Interactive comment on “ Integration of vegetation indices into a water balance model to estimate evapotranspiration of wheat and corn ”

Specific comments 1) “In the 2009 campaign, the spectral data on wheat canopy have been acquired by ground field radiometry, simultaneously to those acquired in the same canopy by multispectral satellite data. No comparison is provided in the text between vegetation index derived from satellite and from field radiometry data. This comparison is relevant because it could provide valuable indications about the quality of the spectral


Introduction
Recent studies have shown that the global demand for food will increase for at least another 40 yr.It is estimated that the global population will reach nine billion people by the middle of this century (Charles et al., 2010).One consequence of the rapid growth in world population is that the pressure on water resources is increasing (Rijsberman, 2006).In the future, less water will be available for agricultural production as a result of competition with the industrial and domestic sectors.At the same time, food production will need to increase to feed the growing population (FAO, 2006).In arid and semi-arid regions, the very availability of water is a major limitation on crop production due to insufficient rainfall to compensate for the evaporative losses of crops.Improvements in water management in irrigated areas and adequate irrigation scheduling are essential, not only to improve water productivity, but also to increase the sustainability of irrigated agriculture (Hsiao et al., 2007).One of the most important components of the water balance is evapotranspiration (ET), i.e. the water transferred to the atmosphere by soil evaporation and plant transpiration.Several techniques, such as Bowen ratio energy balance, eddy covariance and weighing lysimeters, provide ET measurements, but these are expensive, they are limited to point or small experimental field scales and can only be fully exploited by trained research personnel (Allen et al., 1998).Several studies have evaluated F. L. M. Padilla et al.: Integration of vegetation indices into a water balance model remote sensing techniques for estimating crop evapotranspiration on a large scale (Anderson et al., 2007;González-Dugo and Mateos, 2008;Teixeira et al., 2009).In the course of the past few decades, besides advances in sensor development, several methodologies for incorporating optical and thermal remote-sensing data into energy and water balance models have been developed, producing estimates of actual ET (Kustas and Norman, 1999;Allen et al., 2007;Neale et al., 1989).These remote sensing approaches provide an opportunity to extend the area of application of these models from point to basin or regional scales, producing a better representation of vegetation heterogeneity.
The current limited availability of high-resolution thermal satellite sensors hinders their use in irrigation scheduling and water management at field scales, and thus underlines the importance of models based on readily available optical data as a more plausible option for these applications.This approach is usually based on the FAO-56 method, which represents ET as a product of a reference evapotranspiration value (ET o ), which takes atmospheric demands into account, and a crop coefficient that considers the characteristics of the crop (Doorenbos and Pruitt, 1977;Allen et al., 1998).The crop coefficient can be calculated using a single method that combines the effect of crop transpiration and soil evaporation into a unique coefficient (K c ), or a dual one that separates the plant transpiration, represented by a basal crop coefficient (K cb ) and the soil evaporation coefficient (K e ).The single model is widely used because it requires only phenological information and standard meteorological data to produce acceptable estimated ET values (Er-Raki, 2007).The dual model is mainly oriented towards research and real-time irrigation scheduling for high-frequency water applications (Allen et al., 1998).A great deal of research has been done in the course of the past 30 yr on estimating the standard values and temporal evaluation of crop coefficients (Allen et al., 1998;Wright, 1982), which can be estimated from remote spectral measurements because both the basal crop coefficient and the vegetation indices are sensitive to ground cover fraction (fc) (Choudhury et al., 1994).This coefficient may be derived from multispectral vegetation indices (VI) obtained by remote sensing (Jackson et al., 1980;Heilman et al., 1982;Bausch and Neale, 1987;Neale et al., 1989;Calera et al., 2004).Some authors have suggested that relationships between K cb and VI are linear (Bausch and Neale, 1987;Neale et al., 1989;Gonzalez-Piqueras et al., 2003), but others have found non-linear relationships (Hunsaker et al., 2003(Hunsaker et al., , 2005)).These relationships have been studied for several crops and recently for potato (Jayanthi et al., 2007), cotton andsugarbeet (González-Dugo andMateos, 2008), wheat (Duchemin et al., 2006;Er-Raki et al., 2007) and grapes (Campos et al., 2010).
We used a combined methodology of basal crop coefficient derived from vegetation indices obtained initially from a hand-held radiometer and then from a series of satellite images and a daily water balance in the root zone of the crop.
This combined methodology enables us to calculate the daily corn and wheat crop coefficient and daily ET.A further objective was to determine the ability of the model to assess water stress in both crops.A validation was performed using field soil moisture measurements and two different instruments to measure ET; an eddy covariance system and a weighing lysimeter.

