Abstract
Sensitivity analysis (SA) intends to identify the key meteorological variables that affect the performance of reference crop evapotranspiration (ET0) models. It is of importance in assessing the variability of meteorological variables and ET0, especially in the face of increasing climate uncertainties. However, the surging of inconsistencies resulting from global changes in meteorological conditions due to climate change have impacted the ET0 model estimation in different regions, with detrimental effects on water resources and crop production. Therefore, efficient SA is necessary to evaluate the impact of changes in meteorological variables that influence ET0 model estimation. This mini review analyses the various SA methods applied in the field of ET0, based on a comprehensive and comparative analysis of existing SA methods from all around the world. The study discusses the advantages and disadvantages of each SA method, as well as the factors affecting the SA of ET0. The study also provides future prospects that may contribute to more solid and powerful analysis for ET0 model estimations and conclusions.
HIGHLIGHTS
The local and global sensitivity analysis for ET0 estimation were reviewed.
The categories, methods, and limitations for SA were examined.
The factors affecting the SA of ET0 were discussed.
The new possible research directions for SA in ET0 estimations are outlined.
Graphical Abstract
INTRODUCTION
Sensitivity analysis (SA) examines how variations in meteorological variables (input factors) can affect the variations of reference crop evapotranspiration (ET0). SA is utilized to determine the extent to which each meteorological variable contributes to variations in the ET0 modelling (Agrawal et al. 2022). Conventionally, SA has been implemented through physical calibration, which is arduous and error-prone. SA based on automatic calibration procedures can be split into two categories: local and global methods (Haghnegahdar & Razavi 2017). Local methods focus on the effect of variables on the output by varying each variable (input) individually. Global methods focus on the influences of uncertain input by varying all the parameters simultaneously (Song et al. 2015). In practice, various SA methods play an important role in different fields such as medicine (Göksu et al. 2018), food and environmental safety (Sharafi et al. 2019), biomedical sciences (Qian & Mahdi 2020), building performance analysis (Pang et al. 2020) and the list goes on. Despite the limited application of SA methods in ET0 models, it has been gaining attention in recent years. The precise estimation of various crops water requirement depends on the accurate calculation of evapotranspiration (ET) rate of the reference crop (Malik et al. 2021; Gul et al. 2022). Accurate ET0 estimation also plays an important role in achieving sustainable water planning and management (He et al. 2022; Malik et al. 2022).
It is evident that the major challenges for ET0 are climate change and the availability of meteorological data. Climate change has influenced the meteorological variables to varying degrees, subsequently affecting the ET0. The increase in greenhouse gas concentrations in the atmosphere is causing the Earth's surface and lower atmosphere to warm, leading to changes in meteorological variables. Due to global warming, ET0 is expected to increase with rising of the global temperature (Fan et al. 2021; Goh et al. 2021; Theng et al. 2022). Increasing ET0 will thus contribute to a decline in irrigation water availability, which could affect crop yields (Sampathkumar et al. 2021). To understanding the effects of climate change on ET0, SA examines how changes in different meteorological variables affect ET0. The sensitivity of ET0 can provide critical evaluation for identifying the most suitable models for ET0 estimation under climate change conditions (Woo et al. 2021; Ng et al. 2022).
Additionally, the availability of meteorological data, such as temperature, solar radiation, wind speed and relative humidity, plays an important role in ET0 estimation, as it is sensitive to changes or errors in meteorological data (Zhang et al. 2022). Meteorological data is affected by instrumental and human errors that emerged from various sources, such as sensor calibration, settings of measurement sets, and data reading/recording (Biazar et al. 2019). Consequently, this leads to missing or unavailable of the meteorological data, which, in turn, affects the accuracy of ET0 estimation. Thus, SA is necessary to understand the connection between ET0 and meteorological variables. SA can help to identify the most important variables in ET0 estimation, and gain insights into how these missing data might affect ET0 models and predictions (Ndulue & Ranjan 2021).
The goal of this paper is to review and present the application of SA in ET0 modelling, provide practical examples on each SA method, and make future recommendations for applying SA in ET0 modelling. The paper is organized as follows: Section 2 presents different types of SA methods typically adopted in ET0 modelling. Section 3 reviews the degree of influence of ET0 on its meteorological variables around the world. Finally, the future prospect for the use of SA methods in ET0 modelling are presented in Section 4.
