The study area is located in western Nebraska where the South Platte River enters the state (Fig. 1). The site encompasses 55 fields with an average area of 65 ha under irrigated maize production (3500 ha total area). Overhead sprinkler irrigation from center pivots using water from the underlying HPA is the most common form of irrigation in this area as well as throughout Nebraska and the USA; it is a cost-effective and more efficient option than flood irrigation. The study area is semiarid, and annual crop referenced (maize) evapotranspiration (ETc) is significantly higher than precipitation (P) (HPRCC, 2016). The 7-year (2008–2014) average annual P is 440 mm yr-1 and average annual ETc is 820 (mm yr-1), as measured by the High Plains Regional Climate Center weather station (HPRCC, 2016) located within 10 km of the study area near Brule, NE.

Data obtained from SSURGO (Soil Survey Staff, 2016) indicate that soil texture in the area falls within two USDA textural classes: sandy loam and loam (Fig. 2). Historical land management data for the area are available from the South Platte Natural Resources District (SPNRD, 2016). The SPNRD dataset includes field-specific information from 2008–2014 on crop type, irrigation pumping volumes, and irrigated area. Detailed descriptions and quality control of NRD databases can be found in Grassini et al. (2014) and Farmaha et al. (2016). The above datasets provide the needed meteorological forcing, model parameters, and calibration datasets for running and evaluating the suite of irrigation modeling routines described below.

In the following sections, we will describe the four identified irrigation triggering routines: crop model (CM), precipitation delayed (PD), evapotranspiration replacement (ET), and Hydrus-1D (H). The four irrigation triggering routines represent the upper limit of irrigation requirements, in which no plant water stress occurs (CM), and the lower irrigation limit needed to ensure minimal yield loss against a crop model benchmark (H). Moreover, the four routines can be easily coupled or implemented into LSMs where PD is the simplest routine and H the most complex. We also note that the difference between historical irrigation practices and the lower bound of simulated irrigation provides a potential irrigation savings value in the study area. This irrigation savings value will be important for evaluating the economics of new irrigation technologies as well as providing critical information to policy makers and local stakeholders on the sustainable management of the HPA (Butler et al., 2016). Table 1 provides a summary of key needed inputs and a list of tunable parameters for each routine.

Daily precipitation data for the years 2008–2014 were available from seven gauges within a 35 km radius of the study site. In order to help assess the effect of precipitation variability on irrigation application, all seven time series along with the average precipitation time series were used within the four irrigation routines described above. In addition, all irrigation routines that considered soil type were repeated for the two dominant soil types in the study area, i.e., sandy loam and loam.

As expected, significant gauge-to-gauge variability was observed within the seven rain gauge time series within each growing season with a mean of 320 mm and a coefficient of variation (CV) of 35 % (Fig. 3). In general, as precipitation totals increased, the range of seasonal precipitation totals observed by the seven gauges increased as well (slope = 0.246 mm yr-1, R2 = 0.38). There was no consistent year-to-year spatial precipitation gradient, and no gauge consistently reported high or low totals. We hypothesize that this natural variability in rainfall is a large contributor to the irrigation variability we see at the field level. This hypothesis was beyond the scope of the current paper, but we suggest future research in this area (cf. Gibson, 2016). In terms of growing season ETc, the HPRCC reported an average of 815 mm and was within 10 % of the county-level values estimated by Sharma and Irmak (2012).

Average seasonal irrigation over the 2008–2014 period was 380 mm with a CV of 23 %. The distributions of irrigation amounts are provided in the box and whisker plots given in Fig. 4. Normal distributions and non-normal distributions with both negative and positive skewing were observed (D'Agostino–Pearson test, p < 0.05). Growing season precipitation plus irrigation averaged 700 mm (Fig. 5) with a CV of 5 %. The highest seasonal irrigation average occurred during the growing season of 2012 (580 mm) due to an extremely dry growing season with only 80 mm of rainfall. We found that soil texture was not a significant factor affecting irrigation application at the field scale in this region. This finding was consistent with results from central Nebraska (Gibson, 2016). After grouping the fields by soil type (loam and sandy loam), we found that the irrigation means for all years were not statistically different from each other (Student's t test, p = 0.73). This indicates that soil type did not factor into the irrigation decision-making process.

