Sensitivity analysis of reference evapotranspiration to sensor accuracy
Introduction
In irrigated agriculture, accurate and consistent estimates of crop evapotranspiration (ETc) are vital in terms of water management. At the field scale, ETc can be used for irrigation scheduling whereas at regional scales knowledge of evapotranspiration (ET) consumption can be used to evaluate irrigation water resources planning and distribution. However, because ET is very difficult to measure directly, it is often estimated using models based on climatic inputs, which individually can be highly variable. The most common method to estimate ETc is to transform a reference evapotranspiration (grass-based ETo or alfalfa-based ETr) by multiplying with a crop coefficient (Kco or Kcr). The Kc is unique to each crop and reference type, and can vary with several parameters affecting ET such as leaf area, soil and climate conditions, and crop stresses (Doorenbos and Kassam, 1979). While many methods exist to calculate reference ET, physically based approaches such as FAO56 Penman–Monteith (Allen et␣al., 1998) require more input data but are generally accepted as the most accurate estimation. The American Society of Civil Engineers–Environmental and Water Resources Institute (ASCE–EWRI) created a standardized version of the Penman–Monteith method for reference ET calculation (ASCE, 2005), which has notable advantages with respect to commonality and transferability of Kc values (Irmak et␣al., 2006).
Field sensor accuracy is of paramount importance when determining reference ET using a physical model. Droogers and Allen (2002) evaluated reference ET estimates using both the Penman–Monteith (Allen et␣al., 1998) and Hargreaves (Hargreaves and Samani, 1985, Hargreaves et␣al., 1985) methods. They concluded that the more data intensive (e.g., air temperature, humidity, solar radiation, wind speed) Penman–Monteith method is recommended if accurate weather data collection is feasible and available. If data accuracy is questionable the simpler (e.g., air temperature and solar radiation only) Hargreaves method should be considered. While issues such as station siting, proper fetch, and maintaining adequate reference conditions are very important in creating consistent measurement conditions, bias or other measurement errors associated with the sensors themselves can cause tremendous error in the final outputs of the equations. Therefore, it is desirable to fully understand the potential influence of sensor-based measurement error on the final reference ET calculation.
Manufacturers of environmental measurement sensors (e.g., anemometers, pyranometers, temperature/humidity sensors) typically quote an “accuracy” of the device, often in terms of ± a percentage or static value. One way to evaluate and quantify the influence of quoted sensor accuracy on reference ET is through sensitivity analysis (SA), which Saltelli et␣al. (2004) defined as “the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input.” The aim of SA is to determine how sensitive the output of a model is with respect to the elements of the model, which are subject to uncertainty or variability. SA methods are typically classified as local [one-parameter-at-a-time (OAT) and derivative-based] or global (multiple parameters at a time, derivative-based or more often variance-based) (Saltelli et␣al., 2008, Sobol and Kucherenko, 2009). When the purpose of the SA is to study the effects of several input parameters on the model output responses, local sensitivity analysis (LSA) is more simple but less useful than global sensitivity analysis (GSA) where the output variability is evaluated as the input parameters simultaneously vary in their individual uncertainty domains (Monod et␣al., 2006, Saltelli et␣al., 2004). GSA methods, such as Morris (1991), Fourier Amplitude Sensitivity Test (FAST, Saltelli et␣al., 1999), extended FAST (Saltelli et␣al., 1999) and Sobol’ (1993) can determine not only sensitivity to individual parameters, but sensitivity to interactions between parameters as well. GSA methods are commonly used as auxiliary tools for many different types of simulation models, including hydrologic (Ahmadi et␣al., 2014), ecological (Ciric et␣al., 2012, Morris et␣al., 2014), and crop models (DeJonge et␣al., 2012, Vazquez-Cruz et␣al., 2014).
