We apply our analysis to the Coello Irrigation District in Colombia. The Coello Irrigation District is an existing irrigation district located in the upper Magdalena basin, in the Tolima Department, a region subject to considerable climate variability and that is vulnerable to droughts (IDEAM, 2015). The average monthly temperature in the Coello District is 28 ∘C, with maximum daily temperatures reaching 38 ∘C (station 21215080). The reference evapotranspiration is between 137 mm/month in November and 173 mm/month in August with a mean annual evapotranspiration of 1824 mm/year. The irrigation district serves an irrigated flatland of approximately 250 km2, comprising mainly irrigated rice, which is planted continually throughout the year (Urrutia-Cobo, 2006). Rice total growth length is 4 months with high sensitivity to water deficit at the flowering stage. Resulting yields are between 5.5 and 6.8 t ha-1 (DANE, 2016; Fedearroz, 2017). The local authority in charge of the water management of the irrigation district (USOCOELLO) reports a gross irrigation demand rate of 0.2 m3 s-1 km-2. This is a high demand rate mainly due to low application and conveyance efficiencies, and high evapotranspiration demand.

The water available for irrigation depends on the total discharge of two rivers from neighbouring mountainous basins: the Coello and Cucuana rivers (Fig. 2). The Coello basin has an area of 2000 km2, and the Coello River has a length of some 112 km starting at 5300 m.a.s.l. and flowing into the Magdalena River at 280 m.a.s.l. with an average flow of 23 m3 s-1 (Vermillion and Garcés-Restrepo, 1996). In the Coello basin the precipitation is bimodal with two peak months in May (186 mm/month) and October (127 mm/month) and two low months in January (50 mm/month) and August (90 mm/month). The mean annual precipitation is 1268 mm/year. The Cucuana basin has similar physical characteristics to the Coello basin. In this research, we focus only on the Coello basin to estimate the surface water availability for irrigation, as the available discharge data from the Cucuana River (Corea Station) are too short for the purpose of our experiment.

In situ precipitation and temperature data were obtained from the network of meteorological stations operated by the Instituto de Hidrología, Meteorología y Estudios Ambientales (IDEAM), the Colombian hydro-meteorological institute, and interpolated to a gridded dataset with 0.1∘ spatial and daily temporal resolution for the whole Magdalena–Cauca basin (Rodriguez et al., 2017). The temperature data were used to estimate potential evapotranspiration with the Hargreaves method (Hargreaves, 1994).

Two global precipitation datasets were considered: (i) the Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS; Funk et al., 2015) and (ii) the Multi-Source Weighted-Ensemble Precipitation (MSWEP; Beck et al., 2017). CHIRPS precipitation is a remotely sensed and ground-corrected dataset available globally at 0.05∘ resolution, while MSWEP precipitation is a merged gauge, satellite and reanalysis dataset available globally at 0.25∘ resolution. A total of 14 stations were used for the in situ product. For CHIRPS and MSWEP, seven stations and three stations were used, respectively.

All precipitation, temperature and potential evapotranspiration datasets are available for the 1983–2012 period. A preliminary evaluation of the global precipitation datasets was done. The global precipitation datasets (CHIRPS and MSWEP) were compared against in situ data in the selected basin. The performance indicators Kling–Gupta efficiency (KGE), percentage of bias (Pbias) and Pearson correlation (r) were used. The evaluation was done for multi-annual monthly precipitation for the selected 30-year period (Fig. 3). KGE results show that MSWEP performs better than CHIRPS from October to May. Only in July does MSWEP perform poorly (KGE =-0.1, Pbias =100 %). We cannot discard the use of MSWEP or of CHIRPS. At this stage, we can recommend the use of each dataset for specific months.

Daily river discharge data for the 1983–2012 period were obtained from the stations operated by IDEAM at gauging station Payande (21217070) in the Coello River.

