The Arkavathy watershed spans 4253 km2 on the western edge of the city of Bangalore in Karnataka, southern India (Fig. ). It has a monsoonal climate and mean annual rainfall of 820 mm. The monsoon season includes the southwest monsoon from June to September and the northeast monsoon from October to December. We therefore refer to April–May as the pre-monsoon period, June–December as the wet or monsoon season, December–January as the end-of-monsoon period, and January–May as the dry season. We also refer to the “monsoon year”, analogous to the usual concept of the water year, spanning the period from April to March of the following year. The watershed has a relatively stable daily maximum temperature of 27 ∘C, which peaks near the end of the dry season in April around 34 ∘C, before pre-monsoon rainfall arrives sporadically in April and May. The river is gauged at TG Halli reservoir (Location 2, Fig. b) and upstream of Harobele reservoir (Location 5, Fig. b).

The watershed contains a mix of urban, natural, and agricultural land uses. Agricultural land can be divided into rainfed grain crops, irrigated vegetable crops, Eucalyptus plantations, and other irrigated tree plantations (e.g., areca nut). Most present-day irrigation water in the Arkavathy is sourced from a deep, fractured rock aquifer. Irrigation from tanks is now significant in only a few locations, mostly located downstream of Bangalore. The city of Bangalore imports water from the regional Cauvery river and returns some urban wastewater to the Arkavathy system. Although many tanks are no longer in use, the tank structures remain intact and continue to capture inflow.

The watershed can be divided into eight subwatersheds (Fig. ), which include three major tributaries to the Arkavathy (Kumudavathy, Vrishabhavati, and Suvarnamukhi), and five other subwatersheds identified by reservoirs or geographic area (Hesaraghatta, TG Halli East, Manchanabele, Kanakapura, and Harobele). The major reservoirs in the watershed differ from the tanks in that they are actively managed, providing water for urban and agricultural water users. For this reason, we focus our analysis of hydrological change on the behavior of tanks.

The aim of the remote sensing analysis was to generate a time series of the surface area of water stored in each tank (referred to from now on as the “tank water extent”) in the Arkavathy watershed. There is minimal rainfall or flow outside the monsoon period, and analysis of tank areas within the monsoon period is inhibited by extensive cloud cover. The analysis therefore focused on end-of-monsoon images from the months of December and January (< 5 % of rainfall arrives in December).

Landsat satellite imagery was used for analyses, including 16 images taken in December or January between 1973 and 2010 which provided information about end-of-monsoon tank water extent. An additional 32 images were classified to assist in validation, and to provide information about tank water extent variations during the dry season (see Fig. S1 and Table S1 in the Supplement for imagery dates).

A range of pre-processing and quality assurance and control procedures were performed on the imagery, including converting all Landsat imagery to top-of-atmosphere reflectance , identifying missing regions of Landsat 1–3 MSS scenes, accounting for the failure of the scan-line corrector (SLC) in Landsat 7 ETM+ images , and masking of cloud shadows . The location of tanks within the resulting images was determined using a shapefile of tank boundaries obtained from the Karnataka State Remote Sensing Application Centre (KSRSAC, karnataka.gov.in/ksrsac), supplemented by 1970s topographic maps (surveyofindia.gov.in) for the beginning of the study period. The Supplement contains complete information on data sources (Table S2) and pre-processing of imagery (Sect. S1.1).

The tank water classification method relied on separating pixels containing water from pixels containing land in a spatial region defined by the mapped tank boundaries. Land cover surrounding wetted areas of tanks included vegetation, bare soil, and built-up urban land. We grouped these classes into a single land class, which was characterized by high reflectance in the near-infrared (NIR) band and lower reflectance in visible bands . Water stored in tanks in the Arkavathy watershed varied from clear (with low reflectance in all Landsat bands) to turbid (more reflective in the visible, and NIR bands, ). Turbid water exhibited its highest reflectance in the red band due to the red soils in the Arkavathy watershed . A conceptual representation of the classification algorithm is provided in Fig. , and the steps described below are cross-referenced to the numbered panels in the figure.