SENSITIVITY ANALYSIS METHODS USED IN ET0 MODELLING
Local and global sensitivity analysis method
The methods for SA applied in the ET0 estimation can be classified into local sensitivity analysis (LSA) and global sensitivity analysis (GSA). The previous developments in SA were mainly based on the obtaining point-based sensitivity measures. However, this definition is ambiguous and potentially misleading due to the limited practice of SA methods in ET0 fields. This led to the advancement of GSA, which focuses on attributing the variability of the model responses to different factors, including the model variables, forcings, boundary and initial conditions (Razavi et al. 2019). The general overview, advantages and disadvantages of various LSA and GSA techniques in ET0 modelling are outlined in Tables 1 and 2, respectively. Although GSA requires higher computationally efficiency compared to LSA, LSA is inadequate when the model is non-linear and monotonic, which will lead to low accuracy. GSA method can provide high-order interactions therefore it is regarded as a more reliable method.
General overview of various LSA and GSA techniques in ET0 modelling
Approaches . | Local Sensitivity Analysis (LSA) . | Global Sensitivity Analysis (GSA) . | ||
---|---|---|---|---|
One-at-a-time (OAT) method . | Sensitivity Coefficient Method . | Sobol's Method . | eFAST . | |
Sampling Strategy | N/A | N/A | Sobol Sequence | eFAST sampling |
Computational budget | Low | Low | High | High |
Characteristics | Quantitative | Quantitative | Quantitative | Quantitative |
Parameter Interaction | No | No | Yes | Yes |
Coping with non-linearity | Yes | Yes | Yes | Yes |
Robustness | Weak | Weak | High | High |
Approaches . | Local Sensitivity Analysis (LSA) . | Global Sensitivity Analysis (GSA) . | ||
---|---|---|---|---|
One-at-a-time (OAT) method . | Sensitivity Coefficient Method . | Sobol's Method . | eFAST . | |
Sampling Strategy | N/A | N/A | Sobol Sequence | eFAST sampling |
Computational budget | Low | Low | High | High |
Characteristics | Quantitative | Quantitative | Quantitative | Quantitative |
Parameter Interaction | No | No | Yes | Yes |
Coping with non-linearity | Yes | Yes | Yes | Yes |
Robustness | Weak | Weak | High | High |
One-at-a-time (OAT) method
In the One-at-a-time (OAT) method, the effect on model output is established by adjusting one variable (input) at a time while keeping the other variables constant. Since the OAT method does not measure the interaction between various variables, this method is error-prone and can produce uncertain results, especially for models that contain numerous variables with only a few influential inputs (Saltelli et al. 2019). The accuracy of sensitivity results for a certain input variable is associated with the value selected for other model variables. In addition, sensitivity results in OAT sampling mostly depend on the scale by which the input variable is varied (Razavi & Gupta 2015). The advancement based on the OAT sampling has developed more model-based methods such as regression, elementary-effect, factorial design and Monte Carlo.
Sensitivity coefficient (SC) method
Various sensitivity coefficient (SC) methods have been introduced in the application of ET (McCuen 1973; Coleman & Decoursey 1976), hydrological studies (Anderton et al. 2002). Saxton (1975) defined the SC method as the ratio of the amount of increase or decrease in ET0 to the changes in each meteorological variable on a daily basis. The dimensionless SC values allow comparison between each meteorological variable. The larger the SC, the greater of degree of influence of the meteorological variables on ET0 (Koudahe et al. 2018). The correlation between ET0 and each variable relies on the absolute value of the SC. If SC > 0, ET0 increases as the meteorological variable increases; whereas if SC < 0, ET0 decreases as the meteorological variable increases. A SC of 0.1 for a meteorological variable is equal to a 1% increase in ET0 when the meteorological variable increases by 10%. However, the method is sensitive to the magnitudes of ET0 and the meteorological variables. In particular, the SC may not be a good indication of the significance of the meteorological variable sensitivity if the ET0 or the meteorological variable is zero (Beven 1979).
