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A tool for drought planning in Oklahoma: Estimating and using drought-influenced flow exceedance curves
Journal of Hydrology: Regional Studies 10 (2017) 35–46
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A tool for drought planning in Oklahoma: Estimating and using drought-influenced flow exceedance curves R.B. Miller a , G.A. Fox b,∗ a b
Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK, USA Department of Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC, USA
a r t i c l e
i n f o
Article history: Received 19 August 2016 Received in revised form 6 December 2016 Accepted 4 January 2017 Keywords: Drought Flow duration curve Oklahoma Streamflow Water supply
a b s t r a c t Study region: The study region is the state of Oklahoma, USA, which has a varied climate. Precipitation increases west to east, and temperature decreases south to north across the state. Accordingly, Oklahoma has been divided into nine Climate Divisions, which reflect those climatic as well as regional differences in agricultural practices. Study focus: Surface water is the dominant source for public water systems in Oklahoma and these supplies may be impacted by drought or climatic change. Hydrologic modeling is an important component of water resource planning, but may be beyond the budget of smaller communities. To create a freely available tool for initial assessment of drought streamflows, this study uses publicly available long-term precipitation records for climate divisions in Oklahoma to create flow duration curves (FDCs) from the drought-influenced subsets of streamflow records. New hydrological insights for the region: The FDCs created from those subsets showed increased likelihood of reduced streamflows. The reduced flows were shown to increase water supply risk to run-of-river users. To eliminate the need for users to re-create these analytic steps, study results were compared to published FDCs and reasonable estimates of drought-influenced FDCs were produced by offsetting the expected exceedance by 10%. © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction A drought is in its essence a deficit of water, primarily driven by a reduction in precipitation, and which may have significant impacts on human lives. The American Meteorological Society describes drought as a “complex interplay between (1) natural precipitation deficiencies, or excessive evapotranspiration over varying time periods and different areal extents, and (2) the demands of human and environmental water use that may be exacerbated by inefficiencies in water distribution, planning, and management” (AMS, 2013). Hence, the human experience of drought can depend both on the severity (e.g. duration and intensity) of the moisture deficit, and on the means for coping with the drought’s effects.
∗ Corresponding author at: North Carolina State University, Department of Biological and Agricultural Engineering, Campus Box 7625, Raleigh, NC 27695-7625, USA. E-mail address: [email protected] (G.A. Fox). http://dx.doi.org/10.1016/j.ejrh.2017.01.001 2214-5818/© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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Fig. 1. Oklahoma Climate Divisions (OCS, 2016). Climate divisions follow political boundaries, and are based on physiographic factors such as soil type, topography and elevation, meteorological factors such as annual precipitation and temperature, and economic factors such as typical crop types (Guttman and Quayle, 1996).
Fig. 2. Annual precipitation history for Oklahoma CD 3 (Northeast Oklahoma), showing the overall mean precipitation for the period 1895–2015 (39.3 in, 99.8 cm), as well as annual precipitation totals and the 5-year moving average (OCS, 2016). Periods below the overall average are colored brown, and above the average are colored green.
1.1. Oklahoma climate and drought planning Oklahoma has a varied climate influenced by differences in terrain as well as by precipitation that increases west to east and temperature that decreases south to north. The Oklahoma Climatological Survey (OCS) has divided the state into nine distinct Climate Divisions (CDs) (Guttman and Quayle, 1996; OCS, 2016) (Fig. 1). Precipitation plots based on records dating from the 1890’s have been prepared for each of the CDs, reflecting how the climatic and physical gradients affect precipitation in each of those (Fig. 2). Those precipitation plots illustrate the high variability over time including historic droughts in the 1930’s and 1950’s. Additionally, climate change projections for Oklahoma may include higher temperatures and increased periodicity of rainfall over current norms (Liu et al., 2012; OWRB, 2012). Surface water is the dominant water source for users in Oklahoma outside of irrigated agriculture, representing 70% of the supply (Fig. 3). Municipal water suppliers are among the largest single water users in Oklahoma, representing 35% of all water and 60% of surface water use. Variations in the amount and timing of rainfall would be expected to have effects on surface water supplies, and in turn affect much of the state’s population and economy. Drought response involves many aspects of planning, including prediction and monitoring of drought events as well as mitigation of drought effects (Wilhite et al., 2000; Pirie et al., 2004; Goodrich and Ellis, 2006; Wilhite and Svoboda, 2007). Oklahoma is one of a majority of states whose drought-planning emphasis has been placed on prediction and monitoring,
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Fig. 3. Surface and groundwater permitted use by economic sector in Oklahoma (from OWRB, 2016c). Public Water Supply represents the 2nd largest sector overall, the 2nd larger groundwater user, and the largest surface water user. Omitting crop irrigation, the public water sector represents 69% of all remaining permitted water and 60% of surface water permits.
while less has been directed toward planning in advance of a drought crisis (Wilhite et al., 2000; Pirie et al., 2004; NDMC, 2016). Current drought planning tools in Oklahoma serve as response aids once a drought crisis is underway; however, there is little to help in pre-crisis planning, such as assessing the adequacy of established water resources or developing secondary sources to use under drought conditions (OWRB, 2016a,b,c).
1.2. Flow duration curves Flow exceedance curves are a statistical representation of flow probability, in which the probabilities are expressed as the percent of time that a given daily flow will be exceeded within a time period similar to the period of record (Searcy, 1959; Vogel and Fennessey, 1994; Vogel and Fennessey, 1995). By definition, in an FDC the smallest flows have a high likelihood and large flows a low likelihood of being exceeded. The shape of a FDC is useful for evaluating and comparing watershed hydrology (e.g. Searcy, 1959). In relation to this study, FDCs have been utilized for water use planning purposes, including design of run-of-river applications such as calculating minimum wastewater treatment (Searcy, 1959; Vogel and Fennessey, 1995) and for water resource allocation (Vogel and Fennessey, 1995).
1.3. Drought-influenced flow duration curves Planning for drought is an important component of drought resilience for Oklahoma communities. Wilhite et al. (2000) and Svoboda et al. (2011) have identified gathering information about water resources as an important early step in drought planning. However, many communities may not take this step given the expense of preparing a hydrologic model; Engle (2012) identified financial considerations and resource issue awareness as two major barriers for drought planning for community water suppliers. This research used published precipitation trends and streamflow records to create a tool that can indicate the general magnitude of flow reduction that can be expected under local drought conditions. The intent is to lower the threshold for drought planning at the small community level in Oklahoma by creating a publicly accessible and easy to implement first step in the process. We hypothesize that FDCs based on streamflow records from below-average rainfall years will contain valuable information about the general flow tendencies of those streams during drought events. While such records cannot answer questions about how a particular year of drought will affect streamflow, they can describe the important differences between the expected flows under normal and low-rainfall conditions. Finally, by estimating those drought-influenced flow differences in terms of the FDCs that have already been prepared for Oklahoma streams, a tool was developed that will allow smaller communities and public water suppliers to assess the need for further and more advanced drought planning.