The Normalized Difference Water Index by , NDWI = (green - NIR)/(green + NIR), was calculated at a manually selected reservoir containing clear water (step 1). Otsu's method was then used to threshold NDWI into land and clear water classes, and the spectral means of both classes were calculated at the training reservoir (step 2). The minimum NDWI of water pixels at the training reservoir (step 3a) was used as a threshold to create a mask of “apparent” clear water for the entire scene (step 3b) which was then dilated using a 5 × 5 square kernel (a 3 × 3 kernel for MSS scenes). All pixels within the dilated mask were transformed to a single component, x^, parallel to the transect between the spectral means of clear water and land in the two-dimensional space of NIR and green reflectance (step 3c). Pixels falling between the x^ means of clear water and land were assigned a clear water fraction, in the range [0, 1], based on the linear distance between the end members along the x^ transect.

A similar procedure of masking, dilating, and unmixing was performed for turbid water, with minor changes. The criteria for apparent turbid water pixels were determined from land pixels near the training reservoir as the 98th percentile of red reflectance and the 98th percentile of NDWI (step 4a), provided that red reflectance was greater than NIR reflectance. Pixels meeting these criteria were included in the turbid water mask and dilated to include the surrounding area (step 4b). Spectral unmixing was conducted similarly to clear water, except that the component for unmixing, y^, was taken along the transect between the spectral means of turbid water and land in the NIR–red space (step 4c). Finally, the water area in each pixel was taken as the higher value of clear water area and turbid water area (step 5). Tank water extent was calculated as the sum of water area of all pixels within 2 pixels of the mapped tank boundary (step 6).

We did not estimate the area of water in any tank that was flagged for the following quality concern criteria: (i) spatial overlap or adjacency of dry tank boundary or wetted tank area with clouds or cloud shadows, (ii) spatial overlap of greater than 25 % of dry or wet tank area with missing pixels due to the scan line corrector (SLC) error in Landsat 7 images, or (iii) greater than 25 % spatial overlap of dry or wet tank area with the edge of the scene from MSS images (step 7). In each of these cases, the tank area was recorded as “NA”. Examples of the classification and resulting time series of tank water extent are shown in the Supplemental material for a small tank (≈ 25 ha, Fig. S4) and a large tank (≈ 160 ha, Fig. S5).

Remote sensing and spatial processing were scripted in R using the raster , rgeos , sp , and rgdal packages, as well as ggplot for plotting. Watershed delineation and extraction of the cascading tank network were completed in GRASS GIS .

Classification results were validated against a 5 m resolution LISS IV satellite image from 26 February 2014 using a classified Landsat image from 27 February 2014. The LISS IV image was classified in ENVI 4.9 (Harris Geospatial Solutions Inc.) using support vector machine (SVM) classification with four land classes and four water classes. After classification, the water classes were merged into a single water class and resampled to the resolution of Landsat so that the resulting grayscale classification contained a water fraction in the range [0, 1] for each pixel. The classifications were compared at both the pixel scale and tank scale, while ignoring tanks in which there were obvious differences due to the incongruous image capture dates (e.g., cloud cover).

At the pixel level, a traditional confusion matrix is inappropriate for continuous classification data . Thus, we evaluated the error (Landsat water fraction minus reference water fraction) in all pixels within tanks by binning the pixel error into categories representing under-classified (-1 to -0.2), correct (-0.2 to 0.2), and over-classified (0.2 to 1). We further separated pixels into groups by binning the producer (reference) water fraction and user (Landsat) water fraction. We calculated the producer's and user's accuracy for each water fraction bin to form both a producer error matrix and a user error matrix.

We also used Digital Globe imagery available from Google Earth to assess the validity of the classification in normal (680–955 mm) versus wet (> 955 mm) precipitation years during the study period. Given the limited availability of these images, we were unable to find a dry-year image (< 680 mm) within the study period that was suitable for comparison with a mostly cloud-free Landsat image. We manually delineated 18 tanks in the normal year (2009) and 34 tanks in wet years (2004 and 2005), and compared the manual delineation with classification of Landsat images from the same time period using a linear regression.