The Dynamic Water Balance Model (Zhang et al., 2008), a lumped conceptual hydrological model based on the Budyko framework (Budyko, 1974), was selected to simulate the river discharge in the Coello basin at a monthly timescale. The Dynamic Water Balance Model has been applied in several basins around the world (Kaune et al., 2015; Kirby et al., 2014; Tekleab et al., 2011; Zhang et al., 2008), showing reliable river discharge simulations at a monthly timescale. The model has a simple structure without routing, simulating the basin hydrological processes with a reduced number of parameters. There are only four model parameters: basin rainfall retention efficiency α1 (–), evapotranspiration efficiency α2 (–), recession constant d (1/month), and maximum soil moisture storage capacity Smax⁡ (mm). Low (high) values of basin rainfall retention efficiency or evapotranspiration efficiency implies more (less) direct runoff. The recession constant d characterizes baseflow, with parameter values ranging between zero and one. The maximum soil moisture storage capacity relates to the root soil depth and soil texture of the basin. As the Coello basin is small, routing processes can be ignored when estimating monthly water availability, which is calculated as the accumulated runoff in the basin upstream of the point of interest.

In this study, surface water availability for irrigation was established as the discharge in the Coello River, considering an environmental flow of 25 % from the available water resources. An average maximum soil moisture storage capacity Smax⁡ of 176 mm was determined for the Coello basin based on the soil texture and the depth of roots in the region. The soil texture and the depth of roots were derived from soil and vegetation maps provided by the Instituto Geográfico Agustín Codazzi in Colombia at a scale of 1:500 000. Typical values of the available water storage capacity of the soil in millimetres per metres of depth were used based on the soil texture (Shukla, 2013). These values were multiplied by the depth of roots to determine the maximum soil moisture storage capacity in the basin.

The hydrological model was forced with the different precipitation datasets (described in detail in Sect. 2.2). Although river flow data were available for the full 1982 through 2012 period, to explore the influence of limited availability of observed discharge data, six independent samples of 5 years were extracted from the 30-year dataset (1983–1987, 1988–1992, 1993–1997, 1998–2002, 2003–2007 and 2008–2012). Each sample of 5 years was used for calibration of the model parameters (Fig. 4). These samples were extracted as contiguous samples of 5 years to represent different climatological periods, and were applied to calibrate six sets of models, each using one of the observed discharge samples. Preliminary Monte Carlo simulation was developed to obtain the full period of samples and then extract each sample for calibration; 10000 model parameter sets (α1, α2, and d with values uniformly distributed between 0 and 1) were generated and subsequently forced with the full dataset of 30 years of in situ precipitation data (1983–2012). From this simulation, the five best-performing model parameter sets are selected for each of the 5-year samples based on the comparison of the simulated and observed discharges for the corresponding period. Model performance is measured using the KGE metric (Gupta et al., 2009). This resulted in five calibrated models for six 5-year samples, which were used to provide simulated discharge data at the Payande station for the full 30-year period, forced by each of the three precipitation datasets. Performance metrics of the mean discharge simulation of the five models were calculated separately for each month across the six periods to evaluate the hydrological performance, including KGE, Pearson's correlation coefficient (r), and percent bias (Pbias).

Similar to Kaune et al. (2018), the area that can be irrigated is determined based on an operational target monthly water supply reliability (R=75 %), which means that the monthly demand is met for on average 75 % of the years (Eq. 1). The target reliability depends on local requirements and agreed terms. We selected 75 % based on local consultation. The monthly irrigation demand varies depending on the irrigation area, which is the variable to be obtained. A fixed demand rate of 0.2 m3 s-1 km-2 was used in the Coello Irrigation District (Kaune et al., 2017). 1R≤pQa-Ai⋅r≥0, where R is the water supply reliability (or probability of non-occurrence of water scarcity, prNWS), p is the relative frequency, Qa is the multi-annual monthly surface water availability (considering an environmental flow of 25 % from the available water resources), Ai is the planned irrigation area for dataset i (simulated or observed), and r is the demand rate.