2. Materials and methods The purpose of this research was to develop a method to estimate the expected range of drought flows using existing data. The research product was intended to help with drought mitigation planning, especially for small utilities that lack budget flexibility, by allowing a rapid estimate of expected drought impact on stream-based surface water sources. The flowchart shown in Fig. 4 outlines the process that was applied to stream gage records throughout the state. Each step in the process is explained in more detail in the following sections.
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Fig. 4. Flowchart portraying the steps followed to create the ‘normal” exceedance of drought-influenced streamflows. The subset of streamflow records (a., Section 2.1) is created using the below-average precipitation years to select daily mean streamflow records from the full records of streamflow at each gage. Flow duration curves (FDCs, b., Section 2.2) are prepared using the drought-influenced subset of daily mean flows. The full record FDCs are obtained from Lewis and Esralew (2009). The “normal” exceedance probabilities of the drought-influenced flows (c., Section 2.3) are calculated by linear interpolation using the full-record FDC for the gage (Lewis and Esralew, 2009). Finally, drought-influenced vs, “normal” exceedances (d., Section 2.4) are plotted to show the estimated exceedance difference.
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Fig. 5. Annual precipitation record (black symbols) for CD 6 (East Central Oklahoma) with 5-year running averaged periods below the overall mean shaded in brown and above the mean in green. The “below” precipitation periods are used to select “drought-influenced” flows from the stream gage record at Barren Fork near Eldon, OK (7197000) shown below.
2.1. Subsetting the streamflow records A full record of daily average streamflows was obtained for each USGS gage used in the study. Then a subset of daily average streamflows for each USGS gage located in that CD was then prepared by selecting the daily average streamflow records from the tagged below-average precipitation years (Fig. 5). The vast majorities of those gages represent non-reference streams and thus exhibited some degree of hydrologic alteration or flow regulation (Lewis and Esralew, 2009), and only gages directly downstream of dams were eliminated from analysis. The annual precipitation history for each of the nine Oklahoma CDs was examined and each year was tagged as above- or below-average depending on the value of the five-year average relative to the overall mean precipitation calculated for the dataset (Figs. 4 a, 5).
2.2. Creating drought-influenced flow duration curves The USGS public access software program Surface-Water Statistics (SWSTAT), which is included as a module within Basins 4.1 (Basins 4.1; Aqua Terra Consultants, Decatur, GA), was used to prepare drought-influenced FDCs from the subset of streamflow records (Fig. 4b). It should be noted that the term “drought-influenced” was chosen in part to distinguish the subset FDC from FDCs prepared from the full record of streamflows, and to avoid confusion with “hydrologic drought” as defined by Dracup et al. (1980) and others. Lewis and Esralew (2009) have prepared and reported FDCs and other streamflow statistics for the more than 190 active US Geological Survey (USGS) stream gages in Oklahoma with at least 10 years of streamflow record. The full record FDCs for gages used in this study were obtained from that document.
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2.3. Normalizing flow duration curves for comparison Gage records represent different watersheds and flows of different magnitudes, and therefore drought-influenced flow magnitudes are not directly comparable between gages. In order to compare records from different gages, the droughtinfluenced streamflows were normalized by estimating the full-record exceedance for each of the drought-influenced flows (Fig. 4c). The discharges from the drought-influenced FDC were assembled and the exceedances of those flows were calculated from the full-record flow duration curve using linear interpolation. Those calculated values were labeled “normal exceedance”, and correspond to the estimated exceedance probability from the full-record of a drought-influenced flow. The relationship between drought-influenced and normal exceedance is independent of scale, so that gages with different flow volumes can be combined and compared. The pairs of drought-influenced and normal exceedance values were grouped by CD and also for the entire state, and the mean and standard deviation of normal exceedance for each drought-influenced exceedance was calculated. The plotted mean values were generally curvilinear, but there was a relatively linear section between 75% and 15% exceedance, and a line parallel to the 1:1 line in this interval was fitted to the mean normal exceedance values by allowing the intercept to vary and minimizing the RMSE (Fig. 4d). This calculated offset value represents a general estimate of the probability difference in flows between the drought-influenced and full streamflow records for each CD and for the state as a whole. 2.4. Statistical comparisons of flow duration distributions There was a need to compare the drought-influenced and normal exceedance flow distributions to determine if the differences (if any) between the two distributions were significant. However, normal statistical comparisons would not be suitable, since those techniques measure some sort of central tendency weighted by variance in the data, and both distributions ranged from an exceedance of 1–99. Green and Xu (2005) developed a technique to determine the significance of differences between equivalent bins in histograms generated for the reflectance from groups of remotely-sensed clouds. Their technique involved calculating the Euclidean distance between equivalent bins in the histograms representing the averages of two cloud populations, and then comparing that value to the equivalent distance values generated by randomly assigning members to the two classes (Green and Xu, 2005). The approximated significance level (ASL) test, a statistic for the difference, was calculated as: ASL =
C n
(1)
where C is the number of random combinations larger than the actual, and n is the number of random iterations. The ASL is compared to ␣ and assumed significant if ASL ≤␣. Following Green and Xu (2005), an approximation of the statistical significance of differences between the droughtinfluenced and normal exceedance of flows for gages in each CD were calculated. This method was applied to the droughtinfluenced dataset by calculating the Euclidean distance between a given drought-influenced exceedance and its estimated “normal” exceedance percentage (L2 ): L2 =
(ai − bi )
2
(2)
i
where a is a drought-influenced exceedance and b is its equivalent “normal” exceedance. Once the original distance was calculated, groups were randomly assigned 1000 times for each CD, and the L2 calculated. The ASL was considered significant at ␣ = 0.05. 3. Results and discussion A total of 128 USGS gages were utilized in this study (Table 1). There was an uneven distribution of gages within the CDs, ranging from six gages in CD 1–20 in CD 6. The distribution of USGS gages likely corresponds to the local need for information about surface water. Factors that may influence the high density of USGS gages in that region included a high utilization of irrigated agriculture drawn from surface water in CD 7 and CD 8, a combination of irrigation and urbanization in CD 5, and Oklahoma Scenic Rivers, navigable waterways, and urban surface water sources in CD 3 and CD 6. In contrast, while CD 1 (Panhandle) has a high density of irrigated agriculture, the irrigation water is primarily drawn from deep groundwater sources and few stream gages are required. 3.1. Subsets of USGS gage records The USGS stream gages do not have the same period of record as the precipitation records, so the subset of flow records may or may not be reduced relative to the full record. Subsetting the gage records reduced the flow record length, and the ratio of drought-influenced to full record length had a statewide mean of 0.45, meaning that generally less than half of the full years of record were included in the drought-influenced subset. However the reduction ratios for the CDs were not all
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Table 1 The number of gage records used for each Climate Division (CD) and the state as a whole, the fitted values for the intercept of an offset line for “Normal” exceedance between 15 and 75% for plotted drought-influenced vs. normal exceedance values, and the average standard deviation of the normal exceedance values for the range 15 to 75. Although the entire statewide dataset was used in all relevant calculations, CD 1 appeared to be an outlier in many respects and statewide totals without CD 1 are included as reference. Climate Division
Number of Gages
“Normal” exceedance intercept
Standard Deviation
1 2 3 4 5 6 7 8 9 State (with CD 1) State (without CD 1)
6 9 16 9 19 20 17 17 15 128 123
0 8.7 6.8 7.5 12.8 9.0 10.2 8.0 7.6 8.4 8.9
5.9 3.3 2.2 8.3 5.2 3.8 5.8 6.1 2.3 5.6 5.2
Fig. 6. Ratio of drought-influenced to full years of records for USGS gages by Oklahoma CD. The ratio for CD 1 was very high, indicating that the droughtinfluenced record for those gages was very similar to the full-record. That difference was significant (P = 0.03) using the Kruskal-Wallis One Way Analysis of Variance on ranks.