The advantages and disadvantages of various LSA and GSA techniques in ET0 modelling
Approaches . | Advantages . | Disadvantages . |
---|---|---|
One-at-a-time (OAT) method | - Easy of operation and interpret, Low computational cost | - Prone to produce uncertain results - Largely rely on the scale of the chosen parameters. |
Sensitivity Coefficient Method | - Easy of operation and interpret, Low computational cost | - Does not provide detailed interaction between the combinations of input factors. |
Sobol's Method eFAST | - Great precision estimation as it provides error made on indices estimates via random repetition and/or bootstrap methods. - Able to incorporate the influence of input parameters over the whole range of variation. - Model independence (Adequate for non-linear and non-monotonic models) | - High computational cost - Difficult to apply in complex models with a large number of parameters. - If the number of parameters increase, a large number of model evaluations are required to get precise result. |
Approaches . | Advantages . | Disadvantages . |
---|---|---|
One-at-a-time (OAT) method | - Easy of operation and interpret, Low computational cost | - Prone to produce uncertain results - Largely rely on the scale of the chosen parameters. |
Sensitivity Coefficient Method | - Easy of operation and interpret, Low computational cost | - Does not provide detailed interaction between the combinations of input factors. |
Sobol's Method eFAST | - Great precision estimation as it provides error made on indices estimates via random repetition and/or bootstrap methods. - Able to incorporate the influence of input parameters over the whole range of variation. - Model independence (Adequate for non-linear and non-monotonic models) | - High computational cost - Difficult to apply in complex models with a large number of parameters. - If the number of parameters increase, a large number of model evaluations are required to get precise result. |
The advantages of new SC method proposed by Ambas & Baltas (2012)
. | Advantages . |
---|---|
New SC method | 1. Standard deviation cannot be zero. 2. The coefficient is unaffected by the units. 3. The standard deviation expresses the entire data set. 4. The minimum value relies on the magnitude of the time series. 5. The range width of input variables relies on both minimum and maximum values. 6. Some meteorological variables are limited. For instance, the relative humidity and wind speed. The relative humidity must be valued between 0 and 100% whereas the value of wind speed must be positive values. 7. This SC shows the adjustments caused to the model by the variation of the variable. |
. | Advantages . |
---|---|
New SC method | 1. Standard deviation cannot be zero. 2. The coefficient is unaffected by the units. 3. The standard deviation expresses the entire data set. 4. The minimum value relies on the magnitude of the time series. 5. The range width of input variables relies on both minimum and maximum values. 6. Some meteorological variables are limited. For instance, the relative humidity and wind speed. The relative humidity must be valued between 0 and 100% whereas the value of wind speed must be positive values. 7. This SC shows the adjustments caused to the model by the variation of the variable. |
Furthermore, Coleman & DeCoursey (1976) defined the SC coefficient that eliminated the bias caused by the SC method. More recently, Ambas & Baltas (2012) proposed a new SC that emphasizes the use of standard deviation. This method has several advantages (Table 3) as compared to the previous approaches.
From Table 4, numerous studies have assessed the sensitivity of meteorological variable contributing to ET0 estimation using the SC method. These studies highlighted changes of each meteorological variable on ET0 estimation in different climatic conditions and regions. Qi et al. (2017) tested the sensitivity of ET0 of the FAO-56 Penman Monteith model in Heilongjiang Province, China and concluded that relative humidity was the most sensitive variable in spring, summer and autumn seasons and maximum temperature was the most sensitive variable during winter time. Jerszurki et al. (2019) tested the sensitivity of a FAO-56 Penman Monteith model to estimate ET0 under different climate conditions across Brazilian regions. The results demonstrated a strong and linear response of ET0 to changes in meteorological variables for all climate types and vapor pressure deficit, wind speed and solar radiation were the most sensitive variables. Xie & Wang (2020) performed SA on 10 different ET0 models, and they concluded that the wind speed and sunshine hours were the major factors influencing ET0 changes. On the other hand, Yildirim et al. (2021) analysed the sensitivity of ET0 across seven different regions in Turkey and concluded that ET0 was most sensitive to wind speed, followed by air temperature.
The summary of SA methods applied in different regions across the world
SA methods . | Regions . | Parameters . | Key results . | Reference . |
