Estimating irrigation water use over the contiguous United States by combining satellite and reanalysis soil moisture data

2.1 Irrigation practices in the contiguous United States

The amount of water needed by a certain crop for optimal growth mainly depends on three factors: crop type, soil and climate. Irrigation water need is given by the difference between these requirements for optimal crop growth and effective rainfall. In the largely semi-humid climate of the eastern United States, irrigation is supplemental, which means that irrigation is applied to mostly rain-fed crops during times of insufficient rainfall to achieve higher yields than under rain-fed conditions alone. In contrast, the predominantly semi-arid climate of the western US makes artificial water supply a necessity, thus requiring full irrigation.

The 2013 Farm and Ranch Irrigation Survey (FRIS) of the National Agricultural Statistics Service (NASS) of the USDA provides selected irrigation data from surveys conducted at approximately 35 000 farms using irrigation across the US (USDA, 2013). It reports state-level data of both irrigated area and irrigation water withdrawals subdivided by specific crop type, water source and irrigation technique. In addition, these estimates are given for crops cultivated outdoors (“in the open”) and indoors (“under protection”, e.g., horticultural crops grown in greenhouses). Figure 1 shows the per-state irrigated area and irrigation water withdrawals limited to crops grown outdoors, as well as irrigation application rates during the 2013 growing season provided by FRIS.

Figure 1Per-state irrigated area, irrigation water withdrawals and irrigation water application rates for 2013. The data were drawn from the latest Farm and Ranch Irrigation Survey (FRIS) and only reflect irrigation operations in open fields (e.g., excluding crops grown and irrigated in greenhouses).

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It is likely that the sensitivity of satellite soil moisture retrievals to irrigation increases when the irrigation application efficiency of a particular irrigation system or technique deteriorates. Therefore, we expect higher sensitivity towards gravity irrigation systems (e.g., flood and furrow irrigation) and lower sensitivities towards sprinkler and micro-irrigation systems. Figure A1 shows a distinct decline in irrigation rates per area from the semi-arid west to the more humid east. The state of Arizona has the highest irrigation rate per area, followed by California and Nevada. Gravity flow systems show the highest rates in California and Arizona but also depict large values along the Mississippi Delta. This can mainly be attributed to the cultivation of rice, which is primarily grown in these regions and is either flood or furrow irrigated. Finally, micro-irrigation systems are largely limited to the western half of the US.

2.2 Focus areas

In addition to the continental-scale analysis, we chose four irrigation hot spots characterized by different climates and irrigation practices within the CONUS (Fig. 2) to comprehensively assess the spatiotemporal dynamics of irrigation. These regions are the Sacramento Valley and San Joaquin Valley in the California Central Valley; the Snake River Plain, Idaho; the High Plains, Nebraska; and part of the Mississippi Floodplain located within the state of Mississippi. For each focus area, we conducted a time series analysis at a local scale (Sect. 5.3), as well as a cross comparison with reference data on irrigated area (Sect. 5.5) and irrigation water withdrawals (Sect. 5.4).

Figure 2Study regions and locations of the pixels selected for a local time series analysis over the fractional irrigated area map derived from the spatially aggregated MIrAD-US data set (Pervez and Brown, 2010). The focus regions are included in black squares and include the Sacramento Valley (SV) and San Joaquin Valley (SJV) in the California Central Valley (CCV), Snake River Plain (SRP), Nebraska Plains (NPS) and the Mississippi Floodplain (MFP). Green and orange crosses indicate the locations of the irrigated (PI) and non-irrigated (PNI) pixels, respectively, at which we further analyze satellite and model soil moisture time series in conjunction with $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ estimates.

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2.2.4 Mississippi Floodplain, Mississippi

The Mississippi Floodplain region is characterized by a fully humid subtropical climate with hot summers (Kottek et al., 2006). Despite the large amounts of rainfall throughout the year, only approximately 30 % falls in the summer period when the major crops are grown (Kebede et al., 2014), thus requiring the use of supplemental irrigation. The dominant crop types include soybean, corn, cotton and rice. Within the Mississippi Floodplain we chose an area in the state of Mississippi for a local analysis. Here, reports on irrigation water withdrawals (2009 and 2011 growing seasons) are available from the Yazoo Mississippi Delta Joint Water Management District. For the 2011 growing season, average application rates of approximately 180, 400, 330 and 970 mm are reported for cotton, corn, soybeans and rice, respectively, leading to an average of around 490 mm.