Description of the model
The model used to estimate ET was developed in the Bajo-Guadalquivir Irrigation Scheme in southern Spain (González-Dugo and Mateos, 2008).Daily ET was computed using the dual approach in the form popularized by the FAO56 manual (Allen et al., 1998), combined with spectral data provided by remote sensors.A brief description of this approach is presented below and a complete explanation of the FAO model can be found in Allen et al. (1998).
Crop transpiration, represented by the basal crop coefficient, K cb , is separated from soil surface evaporation as follow: Reference evapotranspiration (ET o , mm d −1 ) was estimated using the Penman-Monteith equation (Allen et al., 1998), with daily solar radiation, air temperature, wind speed, and relative humidity data supplied by weather stations.The water stress coefficient, K s , quantifies the reduction in crop transpiration due to soil water deficit, where K s = 1 for non-stress conditions and K s < 1 when there is a shortage of water in the root zone.K e is the soil evaporation coefficient that describes the evaporative component of ET c .The procedure for calculating each coefficient is described below.

Basal crop coefficient
The K cb in Eq. ( 1) may be derived from multispectral vegetation indices obtained by remote sensing.VIs are transformations of two or more spectral bands designed to assess vegetation condition, foliage, cover, phenology and processes related to the fraction of photosynthetically active radiation absorbed by a canopy (fPAR) (Asrar et al., 1989;Baret et al., 1991;Glenn et al., 2008) VIs are also essential tools in land-cover classification, climate and land-use-change detection, drought monitoring and habitat loss, to name just a few applications (Glenn et al., 2008).SAVI (Soil Adjusted Vegetation Index, Huete, 1988) is one of the most used indices highlighting the ability of the index to minimize the effect of the soil on vegetation quantification.It was taken into account due to the positive results obtained in previous work (González-Dugo and Mateos, 2008).The SAVI index was calculated as follow: Hydrol.Earth Syst.Sci., 15, 1213-1225, 2011 www.hydrol-earth-syst-sci.net/15/1213/2011/

SAVI =
where ρ NIR and ρ red are the reflectance in the near-infrared and red spectra, respectively, and L is a soil normalization factor, generally taken to be 0.5 (Huete, 1988).An equation described by González-Dugo et al. (2009) to compute the basal crop coefficient (K cb ) from SAVI was used in this study: where f cmax is the ground-cover fraction (f c ) at which K cb is at its maximum (K cbmax ), and the subscripts max and min of SAVI refer to the values for very large LAI and bare soil, respectively.The values adopted in the model are derived from field measurements, and can be found in Table 1.The change over time in SAVI for each field throughout the growing season was calculated by linear interpolation of the SAVI values obtained by remote sensors.

Water stress coefficient
A soil root-zone water balance was calculated by keeping track of the main incoming and outgoing water fluxes at the boundaries of the root zone in order to calculate K s in Eq. ( 1).The root-zone depth (Z r ) was calculated as a function of K cb .
where Z rmax and Z rmin are the maximum effective root depth and the effective root depths during the early stages of crop growth (Table 1).The minimum effective root depth is treated here as the depth of the soil layer from which the seed can extract water to germinate, and a value of 0.3 m was adopted.The change in the root zone water content, S w , was calculated as the difference between the water inflows and outflows.
where S wf and S wi (mm) are the root-zone water content at the beginning and end of the water balance period, respectively.R is infiltrated rainfall and D is deep drainage, both during the water balance period.Equation ( 7) may be expressed in terms of root-zone water deficit, calculated daily: where the subscript i indicates a given day and RZWD i and RZWD i−1 are the root-zone water deficits on day i and i −1, respectively.
It is understood that the root zone is full of water, RZWD = 0, when its water content is at field capacity, and that it is empty when the water content reduces plants to the wilting point.The root-zone water-holding capacity (RZWHC) is the depth of water between these two extremes: where θ fc is the water content at field capacity (m 3 m −3 ), θ wp is the water content at wilting point (m 3 m −3 ), and Z r is the rooting depth (m).The stress coefficient, K s , is calculated on the basis of the relative root-zone water deficit as: where p is the fraction of the RZWHC below which transpiration is reduced as a consequence of water deficit.According to the FAO-56 manual, the recommended p value is 0.55 for corn, winter and spring wheat when ET c is 5 mm per day.The value for p was adjusted for different values of ET c , using the following approximation:

Soil evaporation coefficient
The estimation of K e requires the daily water balance of the soil surface evaporation layer, of effective depth equal to Z e , to be calculated.The evaporation coefficient is at its maximum when the topsoil is wet following rain or irrigation, and is zero when the soil surface is dry and no water remains near the soil surface for evaporation.K e is calculated as: where K r is a dimensionless evaporation reduction coefficient that depends on the cumulative depth of water depleted from the topsoil and K cmax is the maximum value of K c following rainfall or irrigation.Since evaporation is restricted at any moment by the energy available at the exposed soil fraction, the value of K e cannot exceed the product f ew ×K cmax , where f ew is the fraction of the soil surface not covered by vegetation and wetted by irrigation or precipitation (Allen et al., 1998).
The soil evaporation can be assumed to take place in two stages: an energy-limiting stage, and a falling-rate stage.K r can thus be estimated as: where D e,i−1 is the cumulative depth of evaporation from the soil surface layer at the end of day i − 1. TEW, the total evaporable water, is equal to the maximum depth of water that can be evaporated from the soil during a complete drying cycle, and the readily evaporable water, REW, is the maximum depth of water that can be evaporated from the topsoil layer without restriction during the energy-limiting stage.
It is assumed that shortly following a major wetting event, the water content of the evaporation layer is at field capacity, θ fc , and the soil can dry to a water content level that is halfway between oven dry and wilting point, θ wp .The total evaporable water can be then estimated as (Allen et al., 1998):

Site description
Two experimental sites grown with wheat (Triticum aestivum) and corn (Zea mays) were monitored during the 2008 (corn) and 2009 (corn and wheat) growing seasons (Fig. 1).Soil properties such as texture and depth were measured in the wheat field and in one of the corn fields.Soil water content at field capacity and wilting point were derived from texture data using the Rosetta pedotransfer function model (Schapp et al., 2001).The same water content limits were used for both corn fields, in view of their close proximity and the similarity of their soil types.
Soil and crop parameters values used in the model applications are listed in Tables 1 and 2 respectively.Soil parameters such as the depth of soil surface evaporation layer (Z e ), readily evaporable water (REW) and total evaporable water (TEW) were adapted from values tabulated in Allen et al. (1998).
The water balance computation was initialized on 1 September 2007 and 2008, for 2008 and 2009 corn seasons, and simulated under different starting soil moisture conditions, with all cases indicating that on 1 March 2008 and 2009, just before the planting dates of each season, the root zone could be assumed to be at field capacity due to cumulative precipitations of 310 and 370 mm during the winters of 2008 and 2009, respectively.In a similar way, the soil layer depth was assumed to be at field capacity on 15 December 2008 in the wheat field.