The water availability distribution for each calendar month is established using the multi-annual monthly river discharge, which may be obtained from either the observed or simulated data. Given the small sample size of 30 years, the empirical distribution of water availability is obtained by applying a bootstrap resampling with replacement procedure, with the size of the bootstrap set at 25 000. The bootstrap resampling is applied for each month for the sample of 30 water availability values (multi-annual monthly values). From this sample we randomly draw X values, and leave these out of the dataset. These are then replaced with X values drawn from the remaining values, thus maintaining the same size of the dataset. This process is repeated 25 000 times. The size of the bootstrap is determined iteratively using a progressively increasing sample size until a stable estimate of the empirical distribution is achieved.

A reference irrigated area is established using the empirical distribution derived from the observed monthly river discharges of 30 years (1983–2012). The areas that can be irrigated for each of the six calibrated models are similarly determined but now using the discharge simulations for the full 30-year period. Irrigated areas are additionally obtained for the six 5-year samples of observed discharge, and for comparison also using the 5-year period of simulated discharges for each of the six calibrated models, where the period is commensurate with the period used for calibration. For each irrigation area that is obtained, the real probability of water scarcity is determined using the observed surface water availability (which is also a multi-annual monthly bootstrap resample), and the demand calculated using the estimated area (Eq. 2). 2pr{WS}=pQa^-Ai⋅r<0, where pr{WS} is the probability of occurrence of water scarcity, p is the relative frequency, Qa^ is the observed surface water availability, Ai is the planned irrigation area obtained from Eq. (1), and r is the demand rate. These probabilities are then used to determine the expected annual utility to evaluate the economic value (Table 1 and Sect. 2.5).

The cost of choosing the irrigation area was evaluated with an extended version of the hydro-economic framework developed by Kaune et al. (2018) based on the economic utility theory (Neumann and Morgenstern, 1966). The cost is calculated as the opportunity cost when the irrigation area is selected to be too small, or the production loss due to water scarcity when the irrigation areas are selected to be too large. When the area selected is equal to the reference area, then the cost is zero. Similarly to Kaune et al. (2018), the relative utility value, RUV, is used to compare the expected annual utility between the reference and the irrigated area derived using either the simulated discharge or the shorter 5-year observed discharge sample (Eq. 3). 3RUV=Ui-UrUr, where Ur is the expected annual utility (revenue) obtained with the reference irrigation area from observed river discharge, and Ui is the expected annual utility obtained with any of the irrigation areas obtained from the discharge simulations described in Sect. 2.4.

The expected annual utility U is defined as the expected annual crop production, given monthly probabilities of (non-)water scarcity and considering a loss in crop production if water scarcity does happen in any one month (Eq. 4). 4U=prWS⋅PNWS-LWS+1-prWS⋅PNWS, where prWS is the monthly probability of water scarcity defined in Sect. 2.4; PNWS is the expected annual crop production (PNWS=c⋅Ai⋅ye) which includes the irrigation area Ai obtained from Sect. 2.4 and converted into hectares, price of the crop per ton ($ t-1) and the expected crop yield ye (t ha-1), and LWS is the annual production loss if water scarcity happens in any one month.

