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a Dep. Genética y Producción Vegetal, Estación Experimental de Aula Dei (CSIC), Apdo. 202, 50080 Zaragoza, Spain
b Unidad de Suelos y Riegos, Servicio de Investigación Agroalimentaria (DGA), Apdo. 727, 50080 Zaragoza, Spain
* Corresponding author (jcavero{at}eead.csic.es)
Received for publication December 17, 1999.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Abbreviations: DU, distribution uniformity • ET, evapotranspiration • FC, field capacity • LAI, leaf area index • PET, potential evapotranspiration • RMSE, root mean square error • WP, wilting point
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Surface irrigation systems, even if properly engineered and managed, always result in nonuniform water infiltration within a field (Clemmens, 1986). The quantity of infiltrated water in these irrigation systems depends on both infiltration opportunity time (the time that a given point in the field is inundated) and soil infiltration characteristics. Thus, uniformity of infiltrated water is related to the distribution of these factors over a field (Letey, 1985).
The limitations of surface irrigation uniformity are associated with the spatial variability of soil surface elevation and infiltration (Erie and Dedrick, 1979; Walker, 1989). Different studies have revealed the importance of considering these two variables to explain irrigation water infiltration (Hunsaker and Bucks, 1991; Izadi and Wallender, 1985; Oyonarte, 1997; Playán et al., 1996a; Zapata and Playán, 2000a).
The spatial variability of irrigation water infiltration within a field can be measured by taking soil water measurements. However, this is difficult under field conditions because deep percolation between measurements must be avoided (which will limit its use to deep soils or small application depths), and soil water measurements are only representative of the soil surrounding the measurement point (Or and Hanks, 1992). Besides, some unavoidable delay in soil water measurement after the irrigation event results in underestimation of the water infiltration because it does not take into account evapotranspiration (ET) losses during this period (Hunsaker, 1992). Time-domain reflectometry probes can be used to continuously sample many points at different depths. However, measurements with these probes only represent a small soil volume. Therefore, it would be necessary to install many probes, which could alter the soil and then the infiltration of water. On the other hand, the spatial variability of irrigation water infiltration within a field can be estimated from measurements of infiltration rate and opportunity time. The resulting estimates are independent of deep percolation losses, represent a larger area, and are almost unaffected by ET losses. The spatial variability of irrigation water infiltration within a field can also be simulated using surface irrigation models that take into consideration the spatial variability of infiltration and elevation (Zapata and Playán, 2000a).
Spatial variability of crop yield can be related to spatial variability in soil fertility (Finke and Goense, 1993; Or and Hanks, 1992), soil organic matter content (Kravchenko and Bullock, 2000), and pest attacks (Plant et al., 1999). However, spatial variation in water availability seems responsible for most of the spatial yield variability in irrigated fields (Hunsaker and Bucks, 1987; Letey et al., 1984; Sousa et al., 1995; Warrick and Gardner, 1983). Under semiarid conditions, most crop water requirements are satisfied by irrigation, which can increase crop yield variability due to available water variability (Letey et al., 1984). This is especially important for those crops that are very sensitive to water stress, such as maize.
If spatial variability of crop yield due to spatial variability of water infiltration is correctly predicted, it can be used to obtain an accurate average crop yield for the field and improve irrigation management (Letey, 1985). It could also allow the application of site-specific farming practices when the causes of variability are difficult to change (i.e., infiltration rates) (Pierce and Nowak, 1999). Predicting spatial variability in crop yield from the spatial variability in water infiltration has traditionally been done using crop water production functions achieved under uniform irrigation and the distribution of infiltrated water on the field (Letey et al., 1984; Solomon, 1984; Warrick and Gardner, 1983). However, this prediction is difficult because of the dynamic nature of the effects of water stress on crop growth and yield. In this sense, Paz et al. (1998) have indicated that it is difficult to account for temporal interactions of stress on growth using traditional statistical methods. This could be the reason why relatively low correlations between water infiltration and yield have been found in some studies (Hunsaker, 1992; Hunsaker and Bucks, 1987; Zapata et al., 2000).