Table 1Data products.

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3.1 Remotely sensed soil moisture

3.2 MERRA-2 reanalysis soil moisture

The second Modern-Era Retrospective analysis for Research and Applications 2 (MERRA-2) (Bosilovich et al., 2016) is an atmospheric reanalysis product providing global, hourly fields of land surface and atmospheric conditions for 1980–present at a spatial resolution of $\mathrm{0.625}{}^{\circ }\times \mathrm{0.5}{}^{\circ }$. It assimilates atmospheric satellite observations using the Goddard Earth Observing System Model (GEOS-5). MERRA-2 uses an observation-based precipitation correction over land to fully correct modeled precipitation at latitudes $<\left|\mathrm{42.5}{}^{\circ }\right|$, with a linear tapering between $\left|\mathrm{42.5}{}^{\circ }\right|<\mathrm{latitude}<\left|\mathrm{62.5}{}^{\circ }\right|$, while no correction is applied at more northern and southern latitudes. The precipitation correction has significantly improved the soil moisture simulations with respect to its predecessor (Reichle et al., 2017a). The soil moisture simulations are representative of the first 5 cm of soil and are expressed in volumetric units (m³ m⁻³). We explicitly chose MERRA-2 soil moisture in favor of soil moisture from other global reanalysis data sets, because MERRA-2 does not assimilate surface humidity and surface temperature observations (Reichle et al., 2017c), which are directly impacted by irrigation (Wei et al., 2013; Tuinenburg and Vries, 2017). MERRA-2 surface soil moisture simulations were evaluated in Reichle et al. (2017b) with in situ soil moisture data from 320 sites. It was shown that the modeled estimates are biased by 0.053 m³ m⁻³, which is approximately in the order of the SMAP soil moisture retrieval target accuracy.

3.3 Ancillary data

Despite the drawbacks discussed in Sect. 1.2, the ESA CCI Land Cover data set (Bontemps et al., 2013) was used to create a cropland mask for the CONUS, because the classification of overall agricultural land cover (i.e., irrigated and rain-fed lands) proved to be accurate. For a more detailed analysis of the impact of precipitation, we used CPC Unified Gauge-Based Analysis of Daily Precipitation, which covers the CONUS at 0.25^∘ native resolution (Chen et al., 2008; Xie et al., 2010). Therefore, it is expected to provide more detailed information than the precipitation data set used to force MERRA-2 SM, which has a 0.5^∘ resolution.

3.4 Data preprocessing

As data from SMAP were only available from April 2015 onward, we extended the study period to include available AMSR2 and ASCAT data from 2013 to 2016. Hence, four growing seasons with varying climatic conditions were covered by the AMSR2 and ASCAT sensors and two growing seasons by SMAP. We assumed a general growing season for the entire CONUS from the start of April to the end of September. All data were spatially matched to a common 0.25^∘ regular grid using nearest-neighbor resampling. In order to constrain the analysis to areas where irrigation is feasible, we masked all pixels with < 5 % of fractional cropland area based on ESA CCI Land Cover for 2010 (Bontemps et al., 2013). Unreliable observations in the satellite data were masked, applying their respective quality flags for frozen soil, dense vegetation and radio frequency interference.

The spatial representativeness and observation depth slightly differ among the various remote sensing products and modeled soil moisture. MERRA-2 SM is simulated for a fixed 5 cm thick soil layer (Bosilovich et al., 2016) and thus shows more inertia to changes in the water balance (i.e., through precipitation) than the remotely sensing data. Besides, ASCAT is provided in a different unit than the other products. To account for these systematic differences between products, we applied a linear rescaling approach (Brocca et al., 2013), which forces the satellite soil moisture time series Θ^sat to have the same mean μ and standard deviation σ as the modeled soil moisture Θ^mod:

It is likely that over irrigated areas μ(Θ^sat) increases during the respective irrigation period, which alters the scaling parameters. We expect that this should not affect the temporal evolution of changes in soil moisture. However, the influence of irrigation on the temporal variability of soil moisture (depending on the type of irrigation, general climate conditions, etc.) is a source of uncertainty. In particular over very dry regions, the model soil moisture may never reach saturation, while the remotely sensed soil moisture data do (due to irrigation). Since the variable of interest is irrigation amount, volumetric soil moisture in m³ m⁻³ is converted to the corresponding water column depth D_watertable (mm) by multiplying it with the depth of soil D_soil for which the soil moisture simulations are representative. Thus, for the layer 0–5 cm, for example, 0.3 m³ m⁻³ corresponds to a 15 mm water column covering the unit area of 1 m².

4.1 Theoretical foundation for retrieving irrigation water use from microwave remote sensing

Kumar et al. (2015) first proposed the idea of inferring irrigation from a positive bias between remotely sensed and modeled soil moisture, induced by seasonal water application during the dry season. This idea is based on two key assumptions: first, the satellite soil moisture products are sensitive to large-scale irrigation (as partly confirmed by Escorihuela and Quintana-Seguí, 2016; Lawston et al., 2017); and, second, the model does not account for irrigation, neither explicitly (i.e., in the formulation) nor implicitly through the assimilation of surface humidity or surface temperature observations, which are affected by irrigation (Wei et al., 2013). We build on these assumptions and introduce a new metric to estimate IWU from the difference between satellite-observed and modeled soil moisture. The soil water balance equations describing the respective change in soil moisture for each time step t (day) are described by

for the satellite observations and

for the model simulations. P (mm) is precipitation; I (mm) is irrigation; ET (mm) is evapotranspiration; and Θ^sat and Θ^mod (mm) are satellite and modeled surface soil moisture, respectively, converted to water column depth. ΔS_rest (m³ m⁻³) describes water storage changes below the surface layer, including drainage. Subtracting Eq. (3) from Eq. (2) yields

Hence, estimating irrigation from differences between the temporal variations of satellite and model SM is theoretically feasible.

4.2 Deriving irrigation water use

We define an irrigation event as a simultaneous increase in satellite soil moisture $\left(\frac{\mathrm{d}{\mathrm{\Theta }}^{\mathrm{sat}}}{\mathrm{d}t}>\mathrm{0}\right)$ and a decrease or stagnation in model soil moisture $\left(\frac{\mathrm{d}{\mathrm{\Theta }}^{\mathrm{mod}}}{\mathrm{d}t}\le \mathrm{0}\right)$. This means that rainfall did not cause the satellite-observed increase in soil moisture, which over agricultural land was very likely a result of irrigation. For each event, the amount of irrigation water leading to the increase is derived as the difference $\frac{\mathrm{d}{\mathrm{\Theta }}^{\mathrm{sat}}}{\mathrm{d}t}-\frac{\mathrm{d}{\mathrm{\Theta }}^{\mathrm{mod}}}{\mathrm{d}t}$, if the change in satellite is significant (i.e., above the noise level). The latter is accounted for by applying a threshold of relative soil moisture change thresh_Θ (see Sect. 4.3 and Appendix A). We then calculate seasonal irrigation water use (IWU) summing up the approximated difference quotients over the growing season period:

where

and with

IWU is the accumulated irrigation water use from the start (i_SOS) until the end of the growing season (i_EOS). According to the crop calendars provided by Portmann et al. (2010) and the USDA planting and harvesting dates handbook (NASS, 2010) the period 1 April–30 September generally covers the growing season of most crops receiving irrigation water in the CONUS. ${\mathrm{\Theta }}_i^{\mathrm{sat}}$ and ${\mathrm{\Theta }}_i^{\mathrm{mod}}$ are satellite and model SM on day i, thresh_Θ denotes the relative soil moisture threshold, and ${\mathrm{\Theta }}_{i-n}^{\mathrm{sat}}$ and ${\mathrm{\Theta }}_{i-n}^{\mathrm{mod}}$ are the last available soil moisture observations with a data gap of n days. If an irrigation event is detected during an observation gap of > 4 days, we check if there has been a significant increase in the model soil moisture (e.g., due to rainfall) within that period. When more than one significantly positive model slope (or precipitation events) occurs during the gap period, we cannot say for sure if the observed increase in soil moisture was due to irrigation or precipitation and therefore conservatively disregard the potential irrigation event.