To determine the annual production loss LWS, an approach is applied where each month corresponds to the growth stage distribution of the crop based on information provided by the Coello Irrigation District. We assume that only rice is grown in the Coello Irrigation District with a growing length of 4 months sown over the entire year. The loss in annual rice production LWS due to water scarcity happening in any one month is determined with Eq. (5): 5LWS=c⋅Ai⋅∑monthye-ya, where ye is the expected harvested crop yield in a month (t ha-1) and ya is the actual harvested crop yield in a month (t ha-1) due to water shortage happening in any one month. Water shortage happening in any one month of the 4-month crop period will lead to a yield reduction. The actual harvested crop yield ya obtained is determined with the FAO water production function in Eq. (6) (FAO, 2012): 61-yaye=Ky1-ETaETp, where Ky is the weighted average yield reduction value per month calculated from established yield reduction factors due to water deficit for each growth stage of rice (FAO, 2012) and the distribution of growth stages as reported by the Coello Irrigation District; ETa is the actual evapotranspiration and ETp is the potential evapotranspiration. In our experiment, the actual evaporation is unknown, as this will depend on irrigation scheduling and practice as well as precipitation. As this detail is beyond the scope of this paper, we assume the reduction in evapotranspiration 1-ETaETp to be 20 % for the reference irrigation area when water shortage occurs; 20 % is selected as this is the evapotranspiration deficit that rice farmers can easily cope with (FAO, 2012). To account for the increased deficit for irrigation areas selected to be larger than the reference area, the evapotranspiration reduction is increased proportionally, assuming the available water is uniformly distributed in the new irrigation area. For irrigation areas selected to be smaller, the reduction is decreased proportionally. An average price of 329 $ t-1 and an expected rice yield of 6.8 t ha-1 based on national statistics (DANE, 2016; Fedearroz, 2017) are used to estimate the expected annual rice production.

If RUV is equal to zero, then the expected annual utilities obtained with the reference and simulated irrigation areas are the same, and there is thus no cost associated with using the simulated information. A negative RUV entails an opportunity cost due to the planning of too small an irrigation area (defined as cost type 1). A positive RUV entails an agricultural loss due to the area being planned larger than can be supported by water availability and water shortages thus occurring more frequently than expected (defined as cost type 2). The statistical spread of RUV is derived from the bootstrap resample. The spread depends on the probability of water shortage being larger compared to the reference and on the yield response factor, entailing that the production loss incurred depends not only on the increased occurrence of water shortage, but also on the sensitivity of the crop to water deficit.

RUVs are pooled so as to give a PRUV to evaluate the cost of choosing the irrigation area from the six possible irrigation areas obtained for a river discharge simulation. This is done as it is not a priori clear, when only 5 years of observed data are available, from which part of the full climatological record these may be. The PRUV is a concatenated vector of the RUV obtained for each calibration sample (Eq. 7). 7PRUV=RUV1∥RUV2∥…∥RUV6, where PRUV is the pooled relative utility value and RUVx is the relative utility value for each calibration sample (in this case six samples).

Similar to RUV, the PRUV is a hydro-economic indicator that can be larger than (cost type 2), equal to (no cost) or smaller than zero (cost type 1). The statistical spread of PRUV encompasses the variability of RUV among the six calibration samples. If the statistical spread of PRUV is large, then the variability of planned irrigation areas is large among samples. This means that the cost of choosing the irrigation area based on the available information is high. If on the other hand the statistical spread of PRUV is small, then the variability of planned irrigation areas is also small and the cost of choosing the irrigation area based on the available information is low.

The monthly observed and simulated discharges calculated with the different precipitation datasets from the calibration samples are shown in Fig. 5 (only CHIRPS with the samples for the 1993–1997 and 1998–2002 periods are shown) and in the Supplement (all samples and in situ and MSWEP). Discharge simulations change depending on which precipitation dataset is used as forcing and which sample is used to calibrate the hydrological model. In general, however, the mean discharge simulations show an overall agreement with observations.

The performance metrics for each month are shown in Fig. 6 and in the Supplement. In all months using the discharge simulations with different precipitation datasets, positive KGE values are obtained with the exception of simulations with MSWEP in April and November, which are both wet season months. In February (dry season) the highest KGE value is obtained using the simulations with observed precipitation (0.75). For all samples in February (dry season), the KGE value is higher for discharge simulations with observed precipitation and CHIRPS than those using MSWEP, with the exception of one sample (2008–2012).

In terms of Pbias, simulations with MSWEP consistently overestimate the discharge between October and May for all samples. The largest overestimation occurs in April (wet season) (Pbias = 75 %). For simulations with observed precipitation and CHIRPS, monthly Pbias follows a similar trend, overestimating discharge in April for most samples and underestimating discharge between January and April for only two samples (1983–1987 and 1998–2002). Between May and September underestimated discharges are obtained using simulations with in situ and CHIRPS datasets for all samples. Simulations with MSWEP in June and July are also underestimated, with the exception of sample 1998–2002 (Pbias positive for all months).