We developed a statistical model to identify changes in tank water extent that could be attributed to changes in streamflow production in the Arkavathy watershed. To achieve this, the model should control for drivers of water extent variability other than streamflow. Bathymetric surveys in the Arkavathy watershed indicate that tank water extent is a function of tank volumetric storage . Thus, a volumetric water balance for a tank can be used to consider the drivers of water extent variability, as follows: St2=St1+∑t1t2(P-Drainage-ET)Atank1+∑t1t2Qin-∑t1t2Qout-∑t1t2Withdrawals, where S indicates tank storage at time t2 when the Landsat image was taken, S(t1) is the storage in the tank at some prior time t1, P is the precipitation depth over the tank area, “Drainage” the drainage from the tank floor, “ET” evaporation from the tank surface area, Atank is the tank surface area, Qin the streamflow entering the tank, Qout the overflows leaving the tank, and “Withdrawals” any anthropogenic withdrawal from the tank itself, and sums are taken from t1 to t2.

In order to use a regression model to infer long-term hydrological change using records of water extent and precipitation data, we make the following assumptions to account for each of the terms on the right-hand side of the water balance:

the initial storage S(t1) can be approximated with zero,

Variations in P (2) were accounted for using daily rainfall data from 62 gauges from the Directorate of Economics and Statistics, Government of Karnataka (see Fig. S9 for station coverage). Precipitation trends were analyzed using Mann–Kendall non-parametric tests. Exploratory analysis at the whole-basin scale indicated that tank water extents were most related to precipitation totals from 1 September to the date of Landsat image acquisition. Contemporary observations in the Arkavathy watershed suggest that only the largest or most intense storms generate runoff. The average depth of large storms (> 10 mm day-1) from 1 September to the date of the Landsat image was used as a metric of extreme rainfall occurrence to account for these observations.

Finally, we accounted for losses by treating the sum of “Drainage”, “ET”, and “Withdrawal” fluxes as a lumped linear loss term focusing on the end-of-monsoon and early dry season. Previous analysis of monitored locations shows that since the early 1970s, no streamflow occurred in the Arkavathy watershed other than in months when rainfall occurred , and rainfall was minimal from 1 December onward. Changes in tank water extent from 1 December into the early dry season are therefore dominated by loss terms. We confirmed that these losses were stationary in six of the eight watersheds analyzed by bootstrapping the non-parametric Mann–Kendall trend tests using classified tank water extents obtained from 27 dry season Landsat images (see Fig. S8).

All analyses proceeded by considering two spatial scales: 8 subwatersheds and 42 smaller hydrologically connected subwatershed units, which are referred to as tank “clusters” (Fig. 3). Each cluster contained at least 15 tanks with non-zero water extent in at least 4 end-of-monsoon images (Fig. ). Aggregated tank water extents for each cluster form the basis for statistical analysis. Aggregating data in this way overcomes some of the challenges associated with a relatively short record and frequently dry tanks, while offering enough spatial resolution to identify variability in trends across the Arkavathy watershed. The analysis excluded reservoirs, because the water extent in a reservoir is also influenced by active management and water transfers. Some tanks were constructed during the study period, and these tanks were excluded from the analysis in any years prior to their construction.

These model features (1)–(5) were incorporated into a multivariate regression with interactions between continuous covariates and categorical variables e.g., see. The covariates used were cumulative monsoon season rainfall (from 1 September onward), denoted Ptotal; average depth of large storms during the monsoon season (from September 1 onward), denoted Pextreme; time delay from the beginning of the end-of-monsoon period (1 December) to the date of Landsat image acquisition, denoted DSD for dry season days; and the year in which the observation was made, denoted “Year”. The precipitation variables were calculated for each station, interpolated over the entire watershed using the inverse-distance squared approach, and spatially averaged for each cluster.

The Ptotal, Pextreme, and DSD covariates were modeled as fixed effects which interact with the subwatersheds. In other words, the response of the tank water extent to these variables was allowed to vary for each subwatershed, but was assumed to be consistent for the tank clusters within the subwatershed. The year effect was estimated separately for each tank cluster.

The model can be written as follows: Acluster,ij=C0+C1,kPtotal,ij+C2,kPextreme,ij2+C3,kDSDi+B1,jYeari+eij. The subscripts refer to the Landsat scene (i), tank clusters (j), and subwatersheds (k). Other than the intercept (C0), the fixed effects differ for each subwatershed (C1,k, C2,k, and C3,k) or tank cluster (B1,j). The errors for each observation are included as eij.

The model predicts the tank water extent per cluster (Acluster,ij), normalized by its maximum. Tank clusters were only analyzed for any given scene if ≤ 30 % of the total cluster tank area was missing (due to tanks being omitted for QA/QC purposes in classification, or not having been constructed by the date of analysis). All covariates were centered by subtracting the mean before being input into the model. We confirmed that collinearity between covariates was minimal and did not impact interpretation of confidence intervals or model output using generalized variance inflation factors (see Sect. S2.2 for details). The model performance was assessed using multiple R2 statistics and significance of all effects.

The primary result of interest is the “Year” effect on tank water extent for each cluster, B1,j. This effect represents a temporal trend in total tank water storage over time (as a percent change over time), after controlling for a stationary relationship between tank water storage and the covariates (Ptotal, Pextreme, DSD). In the six  watersheds where dry season losses were stationary, we attribute this change to changing inflows, as all other sources of non-stationarity are controlled for. In the two subwatersheds where a change in the effect of dry season water loss on tank storage was detected, B1,j captures the combined effect of hydrological change and non-stationarity in dry-season tank water losses.

Because the value of B1,j is the key result of interest, additional analyses were performed to confirm its importance. Specifically the model was refit while omitting the “Year” effect B1,j. The performance of the two models (with and without B1,j) was compared via R2 metrics. The significance of deviations between the two model predictions was tested using an F-test (H0: B1,j = 0, HA: B1,j ≠ 0, for at least one value of j).

We used four land use maps developed for 1973–1974, 1991–1992, 2001–2002, and 2013–2014 encompassing the TG Halli watershed, which contains the three subwatersheds upstream of the TG Halli reservoir (TG Halli East, Kumudavathy, and Hesaraghatta) and includes a total of 17 tank clusters. The maps differentiate agricultural land use classes into rainfed crops, irrigated crops, and Eucalyptus plantations. Irrigated agriculture in this region is supplied almost exclusively by groundwater, allowing us to test whether groundwater-irrigated crops, increased water utilization by Eucalyptus plantations , both, or neither, are associated with the identified streamflow trend.

In the early 1970s, rainfed agriculture was the primary land use in the TG Halli watershed. Over the study period, many farmers adopted groundwater irrigation and others converted their fields to Eucalyptus plantations, which have the potential to mine shallow groundwater or to significantly reduce deep recharge. These land use changes have the potential to reduce surface water flows by depleting subsurface water availability and baseflow over time, likely resulting in a non-stationary streamflow response. This non-stationarity, in conjunction with the relatively sparse availability of land cover data over time, complicated a direct analysis of land use against tank water level. Instead, a space-for-time approach was used to compare the differences in time-averaged land use across each tank cluster to the differences in the “Year” effect B1,j found for each cluster. We therefore calculate the time-average land use fraction corresponding to irrigated crops (Airrigated,avg) and Eucalyptus plantations (AEucs,avg) for each of the 17 tank cluster watersheds and regress (B1,j) against these land fractions: 3B1,j=CEucsAEucs,j+CirrigatedAirrigated,j. The coefficients, CEucs and Cirrigated, correspond to the sensitivity of hydrological change to time average Eucalyptus land cover and irrigated agriculture land cover, across all 17 tank clusters. This analysis is not designed to directly infer causation, but rather to understand associations between streamflow decline and agricultural practices.

The Landsat classification performed best for pixels that were fully dry or wet, when compared with the reference (LISS) classification (Fig. a). Producer's accuracy was 84 % for wet pixels and 99 % for dry pixels, and because of the high number of dry pixels the overall accuracy was 98 %. Pixels containing a mix of water and land (20–80 % water) had lower producer's accuracy (41–82 %). Overall, the classification errors were unbiased and the histogram of classification errors (excluding pixels with zero error) was approximately normally distributed (Fig. b).

The Landsat classification agreed well with the reference LISS classification at the tank scale, and accuracy improved with increasing tank size. A regression of Landsat extent versus reference extent (Fig. ) for tanks less than 25 ha (278 pixels) had a slope of 0.98 and a coefficient of determination (R2) of 0.95. When all tanks and reservoirs were included, the regression line had a slope of 1.02 and a coefficient of determination of 0.99. Over 99 % of dry tanks were correctly classified as dry, but error was considerably larger for small tanks with non-zero water extent less than 2.5 ha (28 pixels), due to false positives in the reference classification as well as errors in the Landsat classification. For tanks between 2.5 and 10 ha the classification performed considerably better. The mean absolute error increased as the extent of the water body increased, but mean percent error decreased with water body size. Our automated Landsat classification similarly compared well with the Google Earth manual delineation of tanks in both normal years (R2 = 0.97) and wet years (R2 = 0.97) (see Fig. S6).

Although the time variations in most tanks have not been reported via in situ measurements, trends in water storage over time are widely known for some of the major reservoirs. The TG Halli and Hesaraghatta reservoirs declined from a peak storage in the 1970s to much lower contemporary storage. Large increases in water extent were observed in the Manchanabele reservoir, which was constructed in 1993, and the Harobele reservoir, which was constructed in 2004. These anecdotal trends corroborate our findings for these specific structures (Fig. S7).

Trend analysis of the 62 rain gauges in the watershed showed that there were no statistically significant trends in rainfall at the whole watershed (see Fig. S10), subwatershed (not shown), or tank cluster (see Fig. S11) scales. Precipitation has thus been stationary, although exhibiting considerable inter-annual variability during the period of analysis, and any identified trends in tank water extent over time can exclude consideration of precipitation change as a driver.

The multivariate analysis explained nearly 70 % of the variation in tank cluster water extent (R2 = 0.68). Model residuals were normally distributed (Fig. S12). The effects of both precipitation covariates (Ptotal and Pextreme) were significant (the 95 % confidence interval of the slopes excluded zero) in nearly all subwatersheds, and the effect of dry-season water loss was significant in the two subwatersheds that flow into TG Halli reservoir. Inter-annual variability in precipitation (Ptotal and Pextreme) explained 63 % of the total predicted variability in tank water extent over the study period, while the DSD term explained 10 % of the variability. Variability in tank water extent due to precipitation was fairly similar across clusters, while the variability due to temporal trends varied greatly across clusters.

The multivariate analysis identified significant “Year” effects B1,j (Table S3, Fig. S13) in 13 tank clusters. B1,j varied in its sign and statistical significance among tank clusters, and explained 27 % of the total variation in tank water extent. In the two subwatersheds flowing directly into the TG Halli reservoir, B1,j captured the combined effect of non-stationarity in streamflow generation and non-stationarity in dry-season tank water losses (lower tank losses increase B1,j). If the sign of B1,j is negative in these tanks, it implies that the effect of non-stationarity in streamflow generation must both be negative and exceed the effects of reduced tank water losses. We converted the units of B1,j to an areal rate of change over time per 10 km2 of catchment area (Fig. ). In the three subwatersheds upstream of TG Halli reservoir, most tank clusters exhibit negative Bi,j values, implying reductions in streamflow generation. Tanks within Bangalore generally exhibited negative “Year” effects, and tanks at the city periphery and immediately downstream of the city had positive effects. Other regions of the watershed exhibited mixed values of Bi,j, but none were statistically significant at the 95 % confidence level.

We confirmed that the “Year” effect B1,j was important for understanding the variations in tank water extent. Omitting the “Year” effect from the tank water extent model lowered the R2 from 0.68 to 0.58. Furthermore, the model predictions with and without the “Year” effect were significantly different according to the F-test (p < 3.1 × 10-11). These results allow us to reject the null hypothesis that B1,j = 0, meaning that the “Year” effects could not be ignored.

Overall, the results indicate that, while inter-annual variations in rainfall totals and extremes explain the majority of inter-annual variation in tank water level, a trend in tank water level is present in several regions of the Arkavathy watershed that is independent of rainfall variability. This trend cannot be explained by trends in rainfall, which were negligible (Figs. S10 and S11), by trends in dry season tank water loss rates, which, where they existed, had the opposite sign to the identified trend in water level (Fig. S8), or by changes in outflows, which are constrained to occur when tank storage is at its peak. The results suggest that changes in streamflow production independent of rainfall are occurring in discrete locations in the Arkavathy watershed, and that the sign of these changes varies through space.

The regression of the “Year” effect B1,j on irrigated agriculture and Eucalyptus land use areas explained most of the differences in B1,j between tank clusters (R2 = 0.68). The relationship between irrigated crops and B1,j was statistically significant (95 % confidence intervals of Cirrigated excluded zero), and the relationship with Eucalyptus plantations was not statistically significant (Fig. ).

Tank water extent at the end of the monsoon season can be primarily attributed to the storage of monsoon season streamflow, given that tanks in the Arkavathy watershed rarely overflow, there is little carry-over storage year to year, and loss processes do not extensively deplete the tanks from the end of the monsoon period to the time when tank water extents were observed by Landsat. Thus, storage of water in tanks offers an integrated measure of tank inflows during the previous wet season.

Statistical analysis of the tank water extents suggests that while inter-annual variability in tank water extent is largely explained by precipitation, this variability is superimposed on a longer-term trend in tank water extent that is independent of precipitation, representing a non-stationarity in inflows. Analysis of rain gauges indicated that precipitation has been stationary within the watershed during the study period. Non-stationarity in inflows, coupled with stationarity in precipitation, indicate changes in the runoff ratio (defined as flow production per unit precipitation), a common indicator of changing hydrological processes .

Historical land use maps for the TG Halli watershed indicate that there is an association between the inferred streamflow generation trends (particularly streamflow declines) and human drivers of change. We hypothesized that the inferred decline in streamflow would correspond to agricultural practices associated with groundwater depletion. Although few data exist to describe historical declines of the water table, contemporary farmers typically have to drill new borewells to depths exceeding 100 m to reach any groundwater. If a loss of baseflow due to groundwater depletion and the disconnection of the water table from the stream channel is a primary driver of streamflow decline, we would expect the negative trends in streamflow to correspond to irrigated agriculture, which is supplied almost entirely by groundwater in the TG Halli watershed.

In the linear model relating the “Year” effect B1,j to land use in the TG Halli watershed (Eq. , Sect. ), the time-averaged irrigated crop land use area is a clearer and stronger predictor of declines in tank water extent than Eucalyptus land use (Fig. ). Moreover, other exploratory analyses showed that irrigated crop land use has a higher correlation with B1,j (R2 = 0.68; see Fig. S14) than rainfed crops (R2 = 0.5) and all other land use types (R2 < 0.38). Areas retaining mostly rainfed crops exhibit higher (less-negative) values of B1,j, and lower (more-negative) values of B1,j are associated with areas with higher conversion of rainfed crops to irrigated crops. The finding that Eucalyptus plantations do not play a major role in streamflow decline is consistent with field experiments, which show that that Eucalyptus plantations tend to reduce soil infiltration capacity and therefore would increase infiltration excess runoff . There could be some relationship between Eucalyptus plantations and non-stationary hydrologic processes, but if so it is secondary to that of irrigated crops.

Areas with a high fraction of irrigated agriculture are also likely to contain relatively higher densities of check dams than other land use types, given the desire to recharge diminished groundwater resources. In the absence of datasets describing the spatial distribution and hydrological properties of check dams (or a viable way to develop such a dataset), this analysis is unable to separate the effect of loss of baseflow due to groundwater pumping from the in-stream losses due to check dams. Both processes likely play a role in observed hydrological changes. Recession analyses indicate that the loss of the shallow water table could plausibly explain the observed magnitude of streamflow declines , and check dams exacerbate the loss of streamflow by converting water in the stream channel to groundwater recharge .