Several studies have investigated sensitivity analysis of ET estimation equations, typically using derivative-based LSA methods, with widely varying results due to differences in climate, ET models used, and meteorological and/or physical inputs evaluated (Ambas and Baltas, 2012, Bakhtiari and Liaghat, 2011, Beven, 1979, Coleman and DeCoursey, 1976, Eslamian et␣al., 2011, Gong et␣al., 2006, Hupet and Vanclooster, 2001, Irmak et␣al., 2006, Ley et␣al., 1994a, Liang et␣al., 2008, Rana and Katerji, 1998). A limited number of studies evaluated two parameters at a time but still used derivative-based methods for evaluating sensitivity (Eslamian et␣al., 2011, Porter et␣al., 2012). Monte-Carlo uncertainty analysis of potential ET has even been evaluated on a spatial basis (Phillips and Marks, 1996). However, no study to date has fully utilized variance-based GSA techniques to simultaneously evaluate multiple inputs of ET models. Also, previous studies in the literature somewhat arbitrarily choose an error range for the input parameters, instead of selecting an input error range based on manufacturer quoted sensor accuracy. In one study closely related to this manuscript, Ley et␣al. (1994b) evaluated the effects of sensor measurement variability in the Kimberly Penman alfalfa ETr model, finding that at the limits of specified accuracy the greatest ET error was from solar radiation measurement error followed by dew point, maximum temperature, and finally wind speed measurement errors.
The above studies in the literature explore SA of micrometeorological input variables in ET models; however, they are site specific, do not use GSA methods, and rarely use sensor accuracy limits as a basis for comparison. Thus, the primary objective of this study was to evaluate the effect of manufacturer quoted accuracy of required sensors (i.e., temperature, humidity, wind speed, and solar radiation) on short reference evapotranspiration (ETos) calculations using the ASCE Standardized Reference Evapotranspiration Equation. Multiyear datasets from semi-arid (Colorado) and humid (Florida) meteorological sensor networks were evaluated using a LSA method, as well as two GSA (Morris and eFAST) methods. Secondary study objectives were to compare sensitivity results of the three SA methods used in the study, conduct an uncertainty analysis of eFAST results to further quantify ET error range in high ET months, and to perform a final eFAST GSA on both sites using a “best case” (i.e., sensor set with the best accuracy between both sites) set of input sensors in order to directly compare difference in sensitivity between sites due to climate differences.
Section snippets
ASCE standardized reference ET equation
The ASCE Standardized Reference Evapotranspiration Equation (ASCE, 2005) is intended to simplify the full form ASCE Penman–Monteith method:where ETsz is the standardized reference crop ET rate for short (ETos) or tall (ETrs) surfaces (mm d−1), Rn is the net radiation flux density at the surface (MJ m−2 d−1), G denotes the sensible or soil heat flux density from the surface to the soil (MJ m−2 d−1), γ represents the psychrometric constant (kPa °C−1), T is
Local sensitivity analysis (LSA)
Because ETos values are typically higher in the summer months than the winter months (Fig.␣3) due to increased solar radiation (Fig.␣2), the ETos error range (ERRi, Eq. (6)) was highly influenced by Rs in both Colorado and Florida on the same seasonal basis (Fig.␣4), although the relationship was stronger for Colorado (likely due to the clearer skies typically experienced there in the summer months). The ERRi (based on Rs) was between 0.31 and 0.32 mm/d between May and August for Florida,
Summary and conclusions
In a multiple-input model such as the ASCE Standardized Reference Evapotranspiration Equation (Eq. (1)), it is important to understand and quantify potential errors of input data. Considering the quoted manufacturer accuracy of the three sensors used in each network (with four relevant inputs and five separate sources of error), this study evaluated the relative importance of sensor accuracy for multiple inputs (temperature, relative humidity, solar radiation, and wind) and the subsequent
Acknowledgement
The authors would like to acknowledge Keith Wakefield for creation of the map in Fig.␣1 and assistance in compiling the meteorological data.
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