The correlation values vary among simulations and for each month. The correlation values range between 0.25 and 0.85. In February, using in situ precipitation, correlation values are above 0.6. Simulations with CHIRPS and MSWEP result in correlation values between 0.7 and 0.8 in February. The largest difference between correlations occurs in March (CHIRPS correlation is 0.5, MSWEP correlation is 0.6, and in situ correlation is 0.8).

Simulations with in situ precipitation and CHIRPS are found to behave similarly, which is not surprising as CHIRPS uses station-corrected data. MSWEP also includes station-corrected data, but they are derived in part from the ERA-Interim data which in themselves are not good at capturing convective precipitation (Leeuw et al., 2015). This explains the poor simulation performance with MSWEP in April and November as these are wet months in a tropical region with predominant convective precipitation.

As our work is focused on determining the critical irrigation area under monthly water scarcity, we are less concerned with the simulation performance in wet months, but focus rather on the more critical dry months (e.g. February), which have shown to perform well for the selected precipitation datasets.

The areas that can be irrigated based on the water availability of the Coello River are established using the simulated discharges from Sect. 3.1., a defined environmental flow, a fixed demand rate per unit area cropped, and a water supply reliability target of 75 %. Irrigation areas are established for the reference discharge (observed 30 years); for each of the 30-year discharge simulations using the models derived with each calibration sample; as well as using the observed discharges for each of the six 5-year samples. Finally, for comparison, irrigated areas are derived using only 5 years of simulated data for each of the six 5-year samples, where the simulated 5 years are the same as the 5 years used in calibration. The areas that can be irrigated given the simulated (or observed) discharges are found to vary significantly when compared to the reference irrigated area (which was established as 67.45 km2), with areas ranging from 2 % to 40 % smaller to 1 % to 69 % larger (Table 2). In the case of the 30-year simulations, the irrigation areas obtained are found to be always larger than the reference area, with the overestimation ranging from 3 % to 69 % (Table 2), with the exception of one sample where an underestimation of 3 % when using the observed precipitation is found. The largest estimates of areas that can be irrigated is obtained with MSWEP simulation (69 %), which agrees with discharge model performance (Sect. 3.1), as KGE and r values are the lowest for this model, while the bias values are the highest of all the simulations. For simulations with CHIRPS and observed precipitation, Pbias is positive for sample 1998–2002 in the dry months (e.g. February), leading to an overestimation of the irrigation area of 40 %. For sample 1993–1997, Pbias is negative for these simulations (close to -10 % in February), resulting in a lower estimation of the irrigated area. In this case, an underestimation of 3 % in the area is found for the simulation with observed precipitation, but an overestimation of 3 % in the area is found for the simulation with CHIRPS. This is related to the difference in variability as the water availability is derived based on the distribution and not on the mean.

The areas that can be irrigated that are obtained using the observed discharges for each of the six 5-year periods show relatively small variation when compared to the reference area, ranging from 19 % smaller to 11 % larger. The average area of the six 5-year samples is slightly smaller at 64.99 km2, just 2.5 % smaller than the reference. Conversely, the areas derived using the simulations for each of the 5-year periods show that these vary quite considerably, with an overestimation ranging from 10 % to 62 % and an underestimation ranging from 9 % to 40 % across all precipitation sources. This range is comparable for all three precipitation forcing datasets, indicating that the variability can be attributed primarily to model error, conditional on the 5-year dataset used in calibration.