the same: the ratios for each climate division are close to 0.5 with the exception of CD 1, which was 0.7 (Fig. 6). The larger ratio for CD 1 means that the drought-influenced record is relatively similar to the full record. In CD 1 there have historically been very few stream gages, and many of those were only in place during periods of low precipitation; of the six gages included from CD 1, three showed no difference between the full and the drought-influenced years of record. Although CD 1 appears to be an outlier in terms of gage records, in the interest of geographic completeness those data were included in all analysis and discussion. 3.2. Statistical comparisons The ASL test was conducted to determine if the “normal” exceedance was different from the drought-influenced exceedance. The ASL test results showed that the differences between the drought-influenced and “normal” FDCs were significant at ␣ = 0.05, with the exception of CD 1 (Table 2). As noted above, the drought-influenced subset of flow records for CD 1 was very similar to the full record; hence, there was little difference between the drought-influenced and “normal” exceedances. 3.3. Drought-influenced and full record comparisons The FDCs for the drought-influenced records showed lower flows relative to the full-record FDC. This difference in expected flow magnitude is illustrated in the FDC comparison for the USGS gage Barren Fork Creek (BFC) near Eldon, OK (Table 3, Fig. 7), where the full-record median (50% exceedance) flow was 3.5 m3 s−1 (125 ft2 s−1 ) while the droughtinfluenced record median was 2.3 m3 s−1 (82 ft2 s−1 ). Linear interpolation shows that the drought-influenced median flow would “normally” be exceeded 61% of the time. From another perspective, the drought-influenced median flow at BFC can be approximated by substituting the 60% exceedance flow (∼“normal” exceedance of 61%) from the full record (Table 3).
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Table 2 Calculated Approximated Significance Level (ASL) by Climate Division for the summed Euclidean distance between the drought-influenced and “normal” exceedance flows. The ASL was considered to represent a significant difference between flow duration curves if ASL <0.05. Significant values are shown in bold. Climate Division
ASL
n
CD 1 CD 2 CD 3 CD 4 CD 5 CD 6 CD 7 CD 8 CD 9 Statewide
0.59 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00
1000 1000 1000 1000 1000 1000 1000 1000 1000 6000
Table 3 Flow exceedance probabilities calculated with SWSTAT using full- and drought-influenced record daily average flow data for the USGS gage 7197000 (Barren Fork Creek at Eldon, OK). Also shown is the “normal” exceedance of the drought-influenced flow, which has been calculated by linear interpolation of the drought-influenced discharges on the full-record FDC. USGS 7197000 Barren Fork Creek at Eldon, OK Daily flow (cms) Exceedance probability (%)
Full-record
Drought-influenced
“Normal” Exceedance (%)
98 95 90 80 75 70 60 50 40 30 20 15 10 5 2 1
0.27 0.45 0.71 1.16 1.39 1.67 2.41 3.54 5.07 7.16 10.70 13.79 19.09 31.71 60.60 94.01
0.19 0.34 0.51 0.85 1.05 1.19 1.64 2.32 3.26 4.84 7.25 9.03 12.35 20.67 40.21 62.58
98.8 96.9 93.9 86.9 82.5 79.4 70.5 61.1 52.3 41.4 29.7 24.1 17.3 9.4 4.1 1.9
Fig. 7. Flow duration curves with median exceedance (50%) daily mean flow shown for Full (3.5 m3 s−1 , line with open circles) and Drought-influenced (2.3 m3 s−1 , plain line) flow records from Barren Fork Creek near Eldon, OK (USGS 7197000). The estimated “normal” exceedance (∼61%) for a mean daily flow of 2.3 m3 s−1 is also shown.
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Fig. 8. The statewide average of Drought-influenced exceedance plotted against “normal” exceedance (open circles), with the standard deviation of the exceedance shown as error whiskers. The 1 to 1 is shown as a thin solid line. A best-fit line for the exceedances between 15% and 75%, which is 8.4% for the statewide average, is shown as a dashed line. A suggested 10% estimated exceedance offset is shown as a dark gray solid line.