---|---|---|---|---|
Sensitivity Coefficient method | China | T, RH, SR, WS | ET0 was most sensitive to Rs, followed by RH and T, and the least sensitive to WS | She et al. (2017) |
Songnen Grassland, Northeast China | Tmax, Tmin, T, RH, SR, WS | RH and Tmax were the most sensitive variables to the change in ET0 over the whole region. | Ma et al. (2017) | |
Heilongjiang, China | Tmax, Tmin, RH, SR, WS | ET0 was the most sensitive to RH during spring, summer and autumn whereas Tmax and Tmin were the most sensitive variables during wintertime. | Qi et al. (2017) | |
Greek | Tmax, Tmin, Tdew, T, RH, WS, DL, SR, AR, NR | T and SR were the most sensitive variables for all locations. | Paparrizos et al. (2017) | |
Côte d'Ivoire, West Africa | Tmax, Tmin, RHmax, RHmin, SR, WS | ET0 was most sensitive to SR and Tmax, followed by WS. The SC of SR were high in humid condition whereas Tmax and WS were high under semi-arid condition. | Koudahe et al. (2018) | |
Southwest China | Tmax, Tmin, RH, SR, WS | ET0 was most sensitive to RH, but a significant reduction in SD caused a great decline of ET0. | Jiang et al. (2019) | |
Iran | Tmax, Tmin, RHmax, RHmin, SR,SH | Tmax were the most sensitive variables to the change in ET0 for most of the stations. | Biazar et al. (2019) | |
Brazil | Tmax, Tmin, RH, SR, WS, VPD | ET0 was most sensitive to VPD, WS and SR in all climatic types. | Jerszurki et al. (2019) | |
Beijing, China | T, RH, SR, WS | RH and SR, alternately were most sensitive variables. | Liu et al. (2020 | |
Iran | Tmax, Tmin, RH, WS, SH | ET0 was most sensitive to Tmax and RH in all climatic types. | Nasrollahi et al. (2021) | |
Turkey | T, RH, SR, WS | ET0 was most sensitive to WS across all regions. | Yildirim et al. (2021) | |
Senegal River Basin | Tmax, Tmin, RH, SR, WS | ET0 was most sensitive to RH, Tmax and SR in majority of the regions. | Ndiaye et al. (2021) | |
South Manitoba | Tmax, Tmin, SR, WS, VPD | ET0 was most sensitive to Tmax, followed by SR, VPD, WS and Tmin | Ndulue & Ranjan (2021) | |
Sobol's method | Australia | T, RH, SR, WS | ET0 was generally most sensitive to T. | Guo et al. (2017) |
Global scales | Tmin, VPD, g, C1, β | MOD16 exhibited the highest sensitivity to β for all biome. | Zhang et al. (2019) | |
Peninsular Malaysia | Tmax, Tmin, T, RH, AP, WS | Tmin was found the most sensitive variables, followed by WS and RH. ET0 was least sensitive to SR. | Pour et al. (2020) | |
Bushland, Texas | 37 model input variables for DSSAT | The most sensitive parameters included that initial soil water content, soil parameters, the parameters that controlled crop development, leaf growth or development, seed cotton yield as well as canopy height and width. | Thorp et al. (2020) | |
China | Tmax, Tmin, RH, SR, WS, AP | ET0 was highly sensitive to Tmax, RH and SR. | Zeng et al. (2021) | |
eFAST | China | T, RH, SR and WS | ET0 was more sensitive to SR and less sensitive to T in low latitude than that of high latitude. | Zheng et al. (2015) |
China | NDVI, Ts, Ta, α, τsw, εs, εa | α and τsw were the most sensitive parameters whereas the remained parameters were the least sensitive for the coupled SEBAL, indicating their minor roles on regional ET0 estimations. | Zheng et al. (2015) | |
Colorado | RHmax, RHmin, Tmax, Tmin, Ws and SR | ET0 was most sensitive to WS, followed by RHmin (winter) and SR (summer). | DeJonge et al. (2015) | |
Texas | Root_growth_soil, soil_evap_plant, Microbial_top_soil_coefficient and Max_rain_intercept | ‘soil_evap_plant’ was the most sensitive parameter. | Talebizadeh et al. (2018) |
SA methods . | Regions . | Parameters . | Key results . | Reference . |
---|---|---|---|---|
Sensitivity Coefficient method | China | T, RH, SR, WS | ET0 was most sensitive to Rs, followed by RH and T, and the least sensitive to WS | She et al. (2017) |
Songnen Grassland, Northeast China | Tmax, Tmin, T, RH, SR, WS | RH and Tmax were the most sensitive variables to the change in ET0 over the whole region. | Ma et al. (2017) | |
Heilongjiang, China | Tmax, Tmin, RH, SR, WS | ET0 was the most sensitive to RH during spring, summer and autumn whereas Tmax and Tmin were the most sensitive variables during wintertime. | Qi et al. (2017) | |
Greek | Tmax, Tmin, Tdew, T, RH, WS, DL, SR, AR, NR | T and SR were the most sensitive variables for all locations. | Paparrizos et al. (2017) | |
Côte d'Ivoire, West Africa | Tmax, Tmin, RHmax, RHmin, SR, WS | ET0 was most sensitive to SR and Tmax, followed by WS. The SC of SR were high in humid condition whereas Tmax and WS were high under semi-arid condition. | Koudahe et al. (2018) | |
Southwest China | Tmax, Tmin, RH, SR, WS | ET0 was most sensitive to RH, but a significant reduction in SD caused a great decline of ET0. | Jiang et al. (2019) | |
Iran | Tmax, Tmin, RHmax, RHmin, SR,SH | Tmax were the most sensitive variables to the change in ET0 for most of the stations. | Biazar et al. (2019) | |