The probabilities of water scarcity using the irrigation areas obtained for each of the simulated and observed discharges for the 5-year periods as well as for the reference are shown in Figs. 7 and 8 (samples 1993–1997 and 1998–2002) and in the Supplement (all samples). The probabilities of water scarcity using the irrigation area obtained using the observed discharges are shown in Fig. 7. As expected, the probability of water scarcity in February, which is the most critical month, shows a median value equal to 25 % and probabilities lower than 25 % for the other months when using the irrigation area obtained with the reference discharge (30 years). The spread of the probability of water scarcity indicated by the box–whiskers plot, showing the mean, interquartile range and minimum and maximum, is due to the distribution of the bootstrap, representing the uncertainty in the estimate due to the 30-year period of record.

Figure 7 similarly shows the probability of water scarcity for irrigation areas obtained using observed discharges for the 5-year periods: 1993–1997 and 1998–2002 (results for the other four periods included in the Supplement). This shows that for the period 1993–1997, the median value is lower than 25 % for all months, while for the period 1998–2002 the median value is higher than 25 % for January and February. This reflects the smaller or larger irrigated areas established with each of these datasets. Figure 8 shows the probability of water scarcity for irrigation areas obtained using the discharge simulations of 30 years. The probability of water scarcity in February shows median values higher than 25 %, commensurate with the overestimation found in the hydrological model, with the exception of one simulation using observed precipitation, calibrated with the 1993–1997 sample of observed discharge data. Between April and June and in October to November, using the irrigation areas obtained with the discharge simulations, the probability of water scarcity is always found to be lower than 25 %, as these are the two wet seasons of the bimodal climate. For all samples, the probability of water scarcity is highest for the simulations using MSWEP precipitation. Using the irrigation areas obtained from the simulations calibrated with the 1983–1987 and 1998–2002 samples shows higher probabilities of water scarcity for all months when compared to the simulations calibrated with the other samples. This shows that these years were relatively wet, influencing discharge simulations and resulting in larger irrigation areas being selected. The pattern for sample 1993–1997 is more similar to the pattern found using the reference area found with the 30 years of observed discharge.

The probabilities of water scarcity for irrigated areas obtained with simulated discharges of only 5 years are shown in Fig. 8 (again, results for the 1993–1997 and 1998–2002 samples are shown, with the remaining four periods provided in the Supplement). The monthly probabilities of water scarcity show large differences between samples. In this case, four out of the six samples do not show a median probability of water scarcity higher than 25 % for any month, meaning that the irrigation area is underestimated compared to the reference. For the 1998–2002 sample, the probability of water scarcity is highest, with a median probability of water scarcity between 50 % and 75 % in February.

The annual expected utility is calculated using the economic return of the rice crop and the estimated yield determined using the irrigated areas established with the simulated discharge information, and the probability of water scarcity in each month for the 30-year period based on the observed discharges. Relative utility values are then found by comparing these against the annual expected utility calculated using the reference area and discharge information.

Figure 9 shows the relative utility values obtained for areas determined using the 5-year samples of observed discharge for the 1993–1997 and 1998–2002 periods (again, the remaining four periods are provided in the Supplement), with median estimates of -0.02 and 0.11, respectively.

Relative utility values obtained for areas determined using discharge simulations of 30 years are shown in Fig. 10 (and in the Supplement), with median estimates between -0.03 and 0.65. The relative utility values closest to zero are found for simulations using both the observed and CHIRPS precipitation datasets, -0.03 and 0.03, respectively, both when using the 1993–1997 sample for model calibration. Of the six samples, this 5-year period was already noted to be most representative of the whole 30-year period.

For all samples, the relative utility values for simulations using the MSWEP dataset are found to be largest, with values between 0.3 and 0.65, indicating a higher production loss due to the higher probability of water scarcity. For simulations using the 30-year observed precipitation, consistent median values between 0.18 and 0.45 are obtained, with the exception of one sample (-0.03). Those obtained with CHIRPS simulations are consistent with those found using the observed precipitation.

The relative utility values obtained using irrigated areas determined with the simulated discharges of only 5 years (Fig. 10 and the Supplement) show median estimates between -0.2 and 0.6 (MSWEP), which are larger than the simulations of 30 years. The RUVs closest to zero are found for simulations with CHIRPS (-0.09), while results for simulations using the observed precipitation show more consistent values closer to zero. In this case, results show more negative RUVs for each simulation forcing, and results are less consistent between samples compared to the results obtained with the 30 years.

