### Study area

The Ejina oasis, in the lower reaches of Heihe river, is located in Ejina county, Inner Mongolia, China, and the area is 3328 km^{2} (Figure 1). It is in the hinterland of Asia continent, and is one of the most arid in China. The average annual air temperature is about 6~8.5 °C. The mean annual precipitation, 84% of which occurs during the growing season, is less than 50 mm year^{−1}. Prevailing winds are northwesterly in the winter and spring, and southwesterly to southerly in the summer and fall. Annual mean wind velocity ranges from 2.9 to 5.0 m s^{−1}.

A data set of Ejina meteorological observatory station with daily observations of maximum, minimum and average air temperature at 2 m height, wind speed measured at 10 m height, relative humidity (2 m height) and daily sunshine duration for the period 1988-2007 was used in this study. Data were provided by the National Climatic Centre (NCC) of China Meteorological Administration (CMA). The wind-speed measurements were transformed to wind speed at 2 m height by the wind profile relationship introduced in Chapter 3 of the FAO paper 56 [5].

### The FAO56 Penman-Monteith equation

The FAO56-PM equation for calculating daily reference evapotranspiration is:

ETo=\frac{0.408\text{\Delta}\left({R}_{n}-G\right)+\gamma \frac{900}{T+273}{u}_{2}\left({e}_{s}-{e}_{a}\right)}{\text{\Delta}+\gamma \left(1+0.34{u}_{2}\right)}

where *ETo* is the reference evapotranspiration (mm day^{-1}), *R*_{
n
} the net radiation at the crop surface (MJ m^{-2}day^{-1}), *G* the soil heat flux density (MJ m^{-2}day^{-1}), *T* the mean daily air temperature at 2 m height (°C), *u*_{
2
} the wind speed at 2 m height (m s^{-1}), *e*_{
s
} the saturation vapor pressure (kPa), *e*_{
a
} the actual vapor pressure (kPa), *e*_{
s
} *- e*_{
a
} the saturation vapor pressure deficit (kPa), *Δ* the slope of the vapor pressure curve (kPa °C^{-1}) and *γ* is the psychrometric constant (kPa °C^{-1}). The computation of all data required for the calculation of the reference evapotranspiration followed the method and procedure given in Chapter 3 of the FAO paper 56 [5].

Original measurements of air temperature (*T*), wind speed (*u*_{
2
}), and relative humidity (*RH*) were chosen for sensitivity analyses. The fourth variable that was analyzed is shortwave radiation (*R*_{
s
}). This is because shortwave radiation is one of the input variables in a number of semi-physical and semi-empirical equations that are used to derive the net energy flux required by the Penman method. Following the procedure described by Allen et al. [5], *R*_{
s
} can be estimated with the Angstrom formula that relates surface shortwave radiation to extraterrestrial radiation and daily sunshine duration:

{R}_{s}=\left(a+b\frac{n}{N}\right){R}_{a}

where *R*_{
S
} is solar or shortwave radiation (MJ m^{-2}day^{-1}), *n* is daily sunshine duration (h), *N* is maximum possible duration of sunshine or daylight hours (h), *n/N* is relative sunshine duration, *R*_{
a
} is extraterrestrial radiation (MJ m^{-2}day^{-1}), *a* and *b* are regression constants. The recommended values *a* = 0.2 and *b* = 0.79 were used in this study [26].

### The sensitivity coefficient

In hydrological studies and ecological applications, a number of sensitivity coefficients have been defined depending on the purpose of the analyses [21, 23, 24, 27, 28]. More often, however, a mathematically defined sensitivity coefficient is used to characterize sensitivity [20–25]. For multi-variable models (e.g., the FAO56-PM model), different variables have different dimensions and different ranges of values, which makes it difficult to compare the sensitivity by partial derivatives. Consequently, the partial derivative is transformed into a non-dimensional form [24]:

{S}_{Vi}=\underset{\text{\Delta}Vi\to 0}{\mathsf{\text{lim}}}\left(\frac{\text{\Delta}E{T}_{o}/E{T}_{o}}{\text{\Delta}Vi/Vi}\right)=\frac{\partial E{T}_{o}}{\partial Vi}\cdot \frac{Vi}{E{T}_{o}}

Where *S*_{
Vi
} is sensitivity coefficient and Vi is the ith variable. The transformation that gives the ''non-dimensional relative sensitivity coefficient'' (denoted as ''sensitivity coefficient'' in the following text), was first adopted by McCuen and has been now widely used in evapotranspiration studies [19–25]. Basically, a positive/negative sensitivity coefficient of a variable indicates that ETo will increase/decrease as the variable increases. The larger the sensitivity coefficient is, the larger effect a given variable has on ETo. In graphical form, the sensitivity coefficient is the slope of the tangent at the origin of the sensitivity curve. Practically, the coefficient is accurate enough to represent the slope of the sensitivity curve within a certain ''linear range'' around the origin. The width of the range depends on the degree of non-linearity of the sensitivity curve. If a sensitivity curve is linear, the sensitivity coefficient is able to represent the change in ETo caused by any perturbation of the variable concerned.

Sensitivity coefficients were calculated on a daily basis for air temperature, wind speed, relative humidity and shortwave radiation. Average monthly sensitivity coefficients were obtained by averaging daily values.