While this is a promising method for estimating expected streamflows under low precipitation conditions, it is applicable only to the median flow for a single stream. It would be more useful to be able to estimate a wide range of flows for all gaged streams. To do this the normal exceedances were averaged both for all gages within the state and for gages within each CD and those averages plotted against the drought-influenced exceedance. The statewide averaged normal exceedance (Fig. 8) plotted to the right of the 1:1 line, which indicated drought-influenced exceedances were lower than averaged normal exceedance. The data between 15% and 75% were generally linear, and the intercept of a line fit to values in that interval was 8.4. This indicated that for a wide range of flows for stream gages throughout the state, the drought-influenced exceedance was approximately the full-record exceedance plus 8.4 (Table 1, Fig. 8). Similarly, the fitted intercept for each CD for the range between 15% and 75% ranged from 6.8 (CD 3) to 12.8 (CD 5) and are shown in Table 1. The fitted intercepts for normal exceedance represent a link between the drought-influenced and full record FDCs such that, for a wide range of flows, the normal exceedance of a drought influenced flow is regularly offset by the value of the intercept. Therefore, for the remainder of the paper, the value of the fitted intercept will be termed the “offset”. The offset values for most CDs were relatively close to the state average of 8.4; the exception being CD 1 with an intercept of zero. A zero intercept meant that the drought-influenced and normal exceedances plot along the “1 to 1” line, which was to be expected, since it has been noted earlier that there were few USGS gages in CD 1 and many of those gages had records that included primarily drought years. 3.4. Drought flow estimates Based on the preceding analysis, a user can best estimate the magnitude of drought-influenced flows at USGS stream gages in Oklahoma by locating the prepared FDC in Lewis and Esralew (2009) and the offset for the appropriate CD from Table 1. Then use linear interpolation to determine the flow magnitudes for the range of exceedances between 15% and 75%. Alternatively, it can be noted that the exceedance increment in the FDCs published by Lewis and Esralew (2009) is 10%, and that the standard deviation of the normal exceedance for each CD in Table 1 is such that an offset of 10% is within one standard deviation of the calculated offset. The similarity of the statewide 8.4% offset and the 10% estimate is shown in Fig. 8. Accordingly, estimating drought-influenced flow at a gage can be achieved by simply noting the flow with a 10% greater exceedance in the prepared FDCs in Lewis and Esralew (2009). Although this alternate method is potentially less accurate, the entire rationale for these estimates is not to replace hydrologic modeling, but to provide initial low-cost water supply estimates that can signal the need for more in-depth hydrologic modeling and drought planning. 3.5. Using drought-influenced flow duration curves for water supply analysis There are 437 surface water public water supply permits currently in Oklahoma (OWRB, 2016c) (Table 4). Of those, 321 obtain water from reservoirs with the remaining 116 utilizing water directly from streams. A few USGS gages are located near those stream diversions and an additional few are upstream of water source reservoirs, offering an opportunity to use drought-influenced FDCs to estimate the effects of drought on public water supplies that are dependent on surface water.
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Table 4 Public water supply permits and allowable diversion volumes in Oklahoma utilizing surface water sources with source types (percent of total shown in parentheses). The majority of permits and the largest volume of water diversion utilize reservoir sources.
Total Permits Reservoir Source Stream Source
Number of Permits
Total Diversion, m3 × 106
Mean Diversion, m3 × 106
Standard Deviation
437 321 (73) 116 (27)
2167 1829 (84) 338 (16)
5.0 5.7 2.9
16.8 19.2 6.2
For instance, the USGS gage Illinois River near Tahlequah, OK (7196500) is located about 1.7 km upstream of three runof-river diversion points on the Illinois River that supply the city of Tahlequah, OK with 55% of its water requirements: maximum annual diversion of 21 M m3 , or an average of ∼0.06 M m3 d−1 . Reduced flow at this point of the stream will have a direct impact on the municipal water supply. The median flow at the gage calculated with the full record is 12.2 m3 s−1 , but when calculated with the CD 6 average difference from normal of 9.0% (Table 1), the median is only 9.5 m3 s−1 , representing a 23% reduction in flow. Assuming constant flow at these rates, the 99% exceedance drought-influenced flow (0.05 M m3 d−1 ) would not equal the average daily withdrawal for the City of Tahlequah, and withdrawals taken at the 90% exceedance daily total flow (0.25 M m3 d−1 ) would remove more than 20% of the flow. These values are concerning, since water needs can be high during seasonal low-flow periods. The USGS gage Kiamichi River near Antlers, OK (7336200) is close to permitted stream withdrawal sites for two local rural water districts with permitted withdrawals totaling 1.3 M m3 annually (0.003 M m3 d−1 ). The Kiamichi River is also the main tributary to Hugo Lake, and the City of Hugo, OK is permitted to withdraw 37.6 M m3 annually (0.1 M m3 d−1 ) from the lake storage. The cumulative annual volume for the median discharges for the full-record and drought-influenced FDCs at the Antlers gage are 273 and 182 M m3 , respectively. However, flows at the gage may be inadequate for the stream withdrawals on an annual basis, especially if drought conditions exist. According to the FDCs, flows exceeded 98% of the time based on the full record (0.004 M m3 d−1 ) and 90% based on the drought-influenced record (0.005 M m3 d−1 ) will just meet the surface water demand. Vulnerability of the water supply for the City of Hugo is more difficult to evaluate with the drought-influenced records, since lake storage provides a buffer and is related to cumulative flow and especially to low frequency high volume flow. Calculating the total annual flow from the gage records, then comparing the full record to the drought-influenced years, one can see that the total inflow to Hugo Lake is much reduced, and over a multi-year drought there may be water supply issues for the City of Hugo (Fig. 9).
4. Conclusions Flow duration curves are a useful tool for water resource planning, particularly when the timing of streamflow is not the primary requirement (Vogel and Fennessey, 1995) and they portray the probability of a given flow in terms of the percent of time that it is likely to be exceeded. For this project, drought-influenced FDCs were prepared by selecting daily average streamflow records from years with below-average precipitation according to long-term precipitation records compiled for each of Oklahoma’s nine Climate Divisions. The drought-influenced flows were consistently smaller for a given exceedance, and when the “normal” exceedance for each flow was calculated the distributions were significantly different. The normal exceedances for all gages across the state and within each CD were averaged and the intercept of a line parallel to the 1:1 line calculated. The intercept is equivalent to an “offset” that may be added to an exceedance value on the full-record FDC to estimate the drought-influenced flow. Full-record FDCs are available for Oklahoma in Lewis and Esralew (2009) and those can be used to make drought-influenced flow estimates through linear interpolation. A simpler method is explored that is based on the 10% increments in the published FDCs (Lewis and Esralew, 2009). Noting that a 10% offset is within one standard deviation of the state average, and most of the individual CD offsets, a user can estimate a droughtinfluenced flow directly from a published FDC simply by reading the exceedance that is 10% greater, although it should be noted that this method is potentially less accurate. Additionally, this methodology for investigating drought-influenced streamflows could be applied to any region with long streamflow and precipitation records. The intent of this work is to provide a low-cost means for estimating drought streamflows for small water users and suppliers, and thus increase the likelihood for planning in advance of drought. Small water providers are the least likely to use their scarce budgets to contract hydrological investigations without a strong sense of need. At present, this tool can provide drought flow estimates only at stream gage sites. To be truly useful for the numerous small water suppliers who depend on streamflow, this tool will need to provide estimates at any stream location, and be widely available. Thus, next steps include regional analysis and outreach to the responsible state agency in Oklahoma to incorporate this tool into the Drought Planning toolkit.