Brazil | Tmax, Tmin, RH, SR, WS, VPD | ET0 was most sensitive to VPD, WS and SR in all climatic types. | Jerszurki et al. (2019) | |
Beijing, China | T, RH, SR, WS | RH and SR, alternately were most sensitive variables. | Liu et al. (2020 | |
Iran | Tmax, Tmin, RH, WS, SH | ET0 was most sensitive to Tmax and RH in all climatic types. | Nasrollahi et al. (2021) | |
Turkey | T, RH, SR, WS | ET0 was most sensitive to WS across all regions. | Yildirim et al. (2021) | |
Senegal River Basin | Tmax, Tmin, RH, SR, WS | ET0 was most sensitive to RH, Tmax and SR in majority of the regions. | Ndiaye et al. (2021) | |
South Manitoba | Tmax, Tmin, SR, WS, VPD | ET0 was most sensitive to Tmax, followed by SR, VPD, WS and Tmin | Ndulue & Ranjan (2021) | |
Sobol's method | Australia | T, RH, SR, WS | ET0 was generally most sensitive to T. | Guo et al. (2017) |
Global scales | Tmin, VPD, g, C1, β | MOD16 exhibited the highest sensitivity to β for all biome. | Zhang et al. (2019) | |
Peninsular Malaysia | Tmax, Tmin, T, RH, AP, WS | Tmin was found the most sensitive variables, followed by WS and RH. ET0 was least sensitive to SR. | Pour et al. (2020) | |
Bushland, Texas | 37 model input variables for DSSAT | The most sensitive parameters included that initial soil water content, soil parameters, the parameters that controlled crop development, leaf growth or development, seed cotton yield as well as canopy height and width. | Thorp et al. (2020) | |
China | Tmax, Tmin, RH, SR, WS, AP | ET0 was highly sensitive to Tmax, RH and SR. | Zeng et al. (2021) | |
eFAST | China | T, RH, SR and WS | ET0 was more sensitive to SR and less sensitive to T in low latitude than that of high latitude. | Zheng et al. (2015) |
China | NDVI, Ts, Ta, α, τsw, εs, εa | α and τsw were the most sensitive parameters whereas the remained parameters were the least sensitive for the coupled SEBAL, indicating their minor roles on regional ET0 estimations. | Zheng et al. (2015) | |
Colorado | RHmax, RHmin, Tmax, Tmin, Ws and SR | ET0 was most sensitive to WS, followed by RHmin (winter) and SR (summer). | DeJonge et al. (2015) | |
Texas | Root_growth_soil, soil_evap_plant, Microbial_top_soil_coefficient and Max_rain_intercept | ‘soil_evap_plant’ was the most sensitive parameter. | Talebizadeh et al. (2018) |
Notes: T represents mean temperature (°C); RH represents relative humidity (%) ; SR represents solar radiation (MJ m−2); ER represents extraterrestrial radiation (MJ m−2); NR represents net radiation (MJ m−2); WS represents wind speed (ms−1); SH represents sunshine hours(h) ; DL represents day length (h) AP represents atmospheric pressure; VPD represents vapour pressure deficit (kPa); g represents leaf boundary layer conductance (ms−1); C1 represents the mean potential stomata conductance (ms−1); β represents the sensitivity of soil evaporation to VPD; NDVI represents Normalized Difference Vegetation Index; Ts and Ta are surface and surface air temperature respectively (K); α represents ground surface albedo; τsw represents empirical parameter that accounts for transmissivity of both direct of solar beam radiation and diffuse radiation to the surface; εs and εa denote broadband surface and atmospheric emissivity; ‘soil_evap_plant’ is a parameter that accounts for the effect of plant cover on reduced evaporation from soil surface; ‘Root_growth_soil’ is the soil characteristics on root growth that affect ET; ‘Microbial_top_soil_coeff’ and ‘Max_rain_intercept’ are the parameters that influence the litter transformation on the soil surface and intercepted rainfall amount.
Although the SC method is employed to assess the inconsistencies and root cause of ET0 change, it does not measure the impact of meteorological variables on ET0. Hence, to precisely explain the causes of ET0 change, contribution rate analysis is required to quantify the contributions of change in meteorological variables to change in ET0 (Liu et al. 2020).
Sobol’ method
The Sobol’ method is a GSA approach that uses variance decomposition to determine the attribution of each uncertain input variable to the total output variance of a model. It allows for an assessment of the impact of each meteorological variable on the ET0 model performance, as well as the interaction between the meteorological variables on the ET0 model, which cannot be achieved by LSA methods (Zhang et al. 2019). The variances are estimated by approximate Monte Carlo numerical integration. In addition, the Sobol’ method provides first-order and total indices. The first order indices describe the attribution of each meteorological variable on the output variance without accounting the interaction between other meteorological variables. The total indices indicate the attribution of the meteorological variable and the variance caused by the interactions between other meteorological variables. Not only these two indices develop an understanding by providing a quantitative measure of the contribution of the meteorological variables, it also can be used for factor fixing and prioritization (Pang et al. 2020).