4.3 Masking spurious irrigation detections

It is essential to differentiate between irrigation signals and high-frequency noise in the satellite data. For this purpose, we apply a threshold thresh_Θ to the relative changes in satellite soil moisture similar to the approach applied by Dorigo et al. (2013) to detect spurious in situ data:

Based on an extensive sensitivity analysis (Appendix A) we concluded that a threshold of thresh_Θ≡0.12 is an appropriate generic choice for the whole CONUS.

Potential errors may arise when the model forcing misses or creates false rainfall events. In addition, because of differences in timing of the estimates and differences in represented soil depth between remotely sensed and modeled soil moisture, their response to precipitation events may differ as well. This may lead to spurious irrigation events when irrigation is estimated on days with rainfall. Therefore, we use information from an additional CPC precipitation data set at 0.25^∘ resolution, thus providing an approximately 4× higher spatial resolution than the rainfall product used to force MERRA-2 (see Sect. 3.2). This allows us to make a more educated guess when evaluating if the observations and/or model estimates are affected by rainfall. Furthermore, if a potential irrigation signal coincides with preceding rainfall we assume that irrigation is unlikely and disregard the event. In some extreme cases, capillary rise from deeper soil layers or run-on can wet the top soil. Theoretically, these conditions are reflected by the satellite soil moisture retrievals but are absent in the model soil moisture simulations (i.e., if such effects are not accounted for in the soil hydrology formulation of the LSM, McColl et al., 2017). However, at the large spatial scales represented by the employed satellite (approximately 25 km) and model soil moisture products (approximately 50 km), very few pixels are expected to show positive $\mathrm{\Delta }{\mathrm{\Theta }}_i^{\mathrm{sat}}$ or $\mathrm{\Delta }{\mathrm{\Theta }}_i^{\mathrm{mod}}$ in the absence of precipitation or irrigation. Another impact concerns mismatches between the ancillary data used to force the model and parametrize the respective satellite soil moisture retrieval algorithms, such as land cover and soil parameters. By rescaling to the model dynamic soil moisture range, we implicitly account for mismatches in soil parameters. However, addressing potential mismatches in land cover was out of the scope of this paper and thus represents an intrinsic limitation of the method.

5.1 Growing season correlations between satellite and model soil moisture

To investigate the potential detectability of IWU, we investigated the correlation between satellite and modeled soil moisture during the growing season (Fig. 3). We computed the correlation separately for dry (precipitation =0; ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{dry}}$) and wet conditions (precipitation > 0; ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{wet}}$). If ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{dry}}$ is low or negative over agricultural areas which are known to be irrigated (as inferred from the MIrAD-US product) while ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{wet}}$ is strongly positive, this is a strong indication of irrigation (also see Fig. A2, where the absolute differences between the mean correlations for wet and dry periods $|r_{\mathrm{wet}}-r_{\mathrm{dry}}|$ are shown).

Figure 3Mean correlation $\stackrel{\mathrm{‾}}{r}$ between the daily time series of each satellite soil moisture product (SMAP, AMSR2 and ASCAT) and MERRA-2 soil moisture separated for wet periods (left column; precipitation PCP >0) and dry periods (right column; PCP =0) during the growing season. Correlations were calculated over agricultural areas only.

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Over non-agricultural land cover, low growing season correlations between SMAP and MERRA-2 soil moisture are observed over the densely vegetated south- and northeastern US, as well as over parts of the arid southwest (Fig. 3a, b). AMSR2 exhibits low correlations in coastal areas, complex terrain and over dense vegetation cover (Fig. 3c, d). ASCAT shows negative correlations against MERRA-2 over the arid southwestern deserts and the densely vegetated coastal northwest and southeast (Fig. 3e, f). Overall, for each satellite–model pair there is a clear reduction of ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{dry}}$ with respect to ${\stackrel{\mathrm{‾}}{r}}_{\mathrm{wet}}$ over several irrigation hot spots within the CONUS.