Crop growth simulation models that adequately simulate the consequences of water stress on crop yield can be valuable tools to calculate crop yield spatial variation within a field when spatial data on water infiltration are available. These models simulate crop growth dynamically, taking into consideration that water stress affects the crop differently depending on phenological stage of the crop. They can be used as a tool to explore hypotheses related to crop yield variability, as demonstrated by Paz et al. (1998), who studied the spatial yield variability of soybean [Glycine max (L.) Merr.] due to the spatial variability of water stress. In addition, crop growth simulation models can be used in connection with irrigation models to provide calculations of water stress and crop yield spatial variation within a field. This could help to improve irrigation water management because models can extensively explore different scenarios (Pierce and Nowak, 1999). However, the performance of a combined crop and irrigation model must be assessed before it can be used for this task. Mantovani et al. (1995) used CERES-Maize to analyze the influence of sprinkler irrigation uniformity to determine the optimum irrigation dose to be applied.
The objectives of this work were to (i) determine if a crop growth model can simulate the spatial variability of maize grain yield within a level basin irrigated field using water infiltration depth estimated from measurements of opportunity time and infiltration rate or simulated by a surface irrigation model and (ii) to study the relevance of considering the spatial variability of infiltration rate, opportunity time, and soil surface elevation in simulating yield spatial variability with the crop growth model.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The experiment was conducted in a small level basin (27 by 27 m) located at the Agricultural Research Service experimental farm in Zaragoza, Spain. The soil is classified as Typic Xerofluvent [coarse loamy, mixed (calcareous), mesic] (Table 1). The basin was leveled with laser-controlled equipment. The field was plowed with a moldboard to prepare a seedbed for the crop. Maize (‘Clarissia’) was planted on 17 May 1996 in rows spaced 0.75 m apart. Plant population was 79000 plants ha-1. Fertilization and pest control were conducted according to best management practices of the area.
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The water front location was registered every 10 min during the advance phase or 30 min during the recession phase. Flags were put in the field identifying the observation points. The observer had to consider the 1.5- by 1.5-m plot surrounding a flag and figure out if 50% of this plot was covered by water. At each 1.5- by 1.5-m grid node, the opportunity time was computed from the advance and recession times. Infiltration was characterized using 81 single infiltrometer rings (Jaynes and Hunsaker, 1989; Merriam and Keller, 1978). The rings were 0.23 m in diameter and 0.30 m high and were driven 0.10 m into the soil to ensure good contact between the rings and the soil. Cumulative infiltration curves were measured during the second and fifth irrigation events. When the irrigation front reached each ring, a volume of water was carefully added to each infiltrometer, and the decrease in water level was measured in time. The infiltrometer rings were removed after each measurement.
Neutron scattering (Hanks, 1992) was used to measure the volumetric water content of the soil [calibration: n = 17, r2 = 0.87, and root mean square error (RMSE) = 0.025 m3 m-3] the day before and 1 or 2 d after each irrigation event. A total of 64 access tubes were installed to a depth of 1.20 m (where possible). The access tubes formed a 3- by 3-m regular network starting at the point coordinates (3 m, 3 m) (Fig. 1). For each access tube, the water content was measured at a depth of 0.15 m to represent the upper 0.3 m of the soil profile. The water content at deeper layers was measured at a 0.2-m interval.
Maize plants of a 1.5- by 1.5-m subplot surrounding each node of a 3-m grid starting at coordinates (1.5 m, 1.5 m) were hand-harvested (Fig. 1). The ears were oven-dried to constant weight at 60°C, and the grain was removed from the cob to determine grain yield (dry weight). The plant population in six subplots was <7 plants m-2. Plant populations below this threshold could affect grain yield, so these subplots were not used in the work.
The soil total available water at the nodes where maize grain yield was measured was calculated from soil depth and bulk density values and kriged values of FC and WP (Cuenca, 1989). The soil total available water was the difference in water content between FC and WP, expressed in millimeters, considering a maximum rooting depth of 1.50 m.