Extended Fourier amplitude sensitivity test (eFAST)
The enhanced version of Fourier Amplitude Sensitivity Test (FAST), known as extended-FAST (eFAST) was initially developed by Saltelli et al. (1999). This method is developed to resolve the limitation of FAST as FAST is inefficient for high-order interaction terms (Pang et al. 2020). One of the key features of eFAST is to allow the input variables of the ET0 model to oscillate at different frequencies. The eFAST demonstrates which uncertain input variable has the largest degree of impact on the variability of output. Since it is quantitative and model independent, eFAST has been abundantly utilized to evaluate the model acceptability and establish what factors affect model (Cheng et al. 2020).
Similar to Sobol’ method, eFAST computes both first-order and total-order sensitivity indices of each input variable to the output variance. The first-order sensitivity index accounts for the contribution of an input variable only whereas the total-order sensitivity index accounts for the interactions among all the input variables (Yang et al. 2016). The details can be found in Saltelli et al. (1999). In comparison with Sobol's method, the study that carrying out SA using eFAST for ET0 estimation is relatively limited.
This method has been applied by Zheng et al. (2015) to investigate the variation of the sensitivity of ET0 to relative humidity, wind speed, mean temperature and incoming solar radiation in China. The results depicted that the sensitivity of ET0 varied geographically and seasonally. The stations located in low latitude were more sensitive to solar radiation and less sensitive to mean temperature than the stations in the high latitude. It is apparent that global warming has led to the ET0 variation especially in northeast China and Tibetan Plateau (cold regions) where the Si values of mean temperature were the highest than other meteorological variables. Apart from that, Tadesse et al. (2018) performed SA using eFAST to detect sensitive parameters that influence the ET simulations in Bushland Texas. Among all the parameters, ‘soil_evap_plant_cover’ was the most sensitive.
FACTORS AFFECTING THE SENSITIVITY ANALYSIS OF ET0
Elevation effects
The diversity of the elevation is one of the primary reasons that affects ET0 sensitivity. The variation in ET0 is especially complex in high-altitude regions as these regions experience a faster warming trend compared to low-altitude regions. Zheng & Wang (2015) assessed the sensitivity of FAO-56 PM model to meteorological variables at 688 meteorological stations in China. The study presented the relationship between sensitivity index (Si) values with latitude and longitude at different timescale. They found the stations located at high latitude exhibited higher Si values of mean temperature and lower Si values of solar radiation compared to stations located at low latitudes. The results also indicated that solar radiation and mean temperature were significant correlated with latitude at both annual and seasonal timescales. However, the correlations between meteorological variables and longitude were equivocal. As mentioned by Qi et al. (2017), topography and monsoon circulation have contributed to the changes of ET0 in the northern province of China. The combined effects of temperature and precipitation variations, corresponding with the topographies, lead to the declining trend of annual ET0 from low-altitude to high-altitude mountainous areas. Apart from that, Ma et al. (2017) found clear spatial patterns of ET0 in Songnen Grassland, northeast China. In low latitude areas, due to the presence of valleys, the temperature is relatively low in the northeast and east regions. The lower values of ET0 at high latitude area are due to the continental monsoon climate. The flat topography at low latitude in southwest regions resulted in lower relative humidity and high ET0 values.
In addition, Qi et al. (2017) examined the impact of meteorological variables on ET0 using daily data provided by the China Meteorological Administration for Heilongjiang province in northeast China. They found that all meteorological variables, including wind speed, maximum and minimum temperature, relative humidity and sunshine duration were interconnected with changes in elevation. All the meteorological variables, except for relative humidity, showed a declining trend at high-altitude mountainous areas (greater than 400 m elevation) across all four seasons. Conversely, the average relative humidity showed an increasing trend with increasing elevation. Overall, ET0 showed a decreasing trend from low to high-elevation area in spring, autumn and summer. This trend may be due to the interaction of temperature and precipitation variations that are strongly linked to topography and monsoon circulation in the Heilongjiang region.
Similarly, Jiang et al. (2019) investigated the impacts of meteorological variables on ET0 during 1961–2016 in southwest China and found that relative humidity had high SC values (negative values) in high-elevation regions, which would strongly decrease ET0. In high-elevation areas, relative humidity declined significantly due to a decreasing trend in precipitation in southwest China, leading to a decrease in atmospheric vapour pressure and an acceleration in the process of water vapour released from plants. On the other hand, Sun et al. (2020) analyzed the spatial and temporal changes in seasonal and annual ET0 in the Hengduan Mountains from 1981–2017. They found that the sensitivity of air temperature, actual vapour pressure and solar radiation decreased from low to high-elevation areas, whereas the sensitivity of wind speed increased gradually with increasing elevation. Air temperature was the most sensitive variable at low-altitude regions, whereas wind speed was the most sensitive variable at high-altitude regions.