The results of the comparison between the historical irrigation (2008–2014) and the four irrigation routines are summarized in Fig. 6. Both the CM and PD routines reproduce the trend of the historical irrigation amounts but with a low offset (similar slopes). CM irrigation water requirements were on average 80 mm lower (20 % of total) relative to historical irrigation. For PD, the average seasonal difference was 40 mm lower (10 % of total). For ET and H, simulated irrigation amounts were 80 mm (20 % of total) and 120 mm (30 % of total) lower than the historical average, respectively. We also note that the slopes of the observed irrigations and the CM and PD for the given years were generally similar. However, it is obvious from Fig. 6 that the slopes of ET and H were different from the observations, which results in larger deviations in drier years and thus a potential for greater irrigation savings. The implications for water management will be discussed in the next section.

All irrigation routines responded to differences in the eight rainfall time series, and this response is represented as vertical error bars in Fig. 6. The difference between the highest and lowest irrigation amount for each growing season was on average 75 mm, or 20 % of average irrigation totals. The largest difference in irrigation totals occurred in 2008 for all irrigation routines with an average of 130 mm between all four routines, and the smallest difference occurred in 2012 at an average of 27 mm due to uniformly low precipitation. The analysis illustrates that the variation in irrigation amounts depends on which rainfall gauge is used to make a decision. Given that producers often have fields distributed across a region, the uncertainty in local rainfall directly propagates variations in irrigation amounts (Gibson, 2016). Future research efforts should investigate the effect of spatial rainfall variability on producer decision-making, but this was beyond the scope of the current study.

We found that the two dominant soil textures in the study area did not have a significant impact on irrigation amounts under CM and H. ET and PD do not have a soil component considered in their routine and are therefore not impacted by soil texture. In the case of CM, average irrigation was within 1 % for all years. For H, the irrigation average of the sandy loam soil was 10 % lower than the average of the loam soil. The soil hydraulic parameters used for both soil textures were determined using ROSETTA (Schaap et al., 2001) and are presented in Table 2.

Following the simulated irrigation for the routines of PD, ET, and H, the (P + I) time series were reinserted back into the crop model for all years to estimate yield impacts (Fig. 7). The crop model yielded an average of 14.6 Mg ha-1 over the study period. The yield gap (i.e., the difference between yield potential and actual yield) of US irrigated maize represents approximately 15 % of the potential (Grassini et al., 2013; Global Yield Gap and Water Productivity Atlas, 2016), suggesting an average actual yield of 12.4 Mg ha-1 for the study area, which is within 5 % of the historically reported yield. For the three routines and for all years, simulated yields were on average within 3 % of the simulated yield based on the CM. The results indicate that the various irrigation scheduling strategies did not have a large impact on yield, but they reduced irrigation amounts substantially; hence, they may be a sound economic option for producers.

The daily time series of simulated irrigation application can be seen in Fig. 8. Data for the observed sub-growing season irrigation application are unavailable. Irrigation application tends to begin later in the growing season for the two routines that consider soil (CM and H). This is likely due to the routines allowing soil moisture to be depleted before irrigation is triggered, thus creating the reduced pumping and irrigation savings. The amount of soil moisture storage is typically near field capacity, but in exceptionally dry years (2012) this storage is reduced and thus will lead to less of a delay at the start of the growing season.

Historically, the study area has had a consistent amount of total seasonal water (P + I) from year to year. The percent of irrigation to applied water (I/(P + I)) was on average 55 %; notably in 2012, this was as high as 88 %. The relative weight of irrigation to precipitation highlights the importance of constraining irrigation amounts for proper water balance closure within the study area, as well as in other areas with intense irrigation application. Given the high seasonal rates of irrigation to precipitation, no doubt the soil moisture will be adversely affected when compared to a rainfed area. More importantly, the impacts on the local surface energy balance (Santanello et al., 2011), rainfall recycling, and skill in observational forecasts may be diminished without properly accounting for irrigation. For example, regional mesoscale modeling illustrated that up to 40 % of East African annual rainfall can be attributed to irrigation across India (de Vrese et al., 2016). With the suggested findings here on reduced irrigation needs (up to 115 mm or 30 %), the potential changes to precipitation patterns across the HPA due to the adoption of irrigation scheduling technology should be further investigated.

The study area is currently under groundwater appropriation, with a historical increase in depth to groundwater of 1.2 m from 1971 to 2013 (SPNRD, 2013; Young et al., 2013). Precipitation pattern changes in the area induced by global warming are believed to lead to less frequent but more intense storms with an increase in total precipitation (Dai, 2011). However, the timing of precipitation is of equal concern as totals, as more infrequent rain events may still lead to increased pumping with the same seasonal totals. The scenario of changing precipitation amounts and timing is not unique to the study area, but it is a more general pattern of the region; this highlights the need for explicit treatment of irrigation depths and timing to fully understand the complex feedback that exists beneath the land surface and atmosphere. The irrigation routines suggested in this work can be used as a first assessment of the likely irrigation amounts due to different observed scheduling practices (USDA, 2014).

