4.1. Basin Response
As can be seen, the 3_FAOseas modeled streamflow is slightly lower than the reference model outputs. Actual evapotranspiration is generally significantly higher for January–April, and September (tested with the Wilcoxon Signed-Rank Test at 0.05 significance level). June and July values are significantly lower. Soil moisture deviates negatively from the NDVI-based reference model—the highest deviations happening in spring. During summer, model outputs are closest to each other, with small negative deviations for the three variables; water available for streamflow generation and for evapotranspiration is lower as it has been consumed already in spring. Low rainfall amounts in summer cause soil moisture and evapotranspiration to reach their lowest levels (Figure 4
), thus making the absolute difference between the methods smaller.
Most interestingly, despite a notable seasonal impact on evapotranspiration and soil moisture predictions, deviations in streamflow do not follow a seasonal pattern. The deviation from the NDVI-based reference model is more or less constant throughout the year: approximately −0.3 mm/month, which represents an average of 4% on an annual basis. However, because of the high variability in monthly streamflow, relative deviations of monthly streamflow range between 1% and −15% and is highest in summer and autumn.
The deviations of the other methods from the NDVI-based reference model show similar trends as 3_FAOseas (Figure 6
). The largest deviations are seen for 5_Unity, which assumes a crop coefficient = 1. For this parameterization method, the average monthly deviation of streamflow is −0.7 mm/month, which corresponds to a relative deviation of −10%. For the other NDVI-based methods, deviations are around −0.2 mm/month (−3%) and for the FAO-based methods around −0.3 mm/month (−4%).
For ET, the mean monthly deviation is close to 0 for all methods, but as can be seen in Figure 6
, there is a clear monthly pattern in the deviation: spring and summer deviations are positive, while in summer the deviations are generally negative. The highest values are reached in March (1.3 mm/month, corresponding to a relative deviation of about 3%). For 5_Unity, this goes up to 3.1 mm/month (7%) deviation.
For soil moisture, the highest deviations occur in spring (Figure 6
), when ET deviations are also highest. As could also be seen in Figure 5
, negative deviations in soil moisture correspond with positive deviations in ET. This has interesting implications for streamflow and can explain why for all parameterization methods the deviation in streamflow is less variable over the year than ET and soil moisture. The kc
parameterization method influences the crop water demand and thus soil water extraction by vegetation and evapotranspiration. The effects of ET and soils moisture extractions on streamflow are buffered by soil moisture and groundwater storage components, causing the impact of kc
parameterization on streamflow to be less variable throughout the year.
The relatively small and constant deviation in streamflow can be irrelevant for many applications focusing on basin-scale streamflow prediction, as it can be corrected by model calibration. In fact, it may remain unnoted by the modeller: rainfall forcing is often the main source of input uncertainty in hydrological modelling, most likely leading to comparable or higher deviations than those caused by kc
]. This may explain why often little attention is paid to the crop response to soil water availability in hydrological models used solely for streamflow prediction.
Still, relative deviations in streamflow prediction can be considerable, especially for the autumn period at the start of the rainy season (on average −6% in October for 3_FAOseas and −15% for 5_Unity). In a few days, the basin can change from a dry status to a wet status, so it is likely that small changes in the parameterization will have notable effects on that time scale. The focus of this study has been on the monthly response, since no daily discharge data were available and the model error on such high temporal resolution is generally much higher as well. Nevertheless, more study is required to understand how our findings on the impact of crop coefficient parametrization extrapolate to daily hydrological response and its implications for hydrometeorological extremes and flood risk prediction.
4.2. Sub-Basin Response
shows the same boxplot of monthly deviations for the sub-basins (0.1 to 10 km2
), as for the basin-scale outputs (Figure 5
). Overall, the same seasonal trend can be observed in the deviations of the three variables shown. However, Figure 7
shows that the deviations can be considerably higher at this smaller scale. For a certain portion of the sub-basins, deviations can be several factors higher than what was seen at the basin scale.
More specifically, Table 3
shows how the deviations of the sub-basin outputs differ from those at the basin-level. The table shows the 10th, 50th, and 90th percentiles, and both the absolute (mm) as well as the relative deviations (%). As expected, the median (50th percentile) is very similar between the basin and sub-basin levels: outputs were based on the same simulations, so the overall trend should be the same. However, there are considerable differences in the tail ends of the distribution, i.e. the 10th and the 90th percentile. Absolute deviations (mm) can be more than two times higher at the sub-basin scale than at the basin scale. As an example, 10% of the monthly evapotranspiration predictions deviate −2.3 mm/month or more from the 0_NDVIref run, while at the basin scale this value was −1.1 mm/month. This corresponds to a relative deviation of 5% at the basin scale, and 10% at the sub-basin scale. For soil moisture, similar differences were found between the scale levels.