Climatic conditions and timescales
Generally, changes in ET0 in response to climate change vary significantly depending on time scales and climatic conditions. The changes in meteorological factors are strongly associated with the variability of the spatiotemporal scale of the SCs. Several studies have carried out the SA of ET0 estimation under contrasting climatic conditions and time scales around the world. Dejonge et al. (2015) investigated the SA of ET0 estimation to sensor accuracy in Colorado and Florida, United States. The authors found out that ET0 was highly sensitive to solar radiation during summer, followed by minimum relative humidity and wind speed in early and late summer, respectively. ET0 was most sensitive to wind speed and minimum relative humidity during winter. The results also demonstrated that the solar radiation was the most sensitive in humid areas, Florida throughout the study period.
Koudahe et al. (2018) evaluated the changes of ET0 with respect to its meteorological variables under humid and semi-arid condition in Côte d'Ivoire, West Africa. The authors found out that ET0 was most sensitive to changes in wind speed, solar radiation and maximum temperature at all study areas. Wind speed and maximum temperature showed the highest SC under semi-arid regions, whereas the SC of the solar radiation was highest under humid regions. In semi-arid regions, the increasing wind speed reduced the aerodynamic resistance, which contributed to the increase of ET0. Maximum temperature was ranked as the third important variable and can be attributed to the fact that the importance of maximum temperature is to calculate the net radiation, slope of saturation vapor pressure and net longwave radiation for ET0 estimation.
In Brazilian region, SA was carried out by Jerszurki et al. (2019) to determine the influence of different meteorological variables on the ET0 model under different climatic conditions. ET0 was most sensitive to vapour pressure deficit, followed by wind speed and solar radiation under all climatic conditions. Increased air temperature contributed to the decline of the slope of saturation vapour pressure in the FAO-56 PM model, thus resulting in larger sensitivity during the winter period in the semi-arid region. Besides, the highest sensitivity of wind speed was observed during spring and summer in semi-arid regions due to low relative humidity and high air temperature. Under the conditions of low relative humidity, the wind replaces the saturated air more efficiently, which favours the maintenance of higher vapour pressure deficit and promotes larger ET0 value. On the other hand, increasing solar radiation has led to an increase of ET0 under humid, tropical and sub-tropical regions.
Liu et al. (2020) assessed the SA and contributions of meteorological variables to ET0 change on different time scales in Beijing. Over the period of 60 years (1958–2017), the changes of ET0 varied temporally. On the daily scale, ET0 was most sensitive to the relative humidity during day and night time, while ET0 was most sensitive to net radiation during the afternoon. Relative humidity was most sensitive to ET0 from October to March, and net radiation was most sensitive to ET0 from April to September. Furthermore, net solar radiation was the most sensitive variable during spring and summer, while relative humidity was the most sensitive variable during autumn and winter. The decline in relative humidity and increasing temperature has contributed to the rise in ET0.
Moreover, Zeng et al. (2021) evaluated SA using CMIP5 projections (2021–2050) based on annual and seasonal timescales in China. ET0 was most sensitive to maximum temperature, solar radiation and relative humidity during Spring, Autumn and Winter. In summer, solar radiation, maximum temperature, relative humidity and wind speed were the most sensitive variables that influence ET0. The occurrence of increasing radiative forcing caused by anthropogenic factors of climate change brings abrupt changes in meteorological variables in China. For instance, the most sensitive meteorological variable has changed from maximum temperature to solar radiation and from relative humidity to solar radiation in Summer and Winter respectively.
From the studies above, it is evident that the variation of ET0 is highly diverse across the different regions around the world. This fact further reinforces the necessity to carry out SA in order to study the change in ET0 and its driving factors. The knowledge of identifying the variation in ET0 in terms of spatial and temporal scales is the primary step in estimating the ET0 (Jiang et al. 2019). Studying the effects of meteorological variables on the ET0 using SA would aid in analyzing the future water demands for sustainable agricultural activities, proper water resources planning and management. Farmers can make better decisions regarding irrigation scheduling, leading to improved crop yields and water-use efficiency (Han et al. 2021). For instance, if the ET0 rate is high, farmers can adjust their irrigation schedule to ensure that the crops receive adequate water, while avoiding over-irrigation, which can lead to waterlogging and other negative impacts on the crop growth. Additionally, farmers can optimize the use of fertilizers and other inputs, reducing waste and environmental impacts (Yamaç & Todorovic 2020).