The most negative values of B1,j and thus the largest inferred reductions in streamflow production occurred in the northernmost regions of the Arkavathy where elevation is higher than other areas of the watershed. Although it may appear that the pattern of decline could be related to upstream–downstream processes and the presence or absence of irrigation return flows , we are doubtful that this effect is important in the Arkavathy at present. Indirect evidence (e.g., surveys) indicates that the water table is hundreds of meters below the surface in the northern parts of the Arkavathy watershed . Furthermore, the relief in the watershed is ≈ 100 m over a distance of 50 km in the TG Halli watershed, meaning that system-wide return flows connecting upstream to downstream are unlikely.

Urbanization could result in increased streamflow being routed to downstream tanks, due to increases in impervious surfaces, the fallowing of agricultural land in anticipation of urbanization, and reduced consumptive water use. Increased urban water use produces increased urban effluent, which is discharged to the surface channel network where it can contribute to increases in tank water storage downstream. The observed positive “Year” trends downstream and on the periphery of the Bangalore urban area are consistent with the substantial increases in Bangalore's imports from the Cauvery river, from 185 million L day-1 (million liters per day) in 1974 to 1350 million L day-1 currently . Additionally, as the city has grown, groundwater pumping for urban areas has increased to an estimated 600 million L day-1 . About 40 % of Bangalore's sewage of 1400 million L day-1 flows to Byramangala reservoir . This has contributed to additional inflows to Byramangala reservoir and more irrigated agriculture directly downstream of the reservoir. Tanks within urban areas can also exhibit drying trends. For instance, tanks may be encroached upon as residential areas expand. Additional urban wastewater inflow can lead to expansion of algae blooms covering the tank water surface, which can appear as a “drying” of the tank in this analysis.

The classification of small tanks in the Arkavathy watershed poses challenges associated with harmonization of different Landsat sensors and the variability in the spectral properties of “wet” tanks due to variations in water quality and vegetation extent. The classification tends to overestimate the amount of water in dry pixels and underestimate the amount of water in wet and mixed pixels. Because our classification scheme is designed to avoid bias between images taken with different Landsat sensors, we likely sacrifice some precision with sensors from Landsat missions 5 to 8.

Because these mixed pixels lie at the boundary of the wetted tank area, classification error would be sensitive to geo-registration error in one or both of the Landsat and LISS images. Error could also arise from our specification that water pixels must lie within 60 m of clearly identifiable water bodies, or the assumptions made during spectral unmixing. Although the classification scheme accounted for only two classes, the spectral properties of the land class varied among dry soil, wet soil, sparse vegetation, and irrigated agriculture. Classification of water was complicated by vegetation in tanks, varying degrees of turbidity, and algae blooms in tanks with considerable wastewater inflow.

Errors at the pixel and tank scales are likely unavoidable given the spectral heterogeneity of both land and water pixels. In particular, tanks containing water of variable turbidity, excessive vegetation, or algae blooms are prone to classification errors. Because pixel-scale errors are unbiased, accuracy at the tank scale improves as tank size increases. Error is further mitigated by grouping tanks into clusters in the statistical model.

The uncertainty of the classification (R2 = 0.99 when all water bodies are included) is small compared with the uncertainty of the statistical model (R2 = 0.68). Although the results of our statistical model imply a non-trivial amount of unexplained variation, reported similar performance (R2 = 0.78) for a model relating precipitation and water extent in a single lake, and noted that the correlation was valid only for a 9-year subset of the 5-decade study period. The sources of uncertainty include the complex hydrological processes that relate precipitation, streamflow, and tank water storage, as well as the nonlinear and heterogeneous relationship between water extent and water storage, the neglect of pre-monsoon tank water extent in the model, and the non-stationary behavior of dry-season losses in the two northernmost watersheds. Given this uncertainty, results of our analysis are reasonable given the simplicity of the model and the complexity and heterogeneity of the watershed hydrological response.