Estimation and Simulation of Water Infiltration
Estimation of Water Infiltration
Infiltrated water due to irrigation was estimated using infiltration measurements and opportunity time observations. Infiltration was calculated from measurements made with the 81 single infiltrometer rings. Individual infiltration curves were fitted to each ring data using a Kostiakov equation (Kostiakov, 1932). The adjusted infiltration approach (Merriam and Keller, 1978; Walker and Skogerboe, 1987) was used to estimate the Kostiakov coefficients at each measurement point and each irrigation event. This procedure was used for Irrigations 2 and 5 when infiltration was measured. For Irrigations 3 and 4, the infiltrated water was computed twice at each location using the infiltration parameters corresponding to the infiltration measurements made in the second and fifth irrigations. For a given irrigation, from the two sets of infiltrated water estimates, the set showing the best correlation with the neutron probe measured water recharge was adopted.
Infiltrated water is governed by two sources of spatial variability: the parameters of the infiltration equation (i) and the opportunity time (
). The opportunity time can be determined as the difference between the advance time (the time when a point is covered by irrigation water) and the recession time (the time when the water depth at the same point becomes zero due to infiltration). To separate the influence of the infiltration parameters and the opportunity time on infiltration, they were estimated holding each source of variability uniform (U) or variable (V). We refer to these variables as E(ViU), E(UiV), and E(ViV). In these variables, E denotes that the value of infiltrated water is estimated, as opposed to the set of simulated values (S), which will be discussed in the following section.
At each location, E(UiV) was computed using an adjusted, spatially averaged set of Kostiakov parameters and the local opportunity times. This Kostiakov equation was obtained by regression using data from all infiltrometers simultaneously, and the k parameter was adjusted to match the average opportunity time with the average infiltrated depth:
 | (1) |
and 
are the parameters of the adjusted, spatially averaged Kostiakov equation and j is an index variable for the 81 data points.
At each location, E(ViU) was computed using the spatially averaged opportunity time 
and the local Kostiakov parameters:
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In this work, reference to E(ViU) will be used as an approximation to the estimation of infiltration without consideration of the spatial variability of soil surface elevation. This is due to the fact that opportunity time is very dependent on the surface relief: Advance is strongly dictated by elevation, and recession is completely governed by it.
E(ViV) was computed at each location using the Kostiakov parameters derived at each location from the infiltration measurements and using the opportunity time computed at each location.
Estimations of infiltrated water were performed at the same locations where grain yields were determined. The size of the yield subplot is coincident with the area used to determine the times of advance and recession although this area is much larger than the area covered by an infiltrometer ring.
Simulation of Water Infiltration
The two-dimensional model B2D (Playán et al., 1996a) was used to simulate water infiltration in the experimental plot. This model solves the two-dimensional hydrodynamic Saint Venant equations using an explicit finite difference leapfrog scheme and can accommodate spatially varied elevation and infiltration. Simulations were performed on a 37- by 37-m node network where computational nodes were separated by 0.75 m. Simulating the variability of elevation and/or infiltration involves specifying the location of each measurement point and the local value of the variable. Interpolation routines were used to obtain estimates of each variable at the computational nodes. Elevation data showed a consistent spatial structure (Journel and Huijbregts, 1978) characterized by a spherical semivariogram. Therefore, estimation of elevation at the computational nodes was performed using kriging procedures. A geostatistical analysis on infiltration revealed that the infiltration parameters were randomly distributed at the survey scale. Therefore, an interpolation procedure of inverse distance square was used to estimate the infiltration rate at each node. Additional details can be found in Zapata and Playán (2000a).
The model allows simulation of irrigation events in four ways, depending on whether the spatial variability of infiltration and elevation was introduced or not. The first case consists of simulation of an irrigation event in a plane bed with uniform infiltration for the entire basin. This case will be referred to as S(UiUe) where e refers to soil surface elevation. The second case is to assume a plane bed and consider the spatial variability of infiltration [S(ViUe)]. The third case consists of simulating with spatially varied elevation and uniform infiltration [S(UiVe)]. The last case is to consider both spatial variabilities [S(ViVe)].