5.2 Spatial patterns of estimated irrigation water use

Spatial plots of mean annual estimated irrigation water use $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ (i.e., averaged over the study period of 2013–2016) (Fig. 4a–c) suggest that all satellite products are able to identify the extensive irrigation applied in the California Central Valley. Here, SMAP-derived $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ clearly resembles the irrigation patterns of the MIrAD-US data set in the northern Sacramento Valley and southern San Joaquin Valley (Fig. 2). The AMSR2- and ASCAT-derived $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ are generally higher than SMAP and extend throughout the whole California Central Valley. Although small in magnitude, the $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ pattern derived from ASCAT over the central Snake River Plain is spatially distinct. Similarly, AMSR2 shows a clear signal over the western to central Snake River Plain. Concerning the Nebraska Plains, only AMSR2 $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ shows patterns that agree with MIrAD-US. Over the Mississippi Floodplain, ASCAT shows the highest $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$, followed by AMSR2.

Figure 4Mean annual irrigation water use ${\stackrel{\mathrm{‾}}{\mathrm{IWU}}}_{\mathrm{A}}$ derived from SMAP (a), AMSR2 (b), and ASCAT (c) SM in combination with modeled SM from MERRA-2. All pixels with a cropland fraction of <5 % (as inferred from the CCI Land Cover product) were excluded from the analysis. Note that for SMAP the climatologies represent the growing season mean of 2015 and 2016, while for AMSR2 and ASCAT the estimates are derived from 4 years of data covering the period of 2013–2016.

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ASCAT-derived $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ seems to be affected by vegetation effects in the Corn Belt region and in the southeastern US. For all sensors, the method fails to detect $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ in many irrigated areas, especially those along the High Plains aquifer (Nebraska, Kansas, Texas), which extends from the northern to the southern central US. A plausible explanation for missing these areas is that many farmers in these regions practice supplemental irrigation, thus resulting in a less distinguishable irrigation signal. In addition, the center pivot irrigation systems, which are mainly used in this region, have much higher water application efficiencies compared to the flood and furrow irrigation systems used in the Sacramento Valley and Mississippi Floodplain (see Fig. A1). Rainfall seasonality is another potential reason for the underestimation in the central U.S, where the climate transitions from arid in the west to humid in the east. To investigate its impact, we plotted the average number of days per growing season where IWU >0 (Fig. A3), which sums up to the number of days that went into the $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ estimates shown in Fig. 4. It can be seen that for SMAP-based IWU, a significant number of days with irrigation (mean count) only is detected in the arid west and southwest. For AMSR2, the mean counts are highest in California, although counts in the range of 20–30 occur in the Snake River Valley, Mississippi Floodplain and other agricultural regions. In agreement with the passive products, mean counts for ASCAT are highest in California and southwestern states. There also is a clear pattern in the Mississippi Valley and along the southeastern states.

Furthermore, the chosen global threshold of thresh_Θ=12 % also masks irrigation signals in regions where the noise level of the satellite soil moisture retrievals is rather low (see Sect. A2). Thus, a more site-specific threshold at each pixel might lead to an improved detectability of irrigation events.

5.3 Temporal behavior of soil moisture and IWU and in the four focus regions

For a more detailed analysis on the impact of climate, crop type and irrigation practice on the method performance, we compared remotely sensed and modeled soil moisture time series and monthly IWU estimates at an irrigated (green crosses in Fig. 2) and a non-irrigated pixel (orange crosses in Fig. 2) in the four focus areas (Fig. 5).

Figure 5Comparison of satellite and model SM time series at irrigated (top two sub-panels) and non-irrigated pixels (bottom two sub-panels) in five regions (Fig. 5a–e). Daily CPC precipitation is plotted in grey, while blue and orange shadings in the top sub-panels reflect growing seasons with positive and negative rainfall anomalies, respectively. The second and fourth sub-panels show the estimated monthly irrigation water use (${\stackrel{\mathrm{‾}}{\mathrm{IWU}}}_{\mathrm{M}}$) obtained for each satellite–model pair for the irrigated and non-irrigated pixels, respectively (non-growing season periods have been masked).