Spectral data acquisition and processing
Field canopy reflectance measurements were performed using a hand-held radiometer (ASD-FieldSpec, Analytical Spectral Devices, Boulder, CO) over corn in 2008 season and wheat in 2009.The spectral range of the instrument, between 325 and 1075 nm (with a sampling interval of 1.6 nm), covered the visible and near-infrared (NIR) regions of the spectrum required for computing the vegetation indices and overlapped Landsat red and NIR spectral bands.A fiber optic jumper cable with a field of view (FOV) of 25 • was used in this study.Twenty-point regularly distributed measurements were taken over each field of corn and wheat at midday and under cloudless conditions.A sampling scheme based on knowledge of the row spacing (pairs "on row and off row") was selected for measurements over corn, taking one measurement over the plant (on row) and the second halfway between adjacent rows (off row) at each point of measurement.The altitude of the sensor above the soil was 4.5 m, resulting in a FOV diameter at the soil surface 2.7 times as large as the row spacing (0.75 m).The measurements over wheat were taken in accordance with a simple random sampling scheme with a sensor altitude above the soil of 2.2 m resulting in a FOV diameter at the soil surface 5.4 times as large as the row spacing (0.18 m).Six additional measurements were made over the weighing lysimeter surface inside the wheat experimental field.The reflectance spectrum was calculated as the ratio between the reflected and incident spectra on the canopy, obtaining the incident spectrum from the light reflected by a white reference panel close to a Lambertian surface (Spectralon, Labsphere, North Sutton, NH).Red and NIR reflectance values, required for SAVI calculation, were computed by averaging the reflectance values corresponding to Landsat 5 TM red and NIR spectral intervals (bands 3 and 4) using the spectral response function of each TM band.All the spatially distributed SAVI data were averaged for each measurement day and field.Satellite remote data were provided by TM and ETM+ sensors carried on board LANDSAT 5 and 7, during the 2009 corn and wheat seasons.All cloudless satellite images for both growing periods (a total of 13 images) were calibrated and geometrically and atmospherically corrected.The geometric correction was applied using reference ground control points acquired from a 1-m resolution ortho-photograph taken in 2004.At-surface reflectance was obtained from the correction of the shortwave bands of the images using the atmospheric radiative transfer model MODTRAN 4 (Berk et al., 1998) However, the ETM+ has continued to acquire data with the SLC powered off, leading to images that lack approximately 22 percent of the normal scene area (Storey et al., 2005).When some of these gaps fell within the experimental plots, their values were eliminated from the calculations.
A comparison between satellite-derived and groundderived SAVI was performed to evaluate the ability of satellite imagery to reproduce field measurements and successfully extrapolate field results to a larger scale.The estimates of SAVI derived from the Landsat-5 and 7 imagery were compared with SAVI values calculated from ground radiometry at the wheat experiment site (Table 3).The change over time in ground-derived SAVI was obtained by linear interpolation of the values of SAVI calculated from the radiometric measurements.Seven 2009 cloudless Landsat-5 and Landsat-7 images, overlapping the spectral measurement period, were used for this comparison.
A list of the sensors and dates used throughout the study for both crops is shown in Table 3.

Validation data
The model was validated using field measurements of soil moisture and ET.ET was measured using two different instrumentation sets: an eddy covariance system (EC) mounted on a micrometeorological flux tower, and a weighing lysimeter.

Eddy covariance measurements and adjustment of turbulent fluxes
Half-hourly sensible (H ) and latent (LE) heat fluxes over the corn plot were measured using an eddy covariance system consisting of a datalogger CR23X (Campbell Scientific), a three-axis sonic anemometer CSAT3 (Campbell Scientific), a fine thermocouple (model 127, chromel-constantan 0.013 mm diameter) attached to the anemometer, a krypton hygrometer KH20 (Campbell Scientific), a net radiometer Q-7.1 (Radiation and Energy Balance Systems, Seattle, WA), two soil heat flux plates HFP01 (Hukseflux Thermal Sensors, Delft, The Netherlands) and four parallel soil thermocouples (TCAV).The distance between the sonic anemometer and the hygrometer measuring paths was 0.20 m, and both were located at a height of z = 1.5 m, above the canopy.As the crop height changed along the season, the height of the instruments was checked twice a week and changed whenever necessary.Sampling frequency was 10 Hz.Fetch was at least 200 m in all directions.Corrections were applied to latent heat flux to account for air density fluctuations due to heat and vapor transfer (Webb et al., 1980;Tanner et al., 1993) and O 2 radiation absorption (Tanner et al., 1993).The net radiometer was located 1.5 m above the canopy and net radiation data (R n ) were corrected for wind speed measured with the sonic anemometer according to the manu-facturer's recommendations.Soil heat flux (G) was determined at two locations (within the row and midway between rows).The combination method (Fuchs and Tanner, 1967) was employed, using the measurement of soil thermocouples at 0.02 and 0.06 m and heat flux measured with the soil heat flux plates at 0.08 m.Measurements of R n and G were performed at 10s intervals and the mean reading was recorded half-hourly.The system was installed on the corn field between 28 April and 4 September 2008 and from 16 May until 29 August 2009, measuring continuously except on days with more than 0.2 mm of rain.A total of 96 complete days of eddy covariance measurements were collected during each growing season.Detailed studies have shown how the eddy covariance technique underestimates turbulent fluxes, a finding that has been attributed to many different factors (Massman and Lee, 2002).Twine et al. (2000) compared different energybalance closures; EC measurement of H and LE fluxes can be adjusted for closure, maintaining the Bowen ratio or forcing closure, assuming that H is accurately measured and solving LE as a residual to the energy balance equation (LE = R n -H -G).Brotzge and Crawford (2003) suggested residual LE closure as the best eddy covariance approach because the Bowen ratio technique tends to underestimate LE under highly evaporative conditions.We therefore calculated daily ET values by forcing closure of the energy balance using the residual-LE closure method, and an average closure of 80% was obtained.