Funding This work was supported by NSF EPSCoR [Grant No. OIA-1301789].
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Fig. 9. Histogram of total annual flow recorded at the USGS gage Kiamichi River near Antlers, OK, which represent the major inflows to Hugo Lake. Shown are the distributions for the full record (a), and the drought-influenced record (b). Reduced total inflow to Lake Hugo during drought may impair water supplies for Hugo, OK.
Appendix A. Supplementary data Supplementary data associated with http://dx.doi.org/10.1016/j.ejrh.2017.01.001.
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version,
at
References AMS, 2013. Drought: An Information Statement of the American Meteorological Society (Adopted by AMS Council on 19 September 2013, https://www2. ametsoc.org/ams/index.cfm/about-ams/ams-statements/statements-of-the-ams-in-force/drought/). Dracup, J.A., Lee, K.S., Paulson, E.G., 1980. On the definition of droughts. Water Resour. Res. 16 (2), 297–302. Engle, N.L., 2012. Adaptation bridges and barriers in water planning and management: insight from recent extreme droughts in Arizona and Georgia. JAWRA 48 (6), 1139–1150. Goodrich, G.B., Ellis, A.W., 2006. Climatological drought in Arizona: an analysis of indicators for guiding the governor’s drought task force. Prof. Geogr. 58 (4), 460–469. Green, L., Xu, K.-M., 2005. Comparison of Histograms for Use in Cloud Observation and Modeling. NASA Technical Publication, TP-2005–213274. Guttman, N.B., Quayle, R.G., 1996. A historical perspective of U.S. climate divisions. Bull. Am. Meteorol. Soc. 77 (2), 293–303. Lewis, J.M., Esralew, R.A., 2009. Statistical Summaries of Streamflow in and near Oklahoma Through. USGS, SIR 2009–5135, 633 p. Liu, L., Hong, Y., Hocker, J.E., Shafer, M.A., Carter, L.M., Gourley, J.J., Bednarcyk, C.N., Yong, B., Adhikari, P., 2012. Analyzing projected changes and trends of temperature and precipitation in the southern USA from 16 downscaled global climate models. Theor. Appl. Climatol. 109, 345–360. NDMC, 2016. National Drought Mitigation Center Current State Drought Plans. http://drought.unl.edu/Planning/DroughtPlans/StateDroughtPlans/CurrentStatePlans.aspx. OCS, 2016. Oklahoma Climatological Survey: Oklahoma Climate. http://climate.ok.gov/index.php/climate. OWRB, 2012. Oklahoma Comprehensive Water Plan Update 2012: Executive Report. University of Oklahoma Printing Services, Norman, OK (172 p.). OWRB, 2016a. Oklahoma Water Resources Board: Drought Monitoring. http://www.owrb.ok.gov/drought/. OWRB, 2016b. Oklahoma Water Resources Board: Oklahoma Drought Tool. http://www.owrb.ok.gov/drought/index.php. OWRB, 2016c. Oklahoma Water Resources Board: Water Rights Summary Data (Updated 75/2016, http://www.owrb.ok.gov/maps/pmg/owrbdata WR.html). Pirie, R.L., de Loe, R.C., Kreutzwiser, R., 2004. Drought planning and water allocation: an assessment of local capacity in Minnesota. J. Environ. Manage. 73, 25–38. Searcy, J.K., 1959. Manual of Hydrology: Part2. Low-Flow Techniques Flow-Duration Curves. USGS WSP 1542-A. US Government Printing Office, Washington DC.
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Svoboda, M., Smith, K.H., Widhalm, M., Woudenberg, D., Knutsen, C., Sittler, M., Angel, J., Spinar, M., Shafer, M., McPherson, R., Lazarus, H., 2011. Drought-ready Communities: A Guide to Community Drought Preparedness (Available at: http://drought.unl.edu/Planning/PlanningProcesses/DroughtReadyCommunities.aspx). Vogel, R.M., Fennessey, N.M., 1994. Flow duration curves I: New interpretation and confidence intervals. J. Water Resour. Plann. Manage. 120 (4), 485–504. Vogel, R.M., Fennessey, N.M., 1995. Flow duration curves II: a review of applications in water resources planning. Water Resour. Bull. 31 (6), 1029–1039. Wilhite, D.A., Svoboda, M.D., 2007. Understanding the complex impacts of drought: a key to enhancing drought mitigation and preparedness. Water Resour. Manage. 21, 763–774. Wilhite, D.A., Hayes, M.J., Knutsen, C., Smith, K.H., 2000. Planning for drought: moving from crisis to risk management. J. Am. Water Resour. Assoc. 36 (4), 697–710.
Contents lists available at ScienceDirect
Journal of Hydrology: Regional Studies journal homepage: www.elsevier.com/locate/ejrh
A tool for drought planning in Oklahoma: Estimating and using drought-influenced flow exceedance curves R.B. Miller a , G.A. Fox b,∗ a b
Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK, USA Department of Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC, USA
a r t i c l e
i n f o
Article history: Received 19 August 2016 Received in revised form 6 December 2016 Accepted 4 January 2017 Keywords: Drought Flow duration curve Oklahoma Streamflow Water supply
a b s t r a c t Study region: The study region is the state of Oklahoma, USA, which has a varied climate. Precipitation increases west to east, and temperature decreases south to north across the state. Accordingly, Oklahoma has been divided into nine Climate Divisions, which reflect those climatic as well as regional differences in agricultural practices. Study focus: Surface water is the dominant source for public water systems in Oklahoma and these supplies may be impacted by drought or climatic change. Hydrologic modeling is an important component of water resource planning, but may be beyond the budget of smaller communities. To create a freely available tool for initial assessment of drought streamflows, this study uses publicly available long-term precipitation records for climate divisions in Oklahoma to create flow duration curves (FDCs) from the drought-influenced subsets of streamflow records. New hydrological insights for the region: The FDCs created from those subsets showed increased likelihood of reduced streamflows. The reduced flows were shown to increase water supply risk to run-of-river users. To eliminate the need for users to re-create these analytic steps, study results were compared to published FDCs and reasonable estimates of drought-influenced FDCs were produced by offsetting the expected exceedance by 10%. © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction A drought is in its essence a deficit of water, primarily driven by a reduction in precipitation, and which may have significant impacts on human lives. The American Meteorological Society describes drought as a “complex interplay between (1) natural precipitation deficiencies, or excessive evapotranspiration over varying time periods and different areal extents, and (2) the demands of human and environmental water use that may be exacerbated by inefficiencies in water distribution, planning, and management” (AMS, 2013). Hence, the human experience of drought can depend both on the severity (e.g. duration and intensity) of the moisture deficit, and on the means for coping with the drought’s effects.