For streamflow, deviations (mm) can increase by a factor 3 or more from the basin to the sub-basin level. Table 3
shows that 10% of the predictions show a deviation of −8% or more with the reference run at the basin scale, while deviations can be −28% or more at the sub-basin scale.
The larger the basin, the more diverse in terms of land use, climate, and other biophysical conditions. Therefore, the relevance of bringing in more detail in the kc
parameterization will depend on the size of the basin [61
]. Often, hydrological impacts of land-use and management change are studied using distributed models like the one used in this analysis. What the above results show is that parameterizing crop coefficients from high-resolution observations of vegetative status (0_NDVIref) can deviate substantially from a more classical approach using literature-based values for the kc
values, especially at the sub-basin scale.
For future scenario analysis, remote sensing data to characterize the crop status are not available. Therefore, hydrologists often use the tabulated FAO-56 values for the crop coefficients. However, as was shown previously, there can be considerable deviations with an approach using high-resolution information on crop status, as is provided by remote sensing, especially at the sub-basin scale. When outputs at smaller scale become the focal point of study, for example for prioritizing measures across the landscape [63
], literature-based values will result in a loss of information and consequent inaccurate results.
shows a comparison of all methods at the sub-basin scale. It shows the area between the 10th–90th percentiles (green band) as in Table 3
but for all parameterizations instead of only 3_FAOseas. In addition, it includes the 5th–95th percentiles (reddish colour).
The two NDVI-based methods have the smallest deviation compared to the reference model: the 50th percentile is closest to zero (Figure 8
). Also, the percentile intervals (green and red) are narrower compared to the other methods, so overall less variability in the deviation with the reference model can be expected when choosing one of these two methods. This result is not fully surprising because the same NDVI information was used for these two models and the reference model, but in an aggregated and simplified way. The advantage of these methods is that they can be used for kc
parameterization of hydrological models in future scenario analysis.
The FAO-based methods 3_FAOseas and 4_FAOstat show a similar deviation (50th percentile) for the sub-basins, but using a static (non-seasonal) crop coefficient (4_FAOstat) clearly increases the spread in the deviation of the streamflow predictions. For 5_Unity, the median indicates that the deviation is largest of all methods. On the other hand, positive deviations are less likely to occur compared to the FAO-based methods, causing the bands to be narrower. This is because this method assumes a kc
= 1, while in the other methods the mean kc
is lower (see also Figure 2
), thus causing higher crop water demand and less water available for runoff and streamflow.
The results shown are based on a Mediterranean basin, with a wide range of biophysical conditions, but with a typical hydrological regime (potential evapotranspiration higher than rainfall, and streamflow highly variable and overall much lower than evapotranspiration). Therefore, these findings are limited to this type of hydro-climatic conditions as they are very much influenced by the fact that during most of the year the actual evapotranspiration is limited by soil water availability in semi-arid systems. It can be expected that in more humid or even more arid basins the sensitivity to the evapotranspiration component and the impact on streamflow will be different [64
]. To generalize the findings in this paper, it could be interesting to apply a similar approach in basins with different climate and other biophysical conditions. A statistical analysis could be carried out to identify the dominant factors (rainfall, landuse, slope, catchment area, etc.) that explain the deviations. This could potentially lead to practical guidelines for hydrological modeling and crop coefficients. This should also consider that, for more humid conditions, the use of NDVI to derive crop coefficients has its limitations due to saturation issues that make NDVI a less adequate proxy for the crop coefficient [55
The hydrological model SPHY is a typical bucket-type grid-based model, using process descriptions used in many other hydrological models. So we expect the results of the sensitivity analysis here to be valuable also to many other similar models. The sensitivity of course also depends on the model conceptualization. Hydrological models that use for example the “hydrological response unit” (SWAT, TOPMODEL, etc), instead of cell-based calculation units, or that use conceptualizations and descriptions of soil water dynamics that are different to the typical bucket-approach, may respond differently to different kc parameterizations as is shown here.
This study compared the different kc approaches with a reference model calibrated using streamflow data. Several studies have evaluated the usefulness of actual evapotranspiration estimates derived from remote sensing data and energy-balance methods for the calibration of hydrological models [37
]. This can lead to a more accurate spatial distribution of the model parameters, especially in semi-arid areas like in this study [36
]. A recommendation therefore for follow-up work is to evaluate different kc parameterization approaches by calibrating these independently using remote sensing-based observations of evapotranspiration rates. Calibration performance coefficients—for example those used in this work—could be used to assess which method performs better than others. A more in-depth analysis could be performed for this evaluation as well, by using spatial metrics that assess the degree of similarity between of the spatial patterns in the model simulations [66