Weighing lysimeter
Wheat ET was measured by a weighing lysimeter located in the center of the plot.The surface dimensions of the lysimeter tank are 2 × 3 m 2 and the depth is 1.5 m.It is supported by a counter-weighted platform scale capable of detecting changes in weight of about 0.1 kg (equivalent to 0.02 mm water depth over the lysimeter surface).The lysimeter weight was sensed by a load cell (model TSF-P, Epel Industrial S.A., Alcala Guadaira, Spain) connected to a Datalogger CR10X (Campbell Scientific) and set to measure semi-hourly ET.Daily changes in mass (kg) were converted to equivalent water depths (mm) to obtain daily ET.The outputs were obtained as the average of 120 readings taken every 2 s over a 4-min period centered at the respective sampling times, so that fluctuations in weight due to wind friction on the lysimeter surface were smoothed (Berengena and Gavilán, 2005).Only measured ET from days with precipitation below 0.2 mm were used for comparison purposes.During the dataacquisition period (17 January to 25 June 2009) the lysimeter was drained twice (DOY 42 and 76), on neither of which days its measurements were used.A total of 112 days of lysimeter-measured ET were available for this study.

Soil water content
Soil water content was calculated as the difference between wet and dry weight of soil samples taken at intervals of 9-19 days throughout the wheat and corn-growing season.Four randomly distributed samples were taken each measurement day.The samples were taken at a depth of 120 cm and were extracted as 30 cm-deep layers.The direct weight of these samples represented the wet weight.The samples were placed in an oven at 105 • C for two days to obtain the dry weight.

Sensitivity analysis
A sensitivity analysis was performed to clarify, for this particular application of the model, the range of accuracy required for several input parameters involved in the calculation of the amount of water available for evaporation.A simple parameter perturbation (Chapra, 1997) was applied here, by varying each model parameter while holding all the other terms constant.The corresponding variations of the output variable reflected the sensitivity of the solution to the varied parameter.
The seasonal evapotranspiration (ET t , mm) was selected as output variable and three parameters of the model affecting ET t; maximum effective root depth (Z rmax ), minimum effective root depth (Z rmin ) and TEW were selected to be analysed during the 2008 and 2009 corn and 2009 wheat seasons.The simulated ET t was compared with a reference simulated seasonal evapotranspiration (ET tref ).The reference values of TEW and Z rmax were obtained from the central value of the intervals recommended by Allen et al. (1998) for silt loam soil and wheat and corn crops, respectively.Parameter reference values were varied by ±10%, until they reached similar values to the intervals recommended by Allen et al. (1998).The reference Z rmin was 0.3, the value suggested by the FAO Aquacrop model (Steduto et al., 2009;Raes et al., 2009;Hsiao et al., 2009), which is designed to predict attainable yield based on the available water supply.Little attention has been paid to this parameter in previous studies, and the uncertainty about the variation interval led us to increase the earlier range of variation in the reference value, using intervals of ±33% within limits of 0.1 and 0.5 m.Table 4 shows the range of values used in this sensitivity analysis.

Comparison between satellite-derived and ground-derived vegetation indices
Several studies (Moran et al., 1992(Moran et al., , 1995;;Liang et al., 2002;González-Dugo and Mateos, 2008) have evaluated the accuracy of atmospheric correction algorithms by comparing the retrieved satellite reflectance with ground-based or aircraftbased radiometric measurements and vegetation indices obtained from various sensors.In this study, we compared VIs obtained from Landsat imagery (5 and 7) and a handheld radiometer (ASD-FieldSpec).Satellite-derived SAVI and ground-derived SAVI obtained at the wheat experiment (Fig. 2) agreed with a coefficient of determination (r 2 ) of 0.98 and a root mean square difference (RMSD) of 0.025.Specific limitations pointed out by Jackson and Huete (1991) when using VI obtained from different sensors, such as the use of processed data (reflectance) as input variable and the atmospheric correction of satellite data, have been taken into account in this comparison.

ET estimation using field radiometry data
Daily measured ET fluxes were first compared with daily estimated ET using the hand-held radiometer measurements to assess the basal crop coefficient.Figure 3 shows daily estimated ET from the model and daily measured ET in corn (2008) using the eddy covariance system, and wheat (2009) using the weighing lysimeter.
The performance of the model was measured using the RMSD between estimated and measured ET values and the coefficient of determination.RMSD values of 0.8 and 0.67 mm d −1 were obtained for corn and wheat respectively.These values are slightly higher than those presented by other authors in earlier studies of the same crops.Er-Raki et al. (2007) and González-Dugo et al. (2009) found differences close to 0.5 mm d −1 .The poorer performance found here does not appear to be significant and could be explained by differences in meteorological data quality and/or management practices.The model showed a general trend to overestimate daily ET of 8 and 11% in corn and wheat respectively.A higher dispersion and a reverse of this trend can be observed in corn for low ET values, suggesting that at the beginning of the growing cycle, when crop groundcover is lower, field-measured SAVI may have been less representative of average values for the area covering the flux tower footprint than those measured under conditions of greater vegetation ground coverage.This problem was not encountered with wheat, where six radiometric measurements were taken over the lysimeter area (plot size 6 m 2 ).
The coefficients of determination (r 2 ) were of 0.92 for both crops, slightly higher than the good correlations presented by other authors for extensive and woody crops, including corn, r 2 = 0.70 (González-Dugo et al., 2009), wheat, r 2 = 0.64-0.86(Er-Raki et al., 2007) and vines, r 2 = 0.86 (Campos et al., 2010).The soil water-content measurements were used to validate the water balance employed in the calculation of K e and K s .This may be regarded as an alternative validation of the complete ET computing procedure.Figure 4  where a significant agreement exists between the estimated and measured deficit in wheat (RMSD = 9.78 mm).However, there are some discrepancies at the end of the corn season during crop senescence.The trend in the estimated deficit matched reasonably well the measured data, irrespective of whether particular points, that will require further analysis, correspond to the general behavior of the model.

Satellite scale ET assessment
TM and ETM+ sensors were used to derive the SAVI index as periodic input to the FAO56 model.The comparison between daily estimated and measured ET is shown in Fig. 5.An RMSD of 1 mm d −1 was obtained for corn during this second season.Both RMSD and the 9% overestimate were similar but slightly higher than 2008 corn season values.The computed SAVI represented an average of 7.4 ha, discounting field-border pixels, and taking into account the variability within the field.An RMSD of 0.5 mm d −1 and r 2 = 0.9 was obtained for wheat using satellite inputs.The model showed a tendency to overestimate ET by six percent.The comparison between modeled root-zone water deficit values and measured values at this scale is shown in Fig. 6.The reasonable agreement during most of the time in the corn and wheat seasons indicates that the model is able to estimate the root-zone water deficit under both rain-fed and irrigated con- ditions.However, some discrepancies similar to those observed during 2008 corn senescence were found at the end of the 2009 season.For irrigated crops, there is some uncertainly associated with the amount of irrigation water applied due to problems arising from low uniformity, poor maintenance of the irrigation system or problems with the pipes and drippers during the growing season, which are common under field conditions.Beyond the uncertainly of applied water at the end of the season, discrepancies during the senescence in both years could indicate that the model is not properly estimating corn transpiration during the R6 growth stage, issue that will require further attention in the future.

Water stress monitoring of crops
A further step in irrigation water management is the monitoring and control of crop water stress, essential to guarantee high yields under conditions of water scarcity.This is also required in deficit irrigation systems and to improve fruit or grain quality in certain crops.The degree of water stress can be approximated by following the development of modeled K s coefficients.This approach is supported by the studies of Colaizzi et al. (2003a,b) who pointed out the relationships between the K s coefficient and the temperature-based Water Deficit Index (WDI, Moran et al., 1994) and Crop Water Stress Index (CWSI, Jackson et al., 1981).Only satellitebased campaigns were used in our analysis, due to the better representativeness of satellite-derived VIs of field crop variability.According to FAO-56 methodology, K s values lower than unity indicates that the crop is suffering water stress.
Figure 7 shows the stress and basal crop coefficients for 2009 wheat and corn throughout the growing season.Five periods of water stress can be observed in Fig. 7a for irrigated corn.
The four first periods were mild, and they occurred during the rapid growth stage (April-May), before the beginning of irrigation (22 May 2009).According to the growth dynamics of the crop, represented by K cb curve in Fig. 7a, and the reasonably good tolerance of corn plants to soil-water stress during this stage (Doorenbos and Kassam, 1979), these periods had no impact on the final yield.During the reproductive   and Hanway, 1982) and Zadok's stages for corn and wheat, respectively, are also shown.

DAE Kcb and Ks
stage, the most critical period, enough water was available for the plant.The last period of water stress was observed during the late season, 15 days before harvest.This was the consequence of a common management practice in this area, where most local farmers apply the final irrigation 15 to 20 days before the grain ripens, in order to save water and given the relative tolerance of the crop to water stress during maturity (Doorenbos and Kassam, 1979).However, this dry period was too prolonged and probably contributed to a reduction in yield that in this particular field was around 20% lower than the 12 500 kg ha −1 local average (CAP, 2009).The water stress for wheat affected the entire grain-filling stage, Fig. 7b, corresponding to Zadoks stages 7-9 (Zadok et al., 1974).A lack of water at these stages is known to have a significant effect on grain filling, resulting in lower yields (Rawson and Gómez, 2000).The cumulative soil water content during the winter was not enough to satisfy the evapotranspiration demand of the final two months of the growing season.In this case, the harvested yield of 2100 kg ha −1 was 28% lower than the figure provided by regional agriculture statistics for wheat (CAP, 2009).

Sensitivity analysis
The results of the sensitivity analysis for the three monitored growing seasons are shown in Fig. 8. Relative values are presented to facilitate comparisons between parameters and seasons.The simulated ET tref values were 803 and 712 for corn in 2008 and 2009, respectively, and 342 mm for wheat.In all cases, variations in ET t were more significant for Z rmax than for Z rmin or TEW, with an average variation of 3.8% for 20% variation in the Z rmax parameter, compared to ET t variations of 0.2% and 0.5% for the same change in the values of the other two parameters.
The sensitivity of the model to Z rmax differed slightly between the corn and wheat simulations, with a higher variation for rainfed wheat.The effect of Z rmax on ET t was higher for wheat, with an average variation of 7.2% for a 20% of change in the reference parameter value.However, the maximum ET t variations under irrigated conditions were 2 and 3.1% in 2008 and 2009 respectively, for the same parameter disturbance.An increase or decrease in Z rmax significantly affects the calculation of the control volume for the soil water balance and thus the daily water storage capacity.The influence on ET is more obvious under conditions of water stress and when the soil water content is close to the threshold value that determines the beginning of stress, starting the stress coefficient calculation and the reduction of transpiration.Rainfed wheat suffered a prolonged period of water stress that lasted for 67 days at the end of the season, while only 15 days before harvest was observed for corn in both seasons, a difference that may explain the different effect of Z rmax variation on ET t .
The effects of variations in Z rmin on ET t estimation were very limited for both crops.Z rmin influences the water balance until Z rmax is reached and its effect is probably more significant on daily ET during the initial growth stage.However, a stronger effect was observed for corn (1.9 of ET t variation on average for 66% of parameter variation), in which water was scarce during the stage of rapid growth, than for wheat (0.55 for 66% of variation).TEW appeared to have a negligible effect on ET t under both rainfed and irrigated conditions.The maximum variations of ET t with respect to ET tref were 0.7 and 0.3% for corn in 2008 and 2009, respectively, and 0.8% for wheat.

Conclusions
The results of daily ET obtained for both crops with crop coefficients calculated using field and satellite derived remote vegetation indices were generally consistent with measurements.The modeled results compared well with both ET measurement systems EC and lysimeter, showing average overestimates of 8% on daily ET.The model was also capable of tracing a soil water deficit curve in agreement with point measurements of soil moisture.The use of satellite-borne sensors permitted low-cost, large-scale acquisition of distributed vegetation indices, without significant loss of accuracy in the final ET estimation, thus avoiding problems of representative field measurements for low plant ground coverage.The extension of the method to larger areas using satellite inputs is hindered by the need for a daily water balance that requires accurate soil and irrigation information, which is difficult to gather on a large scale.However, Díaz et al. (2009) have proposed a simplification of water balance calculating a synthetic crop coefficient that accounts for the main effects of rain and irrigation soil wetting on ET that could permit an upscaling of this model, reducing the data requirements.
Analysis of trends in the stress coefficient derived from the water balance provided valuable information about the use of water in both crops along the growing season, helped to quantify the incidence of water stress during individual growth stages and provided insights into its relationship with final yields under both rainfed and irrigated conditions.
This methodology can be used to perform water stress analyses and to decide when and how much to irrigate.The combination of remote sensing-derived basal crop coefficients with the FAO methodology could be an important tool for estimating water requirements and improve water management at irrigation-scheme and basin scales.
. SAVI maps were calculated using the red and NIR reflectance bands for each Landsat image.Average SAVI values were extracted for each study field and the changes in SAVI over time were obtained by linear interpolation of the SAVI values from each image.The Landsat 7 ETM+ scan line corrector (SLC) failed on 31 May 2003, causing the F. L. M. Padilla et al.: Integration of vegetation indices into a water balance model scanning pattern to exhibit wedge-shaped scan-to-scan gaps.

Fig. 2 Fig. 2 .
Fig.2 Satellite-derived soil adjusted vegetation index (SAVI) vs. ground-derived SAVI at the wheat experiment.The thin solid diagonal line represents the 1:1 line, while the dark line segment represents the linear regression through the points.

Fig. 3 .
Fig.3 Daily measured and estimated ET for corn (2008) (a) and wheat

Fig. 4 Fig. 4 .
Fig.4 Daily measured and estimated root zone water deficit for corn (2008) (a) and wheat

Fig. 5 .
Fig.5 Daily measured and estimated ET for corn (2009) (a) and wheat
Fig.7 Satellite-estimated basal crop coefficient and stress coefficient for corn

Fig. 8 .
Fig.8ET t with respect to ET tref for variations in maximum effective root depth (Z max ),

Table 1 .
(Allen et al., 1998)s used for deriving the crop coefficients and computing the water balance following the procedure described in FAO Irrigation and Drainage Paper No. 56(Allen et al., 1998).
a Typical values adjusted for local relative humidity and wind speed.

Table 2 .
Allen et al. (1998)es used for computing the water balance following the procedure described inAllen et al. (1998), being θ FC the soil water content at field capacity, θ WP the soil water content at wilting point, Z e the depth of soil surface evaporation layer, REW the readily evaporable water and TEW the total evaporable water.Parameterθ FC (m 3 m −3 ) θ WP (m 3 m −3 ) Z e (m) REW (mm) TEW (mm) Finally, the two fields were mechanically harvested on 17 September 2008 and 1 September 2009, respectively.The second site was a rainfed bread wheat field of 1.5 ha, located in the IFAPA Alameda del Obispo (City of Cordoba) experimental farm, where a weighing lysimeter has been in operation since 1985.It was planted on 19 December 2008 with the Lubrican cultivar and harvested on 3 July 2009.The Mediterranean climate of this area is characterized by an annual average precipitation of around 600 mm, very dry summers and average air temperatures of 10 Two contiguous drip-irrigated corn fields were selected in the Bembézar Irrigation Scheme of Hornachuelos (Province of Cordoba, southern Spain) for the consecutive field measurement campaigns.Both fields were large enough, 8 and 7.4 ha, respectively, to be clearly observed by a satellite remote sensor with a spatial resolution of 30 m, thus avoiding edge effects.The planting dates were 7 March 2008 and 5 March 2009 respectively, and PR31D58 corn was used in both seasons.• C in winter and 27 • C during the summer.For the period of interest, from planting to harvest date on 2009 wheat season, 301 mm of precipitation and an average air temperature of 15 • C were measured.The corresponding figures for the 2008 and 2009 corn seasons were 356 and 101 mm, and 22 and 23 • C, respectively.

Table 3 .
Sensor, number of selected pure pixels (PP) for each field/date and dates (day of year and day after emergency) used for monitoring corn and wheat fields during 2008 and 2009 growing seasons.