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5.3.4 Mississippi Floodplain

The difference in soil moisture behavior between the irrigated and non-irrigated pixel is much more pronounced for AMSR2 than for the other satellite products (Fig. 5e). This is also reflected by AMSR2-derived IWU at the irrigated pixel, which agrees well with the expected seasonality of irrigation, which peaks in August. At the same time AMSR2-based IWU estimates are close to zero at the non-irrigated pixel. ASCAT soil moisture shows a similar seasonality at the irrigated pixel but is more affected by noise at the non-irrigated pixel. SMAP soil moisture sustains saturation throughout the first half of the growing season, which could either be caused by flood irrigation for rice or point at a problem in the soil moisture retrieval algorithm. At least for AMSR2, IWU shows a meaningful derived seasonality.

Figure 6Comparison of estimated mean annual irrigation water use and reported irrigation water withdrawals. For each satellite–model pair, observed ${\stackrel{\mathrm{‾}}{\mathrm{IWU}}}_{\mathrm{A}}$ was aggregated at the state level. Reported irrigation withdrawals were taken from the 2013 FRIS report and only reflect volumes applied in open fields (e.g., excluding crops grown and irrigated in greenhouses). The data are presented in logarithmic units to reflect both small and large water volumes. Note that the names of the 10 states accounting for the highest irrigation water withdrawals are annotated. R, RMSE and bias between observed and reported estimates are shown in the bottom right of each subplot.

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5.4 Evaluation of estimated irrigation water use against state-level reference water withdrawals

We evaluated the agreement between mean IWU, $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$, aggregated for each satellite–model pair to the state level, and reported irrigation water withdrawals from the 2013 FRIS (USDA, 2013) (IWW_FRI). The median correlation R values for SMAP-, AMSR2- and ASCAT-based $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ and IWW_FRIS are 0.80, 0.56 and 0.36, respectively (Fig. 6). For all satellite data sets, California is correctly identified as the largest consumer of irrigation water, which indicates the overall potential of coarse-resolution microwave soil moisture data in estimating IWU. However, the root-mean-square difference (RMSD) and bias between observed $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ and IWW_FRIS indicate a clear underestimation. The lowest RMSD of 5.21 km³ was found for AMSR2, but values for SMAP and ASCAT are quite similar. ASCAT has the lowest bias (−2.29 km³), but the bias based on the other products is similar. We further discuss the potential reasons for the generally large biases observed in Sect. 5.6. On average, $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ based on SMAP provides the closest similarity with IWW_FRI.

5.5 Evaluating irrigated area estimates with the MIrAD-US data set

We compared spatial patterns of total mean $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ estimates with the MIrAD-US data set at 0.25^∘ resolution. In order to compute a confusion matrix, we converted the continuous ranges of the two data sets into binary representations of irrigated areas. For MIrAD-US, this was accomplished by labeling only areas with >= 5 % irrigation fraction as irrigated. Estimated $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ was converted in a similar way by considering only pixels where $\stackrel{\mathrm{‾}}{\mathrm{IWU}}\ge X$ as irrigated, where X (mm) is a binarization threshold. To compare irrigation estimated from each satellite–model pair with MIrAD-US, we computed the error of omission (EoO), the error of commission (EoC), the overall accuracy (OA) and Cohen's kappa (κ), which is a measure of how the classification results compare to values assigned by chance (Table 2). The binarization threshold X was determined by maximizing κ for each satellite–model pair and focus region, respectively, as well as for the whole CONUS (see Fig. A5).

Table 2Accuracy assessment of irrigated area estimates. For each satellite–model combination a confusion matrix between observed ${\stackrel{\mathrm{‾}}{\mathrm{IWU}}}_A$ and reference irrigated area from the spatially aggregated 2012 MIrAD-US data set was computed after converting the continuous data to a binary representation. Specifically, pixels with observed ${\stackrel{\mathrm{‾}}{\mathrm{IWU}}}_A\ge X$ mm and reported A_{crop-fraction}≥5 % were respectively assigned to the irrigated classes. The binarization thresholds X were found by maximizing the respective kappa scores for each satellite–model combination within each region (see Fig. A5). Results are shown for the four states selected in the regional analysis and the whole CONUS. Italics indicate the best scores within each region, while bold scores show the overall best.