A computational node represents a point, but yield was determined from a 1.5- by 1.5-m subplot. Consequently, the average amount simulated infiltrated water in the nine nodes contained in the 1.5- by 1.5-m subplot was used for crop simulation purposes (Fig. 1).
Distribution uniformity (DU; Burt et al., 1997) was computed for the whole season as the ratio of two average depths, one based on the lower values (low quarter) and the other based on all values, expressed as a percent. Distribution uniformity was computed for the estimated and simulated infiltrated water with the different methods.
Crop Model
Among the existing crop models, we chose EPICphase (Cabelguenne et al., 1999). This model is generic, allowing simulation of different crops, and is a modification of the extensively tested EPIC (Erosion Productivity Impact Calculator) model, especially improved for water and N stress modeling. A modified version of the EPICphase model, with improved simulation of the effect of water stress on leaf area index (LAI) growth and decreased radiation interception by the maize crop due to leaf rolling, was used in this work because it accurately simulated the effects of water stress on maize growth and yield in our conditions (Cavero et al., 2000).
In EPICphase, daily actual ET is equal to crop potential ET (PET) if the available water for the crop is higher than crop PET. However, the daily actual ET is equal to the available water for the crop if this is lower than crop PET. The available water for the crop depends on soil water content, rooting depth, rooting shape, and soil properties. EPICphase considers that water stress affects daily LAI growth, biomass production, and the harvest index. The model considers that the effect of water stress on harvest index differs with the physiological phases of the crop. In the case of maize, it considers that harvest index is affected by water stress during Phase 2 (maximum LAI to end of anthesis) and Phase 3 (end of anthesis to pasty grain), with reductions being double for the same water stress intensity in Phase 2 compared with Phase 3. Crop parameter values for maize used in this study were derived from previous work (Table 2) with different experimental data (Cavero et al., 2000). The number of growing degree days for a crop to reach maturity is a crop parameter whose value depends on the cultivar. We calculated the growing degree days from planting date and black layer stage date and introduced it as input in the model.
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Model Runs
The EPICphase model was run for each individual point, considering its soil characteristics (FC, WP, depth, initial water content, bulk density). For those variables (FC, WP, and initial water content) where the yield sampling point was not coincident with the point of variable measurement, the values at the yield sampling point were derived by kriging (Zapata et al., 2000). Soil depth at the maize yield sampling point was determined as the average of the two or four depth values corresponding to the closest sampled points that bordered the maize yield sampled point. The initial soil water content was obtained with neutron probe measurements 1 d after planting (by kriging). The initial soil water content, FC, and WP for the 1.20- to 1.50-m soil layer were considered to be the same as those measured for the 0.90- to 1.20-m soil layer. Soil texture at soil layers deeper than 0.60 m was considered to be the same for all points and was estimated from another study in a contiguous plot (Cavero et al., 2000). Soil texture is not very relevant for model performance if water retention characteristics (FC and WP) are provided for each point. Bulk density below 0.60 m was considered uniform because no specific data were available. The mean value for the 0- to 0.60-m soil layer was used because the mean values for the 0- to 0.30-m and 0.30- to 0.60-m soil layers were similar (1.46 and 1.44 Mg m-3, respectively) and bulk density was very uniform (CV = 2.7 and 3.5%, respectively).
For each point, the model was run using as input values of water infiltration those obtained either by estimation from infiltration rate measurements and opportunity time observations or by simulation with the surface irrigation model B2D. Thus, seven simulations were run at each point using E(ViU), E(UiV), E(ViV), S(UiUe), S(ViUe), S(UiVe), and S(ViVe) as inputs.
Data Analysis
Comparisons between the measured and EPICphase-simulated values of grain yield (calculated grain yield from this point) for each type of water infiltration estimation or simulation were made. Bias and RMSE (calculated as described by Retta et al., 1996) and linear regression of calculated against measured values were also used. Bias was computed as:
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Two-dimensional plots of the calculated and measured grain yields at each point, made with Surfer (1995), were used for spatial analysis of grain yield simulations.