∗ Corresponding author at: North Carolina State University, Department of Biological and Agricultural Engineering, Campus Box 7625, Raleigh, NC 27695-7625, USA. E-mail address: [email protected] (G.A. Fox). http://dx.doi.org/10.1016/j.ejrh.2017.01.001 2214-5818/© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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Fig. 1. Oklahoma Climate Divisions (OCS, 2016). Climate divisions follow political boundaries, and are based on physiographic factors such as soil type, topography and elevation, meteorological factors such as annual precipitation and temperature, and economic factors such as typical crop types (Guttman and Quayle, 1996).
Fig. 2. Annual precipitation history for Oklahoma CD 3 (Northeast Oklahoma), showing the overall mean precipitation for the period 1895–2015 (39.3 in, 99.8 cm), as well as annual precipitation totals and the 5-year moving average (OCS, 2016). Periods below the overall average are colored brown, and above the average are colored green.
1.1. Oklahoma climate and drought planning Oklahoma has a varied climate influenced by differences in terrain as well as by precipitation that increases west to east and temperature that decreases south to north. The Oklahoma Climatological Survey (OCS) has divided the state into nine distinct Climate Divisions (CDs) (Guttman and Quayle, 1996; OCS, 2016) (Fig. 1). Precipitation plots based on records dating from the 1890’s have been prepared for each of the CDs, reflecting how the climatic and physical gradients affect precipitation in each of those (Fig. 2). Those precipitation plots illustrate the high variability over time including historic droughts in the 1930’s and 1950’s. Additionally, climate change projections for Oklahoma may include higher temperatures and increased periodicity of rainfall over current norms (Liu et al., 2012; OWRB, 2012). Surface water is the dominant water source for users in Oklahoma outside of irrigated agriculture, representing 70% of the supply (Fig. 3). Municipal water suppliers are among the largest single water users in Oklahoma, representing 35% of all water and 60% of surface water use. Variations in the amount and timing of rainfall would be expected to have effects on surface water supplies, and in turn affect much of the state’s population and economy. Drought response involves many aspects of planning, including prediction and monitoring of drought events as well as mitigation of drought effects (Wilhite et al., 2000; Pirie et al., 2004; Goodrich and Ellis, 2006; Wilhite and Svoboda, 2007). Oklahoma is one of a majority of states whose drought-planning emphasis has been placed on prediction and monitoring,
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Fig. 3. Surface and groundwater permitted use by economic sector in Oklahoma (from OWRB, 2016c). Public Water Supply represents the 2nd largest sector overall, the 2nd larger groundwater user, and the largest surface water user. Omitting crop irrigation, the public water sector represents 69% of all remaining permitted water and 60% of surface water permits.
while less has been directed toward planning in advance of a drought crisis (Wilhite et al., 2000; Pirie et al., 2004; NDMC, 2016). Current drought planning tools in Oklahoma serve as response aids once a drought crisis is underway; however, there is little to help in pre-crisis planning, such as assessing the adequacy of established water resources or developing secondary sources to use under drought conditions (OWRB, 2016a,b,c).
1.2. Flow duration curves Flow exceedance curves are a statistical representation of flow probability, in which the probabilities are expressed as the percent of time that a given daily flow will be exceeded within a time period similar to the period of record (Searcy, 1959; Vogel and Fennessey, 1994; Vogel and Fennessey, 1995). By definition, in an FDC the smallest flows have a high likelihood and large flows a low likelihood of being exceeded. The shape of a FDC is useful for evaluating and comparing watershed hydrology (e.g. Searcy, 1959). In relation to this study, FDCs have been utilized for water use planning purposes, including design of run-of-river applications such as calculating minimum wastewater treatment (Searcy, 1959; Vogel and Fennessey, 1995) and for water resource allocation (Vogel and Fennessey, 1995).
1.3. Drought-influenced flow duration curves Planning for drought is an important component of drought resilience for Oklahoma communities. Wilhite et al. (2000) and Svoboda et al. (2011) have identified gathering information about water resources as an important early step in drought planning. However, many communities may not take this step given the expense of preparing a hydrologic model; Engle (2012) identified financial considerations and resource issue awareness as two major barriers for drought planning for community water suppliers. This research used published precipitation trends and streamflow records to create a tool that can indicate the general magnitude of flow reduction that can be expected under local drought conditions. The intent is to lower the threshold for drought planning at the small community level in Oklahoma by creating a publicly accessible and easy to implement first step in the process. We hypothesize that FDCs based on streamflow records from below-average rainfall years will contain valuable information about the general flow tendencies of those streams during drought events. While such records cannot answer questions about how a particular year of drought will affect streamflow, they can describe the important differences between the expected flows under normal and low-rainfall conditions. Finally, by estimating those drought-influenced flow differences in terms of the FDCs that have already been prepared for Oklahoma streams, a tool was developed that will allow smaller communities and public water suppliers to assess the need for further and more advanced drought planning.
2. Materials and methods The purpose of this research was to develop a method to estimate the expected range of drought flows using existing data. The research product was intended to help with drought mitigation planning, especially for small utilities that lack budget flexibility, by allowing a rapid estimate of expected drought impact on stream-based surface water sources. The flowchart shown in Fig. 4 outlines the process that was applied to stream gage records throughout the state. Each step in the process is explained in more detail in the following sections.
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Fig. 4. Flowchart portraying the steps followed to create the ‘normal” exceedance of drought-influenced streamflows. The subset of streamflow records (a., Section 2.1) is created using the below-average precipitation years to select daily mean streamflow records from the full records of streamflow at each gage. Flow duration curves (FDCs, b., Section 2.2) are prepared using the drought-influenced subset of daily mean flows. The full record FDCs are obtained from Lewis and Esralew (2009). The “normal” exceedance probabilities of the drought-influenced flows (c., Section 2.3) are calculated by linear interpolation using the full-record FDC for the gage (Lewis and Esralew, 2009). Finally, drought-influenced vs, “normal” exceedances (d., Section 2.4) are plotted to show the estimated exceedance difference.