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In California, irrigated area estimates based on $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ show very good agreement with MIrAD-US. SMAP-based irrigated areas provides the highest scores for all metrics: the overall accuracy is 76.79 %. A commission error (EoC) of 23.30 % in combination with an omission error (EoO) of 2.47 % indicates that we somewhat overestimate the reference, and a kappa score of κ=0.33 illustrates a fair agreement. ASCAT has a similar performance but shows a slightly higher overestimation (EoC =22.68 %), thus resulting in a lower overall accuracy and κ score. In California, AMSR2 performs worst but still shows an acceptable overall accuracy of 68.75 %. In Idaho, of all satellite products AMSR2 shows the highest agreement with the reference (OA =59.84 %), but EoC and EoO are equally high at approximately 40 %, indicating a moderate amount of confusion in the classification. As a result of a strong under-classification, in Nebraska there is hardly any agreement between IWU-based and MIrAD-US irrigated area. Over the Mississippi Floodplain, AMSR2- and ASCAT-based IWU shows moderately good agreement with the reference data (OA ≈70 %, κ>0.30). We argue that, due to the previously observed problems regarding the representation of soil saturation, SMAP soil moisture data are unreliable in this region. ASCAT-based IWU depicts a high overestimation (EoC =50 %) while SMAP-based IWU does not classify any irrigated areas at all (EoO =100 %). For CONUS as a whole, ASCAT and SMAP depict the best spatial agreement with MIrAD-US irrigated area, which is reflected by an overall accuracy of 74.55 % and 72.96 %, respectively. However, SMAP fails to correctly classify approximately 90 % of areas irrigated according to the MIrAD-US. AMSR2 shows an agreement of OA =59.38 % and misses fewer pixels than ASCAT and SMAP (EoO =49.63 %) but in contrast shows a higher overestimation (EoC =68.37 %).

The results obtained for California are encouraging and emphasize the potential of coarse-scale microwave soil moisture retrievals in correctly detecting the spatial patterns of irrigation. However, consistent with the findings of estimated irrigation volumes, irrigated area estimates reflect a general pattern of underestimation with respect to the MIrAD-US data set. The results further indicate that in areas such as Nebraska, where the climate is semi-humid in large parts of the state and irrigation is mostly supplementary, the method fails in detecting the irrigation signal.

5.6 Sensitivity of microwave soil moisture products to irrigation

By qualitatively examining the obtained results, we find that the sensitivity of the employed microwave soil moisture retrievals to irrigation and the performance with respect to reported irrigation data particularly depend on the following factors.

1. Spatial resolution of the microwave soil moisture products and topography. Likely, the largest restriction is the coarse scale of the satellite soil moisture retrievals with respect to the average field size. For instance, the area irrigated by a typical center pivot system (i.e., 500 m) is approximately 50 ha, which only accounts for approximately 0.0003 % of the satellite footprint area. Thus, around 3200 center pivot systems are needed to create a uniformly irrigated area covering the remotely sensed footprint. In the CONUS, areas with large irrigation fractions exist in the eastern half of the country, but irrigation in the arid western half is a lot more heterogeneous. In these areas, irrigation usually mainly depends on surface water supply and is therefore reserved to narrow river valleys such as the Colorado River valley. As a consequence, coarse-scale microwave soil moisture products may be insensitive to locally significant (but insignificant with respect to the scale of the satellite footprint) irrigation due to the small scale of the irrigation practices and surrounding complex topography (e.g., mountains, valley transitions, water bodies). As discussed in Sect. 5.1, in the Columbia River basin correlation patterns based on the ASCAT soil moisture product (which has a significantly higher nominal spatial resolution than the passive products) matched very well with the MIrAD-US product. An investigation of time series over this region (not shown) revealed that, there, ASCAT soil moisture carries a distinct seasonal irrigation signal. The reason why this pattern cannot be observed in Fig. 4c is that the regional noise level is well below the global threshold and thus irrigation is actually being masked. Lastly, as depicted by Fig. A1, irrigation water application rates are the highest in arid climates. We therefore expect that these drawbacks significantly contribute to the underestimation of reported irrigation water withdrawals.