For the 1993–1997 period, the RUV obtained for the irrigated area determined with observed discharges of 5 years (-0.02) and the RUV obtained for the area determined with simulated discharges of 30 years using either CHIRPS or the observed precipitation (0.03 and -0.03) are similar and close to zero. The extended precipitation period compensates for the model uncertainty and results in reliable RUV estimates.

A large statistical spread in RUV is found in months where the probability of water scarcity is higher than the reference. This is clearly shown for MSWEP simulations, which have the largest estimates of the irrigated area. For months where the probability of water scarcity is lower than the reference, the statistical spread in RUV is low. In these cases the statistical spread of RUV is a result only of the spread of the reference annual expected utility, resulting from the distribution of the probability of water scarcity. The statistical spread of the RUVs is lower when the simulated annual expected utility and the reference annual expected utility are more similar, which means that the RUV is closer to zero, as shown when using the 1993–1997 sample. An absence of statistical spread for the RUVs reflects zero probability of water scarcity in both the simulated and reference expected annual utilities.

Even though the probability of water scarcity is not the highest in November, the statistical spread of the RUV is the largest when water scarcity happens in that month. This is due to the high sensitivity of the crop to water deficit (Ky=1.4) in November, which then becomes the determining factor for obtaining a large statistical spread. On the other hand, the smallest statistical spread, or no statistical spread, of the RUV is found when water scarcity happens in February or May. We select February, May and November as the representative months for further analysis with the pooled relative utility value.

The PRUV is obtained from the RUVs for each of the six samples in Sect. 3.4. In Figs. 11 and 12, the PRUV results for areas estimated using the observed discharges, and for the simulated discharges for 5 and 30 years, are shown for November, February and May. These are the representative months identified in Sect. 3.4, with similar results found for PRUVs when water scarcity happens independently in each month.

The statistical spread of PRUVs represents the risk of randomly choosing one irrigation area out of the six possible irrigation areas given by the six calibration samples of 5 years. Results for the 5-year simulations show a large statistical spread of the PRUVs, with the distribution positively skewed. This skewness is due to the influence of one high RUV sample out of the six RUV samples, resulting in a maximum positive PRUV for each precipitation dataset, 0.18, 0.25, and 0.6. The statistical spread of PRUV for the 5-year simulations with MSWEP precipitation is the largest among the simulations, implying that the cost of choosing the irrigation area using this dataset is the highest. Using 30 years of simulated discharges does reduce the statistical spread in PRUV when compared to the 5-year simulations. For observed precipitation, simulations with 5 years show the range of PRUV to be between -0.38 and 0.18, with an interquartile range between -0.3 and -0.15, while simulations with 30 years show the range of PRUV to be between -0.03 and 0.5, with an interquartile range between 0.18 and 0.4. For CHIRPS and MSWEP precipitation, the reduction in the statistical spread in PRUV with 30-year simulations is more evident. For the 30-year simulations, the smallest statistical spread in PRUVs is found for CHIRPS precipitation (between 0.03 and 0.4). This means that the cost of choosing the irrigation area is lower when using simulations with CHIRPS compared to simulations with in situ and MSWEP precipitation. In addition, using CHIRPS leads to median PRUVs closer to zero; thus, choosing among the irrigation area samples results in an irrigation area closer to the reference irrigation area.

The statistical spread in PRUV when using observed discharge of 5 years (-0.20 to 0.12) is similar to the statistical spread in PRUV when using the best simulation with 30 years (CHIRPS, 0.03 to 0.4). Again, using the longer precipitation record to provide a longer record of simulated discharge results in a reduction in the statistical spread in PRUV and compensates for the model uncertainty. This means that using the 30-year simulation is beneficial, as the cost of choosing the irrigation area is similar to the cost when using the 5-year observed discharge.