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Fig. 5. Annual precipitation record (black symbols) for CD 6 (East Central Oklahoma) with 5-year running averaged periods below the overall mean shaded in brown and above the mean in green. The “below” precipitation periods are used to select “drought-influenced” flows from the stream gage record at Barren Fork near Eldon, OK (7197000) shown below.
2.1. Subsetting the streamflow records A full record of daily average streamflows was obtained for each USGS gage used in the study. Then a subset of daily average streamflows for each USGS gage located in that CD was then prepared by selecting the daily average streamflow records from the tagged below-average precipitation years (Fig. 5). The vast majorities of those gages represent non-reference streams and thus exhibited some degree of hydrologic alteration or flow regulation (Lewis and Esralew, 2009), and only gages directly downstream of dams were eliminated from analysis. The annual precipitation history for each of the nine Oklahoma CDs was examined and each year was tagged as above- or below-average depending on the value of the five-year average relative to the overall mean precipitation calculated for the dataset (Figs. 4 a, 5).
2.2. Creating drought-influenced flow duration curves The USGS public access software program Surface-Water Statistics (SWSTAT), which is included as a module within Basins 4.1 (Basins 4.1; Aqua Terra Consultants, Decatur, GA), was used to prepare drought-influenced FDCs from the subset of streamflow records (Fig. 4b). It should be noted that the term “drought-influenced” was chosen in part to distinguish the subset FDC from FDCs prepared from the full record of streamflows, and to avoid confusion with “hydrologic drought” as defined by Dracup et al. (1980) and others. Lewis and Esralew (2009) have prepared and reported FDCs and other streamflow statistics for the more than 190 active US Geological Survey (USGS) stream gages in Oklahoma with at least 10 years of streamflow record. The full record FDCs for gages used in this study were obtained from that document.
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2.3. Normalizing flow duration curves for comparison Gage records represent different watersheds and flows of different magnitudes, and therefore drought-influenced flow magnitudes are not directly comparable between gages. In order to compare records from different gages, the droughtinfluenced streamflows were normalized by estimating the full-record exceedance for each of the drought-influenced flows (Fig. 4c). The discharges from the drought-influenced FDC were assembled and the exceedances of those flows were calculated from the full-record flow duration curve using linear interpolation. Those calculated values were labeled “normal exceedance”, and correspond to the estimated exceedance probability from the full-record of a drought-influenced flow. The relationship between drought-influenced and normal exceedance is independent of scale, so that gages with different flow volumes can be combined and compared. The pairs of drought-influenced and normal exceedance values were grouped by CD and also for the entire state, and the mean and standard deviation of normal exceedance for each drought-influenced exceedance was calculated. The plotted mean values were generally curvilinear, but there was a relatively linear section between 75% and 15% exceedance, and a line parallel to the 1:1 line in this interval was fitted to the mean normal exceedance values by allowing the intercept to vary and minimizing the RMSE (Fig. 4d). This calculated offset value represents a general estimate of the probability difference in flows between the drought-influenced and full streamflow records for each CD and for the state as a whole. 2.4. Statistical comparisons of flow duration distributions There was a need to compare the drought-influenced and normal exceedance flow distributions to determine if the differences (if any) between the two distributions were significant. However, normal statistical comparisons would not be suitable, since those techniques measure some sort of central tendency weighted by variance in the data, and both distributions ranged from an exceedance of 1–99. Green and Xu (2005) developed a technique to determine the significance of differences between equivalent bins in histograms generated for the reflectance from groups of remotely-sensed clouds. Their technique involved calculating the Euclidean distance between equivalent bins in the histograms representing the averages of two cloud populations, and then comparing that value to the equivalent distance values generated by randomly assigning members to the two classes (Green and Xu, 2005). The approximated significance level (ASL) test, a statistic for the difference, was calculated as: ASL =
C n
(1)
where C is the number of random combinations larger than the actual, and n is the number of random iterations. The ASL is compared to ␣ and assumed significant if ASL ≤␣. Following Green and Xu (2005), an approximation of the statistical significance of differences between the droughtinfluenced and normal exceedance of flows for gages in each CD were calculated. This method was applied to the droughtinfluenced dataset by calculating the Euclidean distance between a given drought-influenced exceedance and its estimated “normal” exceedance percentage (L2 ): L2 =
(ai − bi )
2
(2)
i
where a is a drought-influenced exceedance and b is its equivalent “normal” exceedance. Once the original distance was calculated, groups were randomly assigned 1000 times for each CD, and the L2 calculated. The ASL was considered significant at ␣ = 0.05. 3. Results and discussion A total of 128 USGS gages were utilized in this study (Table 1). There was an uneven distribution of gages within the CDs, ranging from six gages in CD 1–20 in CD 6. The distribution of USGS gages likely corresponds to the local need for information about surface water. Factors that may influence the high density of USGS gages in that region included a high utilization of irrigated agriculture drawn from surface water in CD 7 and CD 8, a combination of irrigation and urbanization in CD 5, and Oklahoma Scenic Rivers, navigable waterways, and urban surface water sources in CD 3 and CD 6. In contrast, while CD 1 (Panhandle) has a high density of irrigated agriculture, the irrigation water is primarily drawn from deep groundwater sources and few stream gages are required. 3.1. Subsets of USGS gage records The USGS stream gages do not have the same period of record as the precipitation records, so the subset of flow records may or may not be reduced relative to the full record. Subsetting the gage records reduced the flow record length, and the ratio of drought-influenced to full record length had a statewide mean of 0.45, meaning that generally less than half of the full years of record were included in the drought-influenced subset. However the reduction ratios for the CDs were not all
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Table 1 The number of gage records used for each Climate Division (CD) and the state as a whole, the fitted values for the intercept of an offset line for “Normal” exceedance between 15 and 75% for plotted drought-influenced vs. normal exceedance values, and the average standard deviation of the normal exceedance values for the range 15 to 75. Although the entire statewide dataset was used in all relevant calculations, CD 1 appeared to be an outlier in many respects and statewide totals without CD 1 are included as reference. Climate Division
Number of Gages
“Normal” exceedance intercept
Standard Deviation
1 2 3 4 5 6 7 8 9 State (with CD 1) State (without CD 1)
6 9 16 9 19 20 17 17 15 128 123
0 8.7 6.8 7.5 12.8 9.0 10.2 8.0 7.6 8.4 8.9
5.9 3.3 2.2 8.3 5.2 3.8 5.8 6.1 2.3 5.6 5.2
Fig. 6. Ratio of drought-influenced to full years of records for USGS gages by Oklahoma CD. The ratio for CD 1 was very high, indicating that the droughtinfluenced record for those gages was very similar to the full-record. That difference was significant (P = 0.03) using the Kruskal-Wallis One Way Analysis of Variance on ranks.