The relationship between the measured and calculated grain yields with the available water for the crop (available water at planting + rain + water infiltration either estimated or simulated) at each location within the level basin was also studied.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Among the different methods to simulate infiltrated water with the B2D model, considering uniform infiltration rate and soil surface elevation resulted in a DU of 98%. The DU decreased to 84% when the variability of the infiltration rate was considered. However, the DU was 74% when the variability of the soil surface elevation was considered. The DU was lowest (70%) when both sources of variabilty were taken into account.
Simulation of the Spatial Variability of Maize Grain Yield from Estimated Water Infiltration
Estimation of water infiltration considering infiltration rate variability was not possible in some nodes because some infiltrometer ring measurements were lost (Table 3).
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), E(UiV), and E(ViV), respectively. The standard deviation for the calculated grain yields with the E(ViU) and E(ViV) water infiltration estimates were similar to the standard deviation of the measured grain yields, but the calculated grain yield with E(UiV) showed less variability than measured (SD = 0.59 t ha-1; Fig. 3). The estimated infiltration E(ViU) resulted in the lowest bias (-0.02 t ha-1) and RMSE (1.30 t ha-1). The calculated grain yield with the estimated infiltration E(UiV) resulted in the highest bias (0.90 t ha-1) and RMSE (1.98 t ha-1).
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)] resulted in calculated grain yields that did not duplicate the variability found in the field (slope = 0.09, r2 = 0.06) (Fig. 5B). The estimated water infiltration without considering opportunity time variability resulted in the best simulation of grain yield variability within the field (intercept = 2.7 t ha-1, slope = 0.69, and r2 = 0.51) (Fig. 5A). However, considering both the spatial variability of infiltration rate and opportunity time resulted in poorer modeling of the spatial variability of grain yield (Fig. 5C). In all cases, intercepts were significantly (P < 0.05) different from 0, and slopes were significantly (P < 0.05) different from 1. Intercepts > 0 and slopes < 1 indicated overestimation of low measured grain yields. One of the measured grain yields seemed to be too low, according to the soil characteristics, to the estimated water infiltrated with all of the methods and to the measured grain yields at the surrounding points. If that point were removed from the regression analysis, the coefficients of determination would be 0.56, 0.08, and 0.43 for E(ViU), E(UiV), and E(ViV), respectively, with intercept values closer to 0 and slope values closer to 1 (data not shown).
Simulation of the Spatial Variability of Maize Grain Yield from Simulated Water Infiltration
As found for the estimated water infiltration, the agreement between the measured grain yields and the calculated ones at the same locations within the field depended on the method for simulating water infiltration (Table 3; Fig. 3 and 6). The differences between the mean calculated grain yields and the mean measured grain yield within the level basin were 7.8, 3.8, 4.0, and 2.4% for the water infiltration simulations S(UiUe), S(ViUe), S(UiVe), and S(ViVe), respectively. Similar values of the standard deviation for the measured and calculated values were found in the case of the S(UiVe) and S(ViVe) infiltration simulations, but calculated grain yields with S(UiUe) showed much lower variability than measured (SD = 0.58 t ha-1; Fig. 3). The simulated infiltration S(ViUe) resulted in lower variability than measured (SD = 1.18 t ha-1). The simulated infiltration S(ViVe) resulted in the lowest bias (-0.19 t ha-1) and RMSE (1.16 t ha-1). These figures are similar to those found for the S(ViUe) and S(UiVe) infiltrations. Simulated infiltration without considering the spatial variability of the infiltration rate and surface elevation [S(UiUe)] resulted in the highest bias (0.64 t ha-1) and RMSE (1.58 t ha-1).
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Relationship between Grain Yield and Available Water
Measured and calculated grain yields from the different locations within the field were plotted against the available water for the crop. This showed the agreement or disagreement between the spatial variability of calculated and measured grain yields depending on the estimation or simulation method used to compute the spatial variability of water infiltration (Fig. 7).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The fact that the best simulation of the grain yield spatial variability within the level basin was obtained from water infiltration simulation with the irrigation model B2D was possibly related to the fact that the simulated water infiltration was obtained as the average of the nine nodes contained in the 1.5- by 1.5-m sampling plot for grain yield. However, the estimated water infiltration is close to being a point variable because the infiltration rate was derived from measurements in one infiltrometer ring 0.23 m in diameter although the opportunity time was observed in the same plot size as the yield. Letey (1985) indicated that it is important to match the scale of uniformity observations to the scale of individual plant root zone because different crop water production functions can be derived from data obtained using infiltrometers of different sizes.