The rainfall sensitivity analysis demonstrated the effects and uncertainty for each of the four irrigation routines investigated. Lower rainfall years had lower spatial variability and, as a result, simulated irrigation for each routine led to similar values. However, this behavior was not consistent with the observed irrigation data, in which the lowest rainfall year (2012) had the largest standard deviation (168 mm) for applied irrigation. The results are likely due to two reasons: (1) producers give up irrigation at some point during the growing season as their crop parishes in the extreme heat and drought conditions and (2) differences in well-to-well pumping capacity become more apparent with increased pumping demand. Although no direct work has been done to confirm differences in pumping capacity or inefficiencies in the study area, the general effect has been explored through modeling in other areas (Foster et al., 2014). With respect to LSMs, these two factors represent significant deviations from water balance closure approaches, making it challenging to include realistic irrigation values in dry years. Therefore, additional studies and datasets similar to those presented here are critical for the calibration and validation of the next generation of hyper-resolution LSMs.

With regard to soil texture differences in the study area, observed irrigation data indicated no difference between fields in these two texture classes. Similar behavior was seen from the irrigation routine simulations, which showed a 10 % difference for H and a 1 % difference for CM. We note that given the similar soil texture classes (and thus the soil hydraulic parameters), this result is not unexpected. In practice, producers are beginning to adopt precision irrigation techniques (Hedley and Yule, 2009; Hedley et al., 2013). Small-scale features within a field (e.g., sandy or gravelly areas, underperforming parts of the field, waterways, pivot roads, etc.) can be better managed with the new technology. Therefore, managing fields by following one dominant soil type (i.e., irrigation pressure trigger point) may be highly inefficient (Kranz et al., 2014). More refined and consistent soil texture data across arbitrary political boundaries (Chaney et al., 2016) are needed to better account for differences in irrigation water application on the subfield scale, especially in areas with increasing adoption of precision agriculture technology.

The four irrigation routines represent different levels of allowable water stress that develop in the maize. The CM routine is the lowest risk approach with respect to yield and represents the modeled upper limit of required irrigation to maintain a stress-free management scenario. It is hypothesized that any irrigation application above this represents irrigation application due to risk aversion and will not appreciably increase yield. Comparisons between 2008 and 2014 indicate that the slopes of the applied irrigation from observed irrigation are indistinguishable, but with a bias of ∼ 80 mm yr-1 more observed irrigation. This indicates that producers are averaging an additional three to four irrigation cycles beyond what the CM indicates. The differences in irrigation totals from the other three irrigation routines are the result of increasing allowable water deficits in the routines. A reduction of 115 mm or 30 % in irrigation was observed for H when compared to the historical average. We note that this hypothetical scenario requires perfect management with full trust of the technology and may not be achievable in practical applications. However, we anticipate that a 50–75 mm reduction over a short technology adoption period (2–4 years) is feasible, particularly in areas with strong university extension programs and/or producer-to-producer knowledge exchange (Irmak et al., 2012). In addition, these hypothetically reduced pumping numbers may be useful to local, state, and federal policy makers in future water management decisions and investment in cost-sharing technology programs.

The four irrigation routines, although biased (i.e., containing an offset), capture year-to-year variation in irrigation in western Nebraska. Given the widespread use of center pivots, we expect the irrigation routines to capture year-to-year variation for the HPA and parts of the eastern USA. We note that the magnitude of the offset is likely related to local producer behavior and influenced by social norms and risk aversion. Gibson (2016) provides a fuller assessment of irrigation behavior throughout central Nebraska. We note that it is unclear how these routines would behave in areas with center pivots outside the USA (i.e., Brazil, South Africa, and Australia), where energy costs for pumping may be more restrictive drivers of human decisions on irrigation. An assessment of these routines in those areas would require further validation.

We believe that the routines, combined with a reasonable offset correction, could be easily incorporated into future hyper-resolution LSMs with the above routine descriptions and readily available LSM model output or datasets (see Table 1). Clearly, accurate and local precipitation is critical in driving these irrigation routines and capturing producer behavior. This topic deserves more research, particularly the opportunity to combine low-cost in situ gauges with radar and remote-sensing products. Additionally, we note that the four routines could be run offline in order to provide reasonable guesses of applied irrigation for a given irrigation season. This may be beneficial in representing processes not explicitly considered in LSMs (Kumar et al., 2015) or making future assessments and recommendations about water availability for managers. Finally, the four routines provide reasonable irrigation bounds and, more importantly, predictions about decreases in irrigation as technology is introduced and adopted in novel areas.