2. Climate. As discussed in Appendix A, the method in its current formulation is only applied to rain-free periods during the growing season. We believe that this constraint accounts for a substantial part of the underestimation of $\stackrel{\mathrm{‾}}{\mathrm{IWU}}$ with respect to reported IWW. If rainfall cannot meet the plant's total daily evaporative demand, farmers may decide to irrigate even on rainy days. Farmers often irrigate on days with rainfall, on which evapotranspiration rates are lower and, hence, irrigation water loss decreases. Nevertheless, we did not come up with an adequate way of decomposing the impact of rainfall and irrigation in the soil moisture signal on a daily basis. At daily temporal sampling, in some cases satellite and model soil moisture show markedly different responses to precipitation events both in terms of temporal characteristics and intensity. This results in spurious irrigation events, which motivated us to constrain the method to dry periods. When full irrigation is applied in arid climates, the microwave soil moisture retrievals generally show promising skills in detecting the irrigation signals. In contrast, for the predominantly semi-humid climate (e.g., High Plains and Mississippi Floodplain) irrigation mainly aims at increasing yield or bridging dry periods (i.e., supplementary irrigation). Consequently, less irrigation water is applied and thus the microwave soil moisture retrievals may not appropriately capture less pronounced soil wetting.

3. Crop type and irrigation system. Water requirements naturally vary between crop types. Of the main crop types grown in the CONUS, alfalfa and rice typically require most irrigation water. In particular, flood irrigation for rice leads to a strong irrigation signal in the Sacramento Valley. The signal of flood irrigation is less distinct in the semi-humid climate of the Mississippi Floodplain, yet SMAP sensed a prolonged period of soil saturation which may be attributed to flooded fields (Sect. 5.3, Fig. 5e). However, the consistent rainfall in this region reduces the method performance, as the irrigation and precipitation signals in the soil moisture data cannot be disentangled. On the other hand, the extensive supplementary irrigation applied by center pivot systems in the High Plains does result in a minor irrigation signal in the soil moisture retrievals (Sect. 5.3, Fig. 5d). Intriguingly, the same dynamic was observed for other irrigated areas along the Ogallala Aquifer (Kansas, Oklahoma, Texas; not shown).

   We suggest that the differences in detectability may be related to the application efficiency of a particular irrigation system, which is defined as the ratio between the average low quarter depth of water added to root zone storage and the average depth of water applied to the field (in mm) (Pereira et al., 2002). Gravity irrigation systems have the lowest efficiency (approximately 60 %), followed by sprinkler (approximately 75 %) and micro-irrigation systems (approximately 90 %). Consequently, microwave soil moisture retrievals are expected to be most sensitive to flood irrigation, followed by sprinkler and micro-irrigation. The highest irrigation water consumption per area occurs in the western parts of the CONUS, particularly in the southwest (Fig. A1). Besides, farmers separately control their fields and focus on a different variety of crops based on market conditions, which in turn require different irrigation amounts and timing. This means that between satellite overpasses only a fraction of the fields within the satellite footprint will have received irrigation (based on the individual water management of each farmer). In addition, a center pivot irrigation system takes between 12 and 24 h to complete a full rotation circle, which means that at the time of satellite overpass only a fraction of a field has recently received irrigation. The same is true for other irrigation techniques, as irrigation equipment (e.g., pipes) has to be manually transferred across fields.

4. Satellite observation system and wavelength. Our results indicate that the observation systems (i.e., active or passive remote sensing system) have an impact on the sensitivity of soil moisture retrievals to irrigation. For instance, the water applied by certain types of irrigation (i.e., flood irrigation for rice) could not be comprehensively detected by the active ASCAT sensor due to specular reflection of the radar signal (see Sect. 5.3, Fig. 5b). On the other hand, the active microwave data (i) provided valuable information on the timing of both flood irrigation onset and field drainage and (ii) additionally allowed insights into the crop development cycle (i.e., backscatter increases when the vegetation starts to break through the standing water surface, potentially causing double-bounce effects, Nguyen et al., 2015). These dynamics largely agree with the observations reported by Lawston et al. (2017). Regarding the observation wavelength, we found that the SMAP L-band data showed more sensitivity than AMSR2 C-band data to the flood maintenance flow that is commonly established after the start of the growing season at the rice irrigated site in the Sacramento Valley, California. However, we cannot safely conclude whether this is actually due to the observation wavelength or to differences in the retrieval algorithms.