Apart from improving the agricultural practices, SA plays an important role in climate change adaptation and drought management. ET is also affected by climate change, which has important implications for water resources management (Khaydar et al. 2021). By understanding how ET will change in response to climate change, water resources engineers and policy makers can better plan for the future and take steps to adapt to changing water availability. Furthermore, ET0 can be used as an indicator of water stress during drought events, which can guide water management decisions. By monitoring ET0, water resources engineers can identify areas that are experiencing water stress and prioritize water allocation to areas that are most in need (Ng et al. 2022).
FUTURE PROSPECTS
The employment of GSA methods should always be considered in order to overcome the limitations of LSA methods. This would greatly reduce the likelihood of errors when making decision that need to be carried out by policymakers or researchers. The future prospects of this study field can be sorted as follows:
- 1.
Development of multi-method SA toolboxes to resolve the constraints of each SA method.
While some multi-method toolboxes have been developed, it is able to comprehensively resolve the constraints of each SA methods, particularly for such a complex hydrological process. For instance, VARS-TOOL is a toolbox that utilizes directional variogram and co-variogram functions, providing comprehensive sets of global sensitivity indices with minimal computational burdens. It could be a promising approach to explore for the modelling of ET0.
- 2.
Employment of high-resolution meteorological data
Higher resolution meteorological data with detailed information such as geographical information system (GIS) and satellite data may be utilized for ET0 modelling. This will be particularly favourable for regions that always encounters issues like scarce or missing meteorological data.
- 3.
Improve methods to study the interactions between meteorological variables (inputs)
Based on the knowledge, it is undeniable that there is no SA method that is capable of studying the interactions between meteorological variables for ET0 modelling effectively. The information about meteorological variables interactions can be compiled as a by-product of several SA methods. For such, the standard deviation of the elemental effects and the dissimilarity between total-order and first order indices.
- 4.
Analysis of other input factors that are affecting ET0
Apart from mentioned climatic factors, other factors affecting ET0 such as leaf area index (LAI) and crop coefficient should be taken into account for ET0 estimation.
CONCLUSION
The application of SA in ET0 estimation is to determine the degree of influence of the meteorological variables on the ET0 estimation. The sensitivity of ET0 can provide critical evaluation to determine the most suitable models for ET0 estimation under the influence of climate change. Different SA methods are adopted in ET0 estimation but each of the methods has its own limitations. SA methods are simple and easy in terms of implementation and interpretation; thus, they may be still the first choice due to its low computational burden with ET0 models. However, the Sobol's and eFAST may be preferred for models with high number of meteorological factors. They can measure the changes of each meteorological variable in the output variance.
While each SA method distinguishes the sensitivity of the ET0 in a different way, it can be found that the majority of the studies have adopted only one SA method (either LSA or GSA method). It is suggested that both local and global SA methods should be employed for better comparative assessment. To provide a more comprehensive SA, additional factors that affect ET0, such as LAI and crop coefficient, should be considered. Despite the advancements in the developments of GSA methods, the intensive computational costs remain a major challenge. This fact reinforces the future need to build an integrated and realistic multi-method SA toolbox that integrates various theories and strategies to handle high-dimensional models with minimal computational costs. The development of an efficient and effective multi-method SA toolbox will definitely provide high accuracy and robust results, allowing farmers, engineering and decision makers, to identify adequate solutions for water resources planning and management as well as improving the agricultural crop production.
The paper has reviewed the SA methods in ET0 modelling. The findings and recommendations of the application of SA in ET0 modelling are summarized as below.
- •
The LSA is the simplest and easiest in terms of ET0 modelling. It requires low computational cost, simple implementation, and easy interpretation. The drawback of this method is that it only explores a small portion of the possible space of input values.
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The application of GSA methods to study the dominant meteorological variables affecting the ET0 estimation is still limited. It could be a better choice in comparison with LSA methods as it can determine the changes of uncertain inputs over the whole input space.
- •
The choice of SA methods is dependent on the research purpose, the computational costs and the number of input variables. The feasible suggestions of performing SA are:
- (a)
The SC method may be still the first choice because it only requires low computational cost.
- (b)
The variance-based method (i.e. Sobol and eFAST method) provides more robust analysis provided with high computational demanding.
- (a)
- •
It is of importance to select an appropriate SA method for ET0 estimation. This is because ET0 is a complex and non-linear process that is difficult to measure and estimate accurately. Thus, adequate SA methods must be selected carefully to achieve the research requirements.
ACKNOWLEDGEMENT
The authors would like to express their gratitude to the Ministry of Higher Education Malaysia for funding this research project through Fundamental Research Grant Scheme (FRGS) with project code: FRGS/1/2021/TK0/UCSI/03/3. The authors also would like to thank Malaysian Meteorological Department (MMD) for the provision of the meteorological data.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.