The traditional scheme to estimate water infiltration in surface irrigation considers only the spatial variability of opportunity time [E(UiV)] (Merriam and Keller, 1978). In our study, this estimation of water infiltration resulted in an inadequate simulation of the spatial variability of grain yield and in an overestimation of the mean grain yield in the level basin by 8.5%. Correlation analysis showed that the spatial variability of the infiltration rate was the principal variable affecting E(ViV) and that the spatial variability of the opportunity time had a low influence on E(ViV) (Zapata et al., 2000). When the value of the Kostiakov infiltration parameter a is low (as in this case, with an average of 0.295), the long-term infiltration rate is very small; therefore, does not control the amount of infiltrated water. This could explain why the best simulation of the spatial variability of grain yield and mean grain yield was obtained when only the spatial variability of the infiltration rate was taken into account. Letey (1985) has indicated that the variability of infiltration caused by variability of soil properties is likely to have a dominant effect compared with the opportunity time for most fields.
Surface irrigation simulation has been customarily based on a S(UiUe) approach (Playán et al., 1996a). Our results show the advantage of introducing both the spatial variability of infiltration rate and soil surface elevation in irrigation models. When the spatial variability of both variables was not accounted for, the calculated grain yields with the model EPICphase did not reflect the spatial variability measured, and the mean calculated grain yield of the level basin diverged by 7.8% from the mean measured grain yield. The variability of soil surface elevation seemed to be more important than the variability of infiltration rate to calculate grain yield variability. In our experiment, the coefficient of variation of the elevation (standard deviation of elevation divided by the infiltrated depth) ranged between 0.17 and 0.29. These values could decrease the DU considerably (Clemmens et al., 1999), from 98 to 74% in our study, which caused spatial variability of grain yield. The results indicated that around 50% of the spatial variability of grain yield within a level basin can be calculated with the crop growth model considering only the spatial variability of soil surface elevation.
In this work, estimated infiltrated water considering only the spatial variability in the opportunity time [E(UiV)] has been considered as an approximation to the estimation of water infiltration considering only the spatial variability of soil surface elevation. Consequently, similar results for E(UiV) and S(UiVe) were expected. The poorer simulation of the spatial variability of grain yield with water estimations based on the spatial variability of the opportunity time suggests that the field determination of the opportunity time was not sufficiently accurate. While the accuracy of the advance measurements is generally accepted, the determination of the location of the recession front is often recognized as a subjective task (Walker, 1989). Moreover, advance and recession times were estimated as average values corresponding to 1.5- by 1.5-m plots, thus neglecting the intraplot variability. The coupling of the elevation survey and the irrigation simulation model proved to be a more reliable way to reveal the relevance of soil surface elevation on water infiltration due to irrigation.
As limited water supplies, expensive energy, and increasing capital costs force farmers to manage resources more efficiently, the limitations imposed by the spatial variability of the irrigation system and the soil parameters will become more relevant (Hunsaker and Bucks, 1987). The EPICphase crop model can be used to simulate the spatial variability of maize grain yield within a irrigated level basin field. However, the crop model explained, in the best case, 56% of the measured variability on yield.
The best simulations of grain yield spatial variability were obtained from water infiltration estimated considering the spatial variability of the infiltration rate and from water infiltration simulated with the irrigation model B2D considering the spatial variability of the infiltration rate and the soil surface elevation. Irrigation models and crop models can be jointly used to simulate maize grain yield variability within a level basin, but at least the spatial variability of soil surface elevation should be considered in irrigation models. Further research is needed to establish the minimum survey scale for infiltration, opportunity time, and elevation required to maintain the desired accuracy of the grain yield variability calculations.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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