Data and methods

For each watershed, we used a digital elevation model (DEM) with 30 m resolution. We obtained the National Hydrography Datasets (NHDPlus) DEM from the Horizon System Corporation website (www.horizon-systems.com). NHDPlus was developed with the assistance of the United States Environmental Protection Agency (EPA) in collaboration with the United States Geological Survey (USGS). Based on the DEM, watershed slopes were computed to differentiate hilly terrains from plains. In particular, the variability in slope across the watersheds was determined using a 5% slope as a threshold. This threshold was chosen based on previous studies involving the Lower Colorado watershed (e.g., Wang et al., 2009; Ahmad et al., 2010), which reported that the spatial contrast in topography is best resolved by applying a 5% threshold.

2.4.2. Precipitation data

The spatial domain is characterized by a sharp east-west precipitation gradient.

Studying summer precipitation in the monsoon region of the southwestern United States,

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which coincides with our study domain, Gutzler (2000) considered precipitation data for the months of July and August. Here, we consider monthly precipitation amount and number of wet days with precipitation greater than 13 mm (i.e. 0.5 inches) for JJA. The correlation between the rain event days and monthly precipitation totals was higher when the threshold for the rain event days definition was set lower. Across the precipitation stations considered, on average the number of rain event days with precipitation depth >3 mm (0.1 inches) explained more than 72% of the variance in JJA total precipitation time series , while this variance was less than 58% for depth >13 mm. However, defining rain event days as days with precipitation >13 mm reduces the potential collinearity inference on the robustness of the study.

Precipitation data for the last five decades, 1960–2010, were used from 370 precipitation stations over the selected watersheds (Figure 2). We collected the data from the National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center (NCDC) (http://www.ncdc.noaa.gov). NOAA’s NCDC provides historical precipitation data from land based stations. Of those 370 stations, 62 are in Arizona, 71 in Arkansas, 36 in Louisiana, 59 in New Mexico, 69 in Oklahoma, and 73 in Texas. A number of criteria were defined for selecting precipitation stations. First, we only considered stations with historical data for the period 1960 to 2010. Note that from the thousands of operating rain gauge stations, only a low percentage of them met this criterion. As a second criterion, we only retained rain stations having less than 5% of missing data. We used the inverse distance weighted (IDW) method (Di Luzio et al., 2008), based on the three nearest stations to in-fill missing values.

21 2.4.3. Measurement of precipitation disorder

Various indices and statistics have been used to analyze the variability of biophysical phenomena in time and space. Among them, approaches based on variance are common. Variance is an expression of the dispersion from the mean. However, variance is unit based and is amplified, depending on the scale of measurement. The unit issue can be corrected using the coefficient of variation (CV), which is the ratio of the standard deviation (σ) to the mean (μ), CV  . The coefficient of variation can be viewed as the rate of departure from the mean. In the case of seasonal precipitation the magnitude depends on the spatial location. Two precipitation stations may have records following the same probability distribution but they may have different statistics because the range of precipitation totals is high at one station and low at another. Thus, it may be problematic to compare an arid region to a humid region using standard deviation for assessing variability in precipitation records. However, there are unique approaches to overcome these shortcomings in quantifying precipitation variability that are not biased by the spatial heterogeneity of precipitation. One of these approaches is based on Shannon entropy, which has been successfully used in a number of studies (e.g., Kawachi et al., 2001; Singh, 1997).

The entropy theory, developed by Shannon (1948), is probabilistic and therefore applies to random events. Two locations with precipitation data of similar probability distributions will have the same entropy value. At each rain gage k, the historical precipitation data were binned in order to derive a probability distribution. The Shannon entropy Hk was then computed using the formula:

22 where Hk has units in bit, N is the number of discrete intervals for events (precipitation amount, number of rainy days), and pi is the probability associated with bin i. While assessing the entropy based precipitation variability over the state of Texas, Mishra et al.

(2009) used a Disorder Index (DI), which is the difference between the maximum entropy value Hmax and the computed entropy value at a specific rain gage k (Hk): distribution (Mishra et al., 2009). The DI is a measurement of the difference between the maximum entropy and the actual entropy. A lower entropy value is equivalent to a bigger difference, or DI, which indicates higher variability.

We also employ this DI approach and, from the entropy based disorder indices generated for the stations, produce maps of the precipitation variability distribution across our domain. Combined maps of precipitation disorder and terrain slope were constructed for each watershed and comparative analyses are then employed.

2.4.4. Investigating watershed topography effect on summer precipitation disorder We compare how precipitation disorder varies across hilly versus flat terrains to infer the potential role of watershed topography. We focus on the lower Colorado basin, as it presents a clear differentiation between these two reliefs (hilly/plain). The central part of the Lower Colorado River basin, which also encompasses central Arizona, is particularly hilly and was therefore also considered by Wang et al. (2009) as part of the

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intermountain region of the Western United States. Using a threshold of 5% slope, we produce a map where hilly regions are differentiated from the plains regions and the intermountain region of the watershed (Wang et al. 2009).

To assess the role of watershed topography on the disorder in summer precipitation patterns, we first selected transects of 2 km regions across the watershed. The averaged slope and entropy-based disorder indices were derived for each region and analyzed via regression analysis. We then used spatial regionalization based on principal component analysis (PCA). PCA is widely used in climate regionalization analyses (e.g., White et al., 1991; Comrie and Glenn, 1998; Frauenfeld and Davis, 2002; Gutzler, 2004). Our purpose is to identify similar topographic regions in the Lower Colorado basin based on the disorder in summer precipitation records. Indeed, in the western U.S region, the topography influences warm season precipitation, particularly in terms of precipitation totals (Leung et al., 2003).