the same: the ratios for each climate division are close to 0.5 with the exception of CD 1, which was 0.7 (Fig. 6). The larger ratio for CD 1 means that the drought-influenced record is relatively similar to the full record. In CD 1 there have historically been very few stream gages, and many of those were only in place during periods of low precipitation; of the six gages included from CD 1, three showed no difference between the full and the drought-influenced years of record. Although CD 1 appears to be an outlier in terms of gage records, in the interest of geographic completeness those data were included in all analysis and discussion. 3.2. Statistical comparisons The ASL test was conducted to determine if the “normal” exceedance was different from the drought-influenced exceedance. The ASL test results showed that the differences between the drought-influenced and “normal” FDCs were significant at ␣ = 0.05, with the exception of CD 1 (Table 2). As noted above, the drought-influenced subset of flow records for CD 1 was very similar to the full record; hence, there was little difference between the drought-influenced and “normal” exceedances. 3.3. Drought-influenced and full record comparisons The FDCs for the drought-influenced records showed lower flows relative to the full-record FDC. This difference in expected flow magnitude is illustrated in the FDC comparison for the USGS gage Barren Fork Creek (BFC) near Eldon, OK (Table 3, Fig. 7), where the full-record median (50% exceedance) flow was 3.5 m3 s−1 (125 ft2 s−1 ) while the droughtinfluenced record median was 2.3 m3 s−1 (82 ft2 s−1 ). Linear interpolation shows that the drought-influenced median flow would “normally” be exceeded 61% of the time. From another perspective, the drought-influenced median flow at BFC can be approximated by substituting the 60% exceedance flow (∼“normal” exceedance of 61%) from the full record (Table 3).
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Table 2 Calculated Approximated Significance Level (ASL) by Climate Division for the summed Euclidean distance between the drought-influenced and “normal” exceedance flows. The ASL was considered to represent a significant difference between flow duration curves if ASL <0.05. Significant values are shown in bold. Climate Division
ASL
n
CD 1 CD 2 CD 3 CD 4 CD 5 CD 6 CD 7 CD 8 CD 9 Statewide
0.59 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00
1000 1000 1000 1000 1000 1000 1000 1000 1000 6000
Table 3 Flow exceedance probabilities calculated with SWSTAT using full- and drought-influenced record daily average flow data for the USGS gage 7197000 (Barren Fork Creek at Eldon, OK). Also shown is the “normal” exceedance of the drought-influenced flow, which has been calculated by linear interpolation of the drought-influenced discharges on the full-record FDC. USGS 7197000 Barren Fork Creek at Eldon, OK Daily flow (cms) Exceedance probability (%)
Full-record
Drought-influenced
“Normal” Exceedance (%)
98 95 90 80 75 70 60 50 40 30 20 15 10 5 2 1
0.27 0.45 0.71 1.16 1.39 1.67 2.41 3.54 5.07 7.16 10.70 13.79 19.09 31.71 60.60 94.01
0.19 0.34 0.51 0.85 1.05 1.19 1.64 2.32 3.26 4.84 7.25 9.03 12.35 20.67 40.21 62.58
98.8 96.9 93.9 86.9 82.5 79.4 70.5 61.1 52.3 41.4 29.7 24.1 17.3 9.4 4.1 1.9
Fig. 7. Flow duration curves with median exceedance (50%) daily mean flow shown for Full (3.5 m3 s−1 , line with open circles) and Drought-influenced (2.3 m3 s−1 , plain line) flow records from Barren Fork Creek near Eldon, OK (USGS 7197000). The estimated “normal” exceedance (∼61%) for a mean daily flow of 2.3 m3 s−1 is also shown.
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Fig. 8. The statewide average of Drought-influenced exceedance plotted against “normal” exceedance (open circles), with the standard deviation of the exceedance shown as error whiskers. The 1 to 1 is shown as a thin solid line. A best-fit line for the exceedances between 15% and 75%, which is 8.4% for the statewide average, is shown as a dashed line. A suggested 10% estimated exceedance offset is shown as a dark gray solid line.
While this is a promising method for estimating expected streamflows under low precipitation conditions, it is applicable only to the median flow for a single stream. It would be more useful to be able to estimate a wide range of flows for all gaged streams. To do this the normal exceedances were averaged both for all gages within the state and for gages within each CD and those averages plotted against the drought-influenced exceedance. The statewide averaged normal exceedance (Fig. 8) plotted to the right of the 1:1 line, which indicated drought-influenced exceedances were lower than averaged normal exceedance. The data between 15% and 75% were generally linear, and the intercept of a line fit to values in that interval was 8.4. This indicated that for a wide range of flows for stream gages throughout the state, the drought-influenced exceedance was approximately the full-record exceedance plus 8.4 (Table 1, Fig. 8). Similarly, the fitted intercept for each CD for the range between 15% and 75% ranged from 6.8 (CD 3) to 12.8 (CD 5) and are shown in Table 1. The fitted intercepts for normal exceedance represent a link between the drought-influenced and full record FDCs such that, for a wide range of flows, the normal exceedance of a drought influenced flow is regularly offset by the value of the intercept. Therefore, for the remainder of the paper, the value of the fitted intercept will be termed the “offset”. The offset values for most CDs were relatively close to the state average of 8.4; the exception being CD 1 with an intercept of zero. A zero intercept meant that the drought-influenced and normal exceedances plot along the “1 to 1” line, which was to be expected, since it has been noted earlier that there were few USGS gages in CD 1 and many of those gages had records that included primarily drought years. 3.4. Drought flow estimates Based on the preceding analysis, a user can best estimate the magnitude of drought-influenced flows at USGS stream gages in Oklahoma by locating the prepared FDC in Lewis and Esralew (2009) and the offset for the appropriate CD from Table 1. Then use linear interpolation to determine the flow magnitudes for the range of exceedances between 15% and 75%. Alternatively, it can be noted that the exceedance increment in the FDCs published by Lewis and Esralew (2009) is 10%, and that the standard deviation of the normal exceedance for each CD in Table 1 is such that an offset of 10% is within one standard deviation of the calculated offset. The similarity of the statewide 8.4% offset and the 10% estimate is shown in Fig. 8. Accordingly, estimating drought-influenced flow at a gage can be achieved by simply noting the flow with a 10% greater exceedance in the prepