.06–0.002 * T + 0.19 * VPD + 0.02 * Q* + 0.11 * V | 0.57 | 0.12 | 0.17 |
MLR2 (T, VPD) | Spring | ET0 = 0.6 + 0.06 * T + 0.14 * VPD | 0.56 | 0.51 | 0.64 |
Summer | ET0 = 1.88 + 0.003 * T + 0.21 * VPD | 0.48 | 0.54 | 0.67 |
Autumn | ET0 = 0.18 + 0.05 * T + 0.2 * VPD | 0.62 | 0.32 | 0.43 |
Winter | ET0 = 0.19 + 0.007 * T + 0.33 * VPD | 0.35 | 0.14 | 0.20 |
MLR3 (T, VPD, V (Wind speed)) | Spring | ET0 = 0.08 + 0.07 * T + 0.15 * VPD + 0.2 * V | 0.60 | 0.48 | 0.61 |
Summer | ET0 = 1.22 + 0.012 * T + 0.22 * VPD + 0.3 * V | 0.53 | 0.51 | 0.64 |
Autumn | ET0 = 0.006 + 0.005 * T + 0.2 * VPD + 0.08 * V | 0.63 | 0.31 | 0.42 |
Winter | ET0 = -0.04–0.001 * T + 0.2 * VPD + 0.11 * V | 0.57 | 0.12 | 0.17 |
In the winter season, the MAE and RMSE values are the lowest however, during this period evapotranspiration reaches very low values at 0.3–0.4 mm d− 1 (Fig. 7), which means that the indicated error represents 30–50% of the daily evapotranspiration value. In other seasons, the obtained error values represent 10–20% of the observed E_EC values.
Evaluation of modelled evapotranspiration
Due to the great difficulty in measuring actual evapotranspiration, indirect methods using the relationship between evaporation and meteorological conditions are widely applied. A comparison of daily values of actual evapotranspiration (determined from covariance measurements) with the results of modeling this parameter using the standard Penman-Monteith (ET0 _PM), Prstlay-Taylor (ET_PT) formulas, as well as the method using the Bowen Ratio-Energy Balance (ET_BREB), shows a fairly high agreement (Fig. 10). The values of the linear regression coefficient are in the range of 0.8–1.3 and the values of the determination index R2 during the period of the greatest development of wetland vegetation (May-September) reach 0.6–0.7 (Table 3). Slightly higher values in relation to covariance measurements are those obtained from the application of the ET0 _PM formula. This is especially evident in the spring and summer seasons. At the same time, it is worth mentioning that with the use of this formula, we obtain the so-called reference evapotranspiration on the basis of which, by applying the so-called plant indices Kc (depending on the type of vegetation and their stage of development), the actual evatranspiration (ETKc _PM) can be obtained. This approach was also used in this case. Through covariance measurements, the values of the vegetation index Kc (formula 3) were determined for wetland vegetation. The obtained values (monthly median) are characterized by a seasonal cycle. They change from 0.7 in the spring season (April) to 0.9 in the summer (July and August) (Table 4). As a result of using the determined values of the plant factor, the obtained evapotranspiration values of ETKc _PM are more similar to those obtained from covariance measurements in relation to those obtained from the Penman-Monteith FAO-56 formula (formula 2). This is confirmed by both the correlation plots of the values in question (Fig. 10) and the MAE and RMSE values (Table 3). In general, these values are lower by about 0.3–0.4 mm/day than those determined by applying the ET0 _PM formula. The determined values of the vegetation coefficient Kc in monthly intervals vary from 0.7 (April) to 0.9 (in July and August) and are within the range indicated in many similar studies in different parts of the world. For example, in measurements in wetlands in different areas of the US, published Kc values range from 0.3–1.6 (Drexler et al. 2008;Allen 1995;Wu and Shukla 2014). A similar range of variability has also been indicated in Chinese studies (eg.Zhou and Zhou 2009,Zhang et al. 2016). Higher values of reference evapotranspiration (relative to covariance measurements) are also confirmed by studies based on data from more than 100 meteorological stations from different parts of the world, whose results of covariance measurements were published in the FLUXNET2015 database (Maes et al. 2019). The high variability of the obtained Kc values can be explained by the strong influence (on the achieved reference evapotranspiration values) of individual meteorological parameters (Wu and Shukla 2014;Maes et al. 2019).
Table 3
Selected statistics of comparison daily actual (eddy covariance measurement) and potential evapotranspiration calculated based on Penman-Monteith FAO formula (ET0_PM), Prestlay-Taylor (ET_PT), BREB formula (ET_BREB).
| ET0_PM | ETKc_PM | ET_PT | ET_BREB |
R2 | MAE | RMSE | R2 | MAE | RMSE | R2 | MAE | RMSE | R2 | MAE | RMSE |
Mar | 0.5 | 0.3 | 0.2 | 0.52 | 0.29 | 0.36 | 0.32 | 0.34 | 0.43 | 0.3 | 0.6 | 0.3 |
Apr | 0.3 | 0.9 | 1.3 | 0.3 | 0.6 | 0.7 | 0.31 | 0.51 | 0.63 | 0.3 | 0.5 | 0.6 |
May | 0.7 | 0.9 | 1.3 | 0.7 | 0.46 | 0.56 | 0.7 | 0.41 | 0.53 | 0.6 | 0.4 | 0.6 |
Jun | 0.7 | 0.8 | 0.9 | 0.7 | 0.48 | 0.58 | 0.6 | 0.45 | 0.58 | 0.6 | 0.5 | 0.6 |
Jul | 0.6 | 0.6 | 0.6 | 0.64 | 0.46 | 0.63 | 0.7 | 0.41 | 0.59 | 0.6 | 0.4 | 0.6 |
Aug | 0.8 | 0.5 | 0.4 | 0.8 | 0.4 | 0.5 | 0.8 | 0.32 | 0.4 | 0.7 | 0.4 | 0.5 |
Sep | 0.6 | 0.4 | 0.2 | 0.6 | 0.35 | 0.44 | 0.5 | 0.3 | 0.4 | 0.5 | 0.4 | 0.5 |
Oct | 0.2 | 0.4 | 0.2 | 0.2 | 0.3 | 0.4 | 0.2 | 0.4 | 0.5 | 0.1 | 0.4 | 0.5 |
Table 4
Monthly characteristics (median, 1st and 3rd quartile) of key parameters (Kc, αPT, and β)
| Kcwet | αPT | Bowen ratio |
Mar | 0.8 (0.6–1.3) | 1.1 (0.7–1.6) | 1.1 (0.25–1.96) |
Apr | 0.7 (0.5–1.1) | 0.95 (0.7–1.3) | 1.1 (0.5–1.9) |
May | 0.75 (0.6–0.9) | 0.92 (0.8–1.1) | 0.8 (0.5–1.5) |
Jun | 0.85 (0.8–1.0) | 0.98 (0.9–1.1) | 0.6 (0.4–0.8) |
Jul | 0.9 (0.8–1.1) | 1.03 (0.9–1.2) | 0.4 (0.3–0.6) |
Aug | 0.9 (0.8–1.1) | 1.0 (0.9–1.2) | 0.5 (0.3–0.8) |
Sep | 0.86 (0.8–1.2) | 1.0 (0.9–1.3) | 0.7 (0.3–0.9) |
Oct | 0.85 (0.7–1.8) | 1.1 (0.8–1.7) | 0.7 (-0.2–1.3) |
Similarly, an adaptation to wetland conditions of the Priestlay-Taylor formula was carried out. In this case, based on the results obtained from the covariance method, the values of the coefficient α (formula 5) were determined, the values of which (monthly median) (Table 4) were used to estimate the daily values of potential evapotranspiration ET_PT. The results obtained show high agreement with those from covariance measurements (Fig. 10). The values of the slope of the regression line in successive seasons of the growing season are close to 1.0 and the values of R2 similarly to those for ETKc _PM are in the range of 0.3–0.8 (Table 3). The highest differences between ETa_EC and ET_PT values are marked at the beginning of the growing season (April) when the obtained MAE and RMSE values reach 0.5 and 0.6 mm/day, respectively. In subsequent months, these values gradually decrease to 0.3, 0.4 mm/day in August and September (Table 3).
For the BREB method, the median values of the monthly Bowen ratio were used. In general, as indicated in the section on the description of the components of the heat balance (energy partitionig), the values of β are characterized by a clear seasonal cycle. The obtained monthly median values change from 1.1 (in April) to 0.4 in July (Table 4). Comparing daily ET_BREB evapotranspiration with those from covariance measurements, it turns out that the best compliance is obtained for the summer season (Fig. 10). The values of the coefficient of determination for the months of June-August are in the range of 0.6–0.7 For the spring and autumn seasons, the ET_BREB values are generally lower than those from covariance measurements. On the other hand, the obtained values of error assessment (MAE and RMSE) in both spring, summer and autumn seasons are very similar - at the level of 0.4–0.6 mm/day (Table 3). At the same time, the daily evapotranspiration values in spring and autumn are lower than those in summer.
Complementing the evaluation of the applicability of the selected methods for assessing the evapotranspiration of wetlands is a comparison of monthly values with those from covariance measurements (Table 5). The trend toward higher values obtained from the formula ET0 _PM indicated earlier also results in monthly totals that are 10–20 mm higher than those from covariance measurements. In contrast, the use of the vegetation coefficient results in monthly ETKc _PM evapotranspiration totals varying by 1–5 mm during the growing season (Table 5). Similar differences characteristic of the other methods.
Table 5
Mean monthly totals of evapotranspiration (mm/month) during the investigation period
month | ETa_EC | ET0_PM | ETKc_PM | ET_PT | ET_BREB |
Mar | 24.6 | 28.7 | 24.2 | 21.9 | 21.9 |
Apr | 44.5 | 66.3 | 47.3 | 46.0 | 44.3 |
May | 76.2 | 99.5 | 75.0 | 76.1 | 76.7 |
Jun | 102.9 | 119.5 | 102.0 | 98.7 | 98.2 |
Jul | 103.5 | 108.7 | 100.0 | 101.0 | 106.2 |
Aug | 83.4 | 89.8 | 82.0 | 81.8 | 84.7 |
Sep | 49.5 | 50.1 | 43.6 | 44.5 | 48.7 |
Oct | 21.7 | 19.9 | 17.0 | 16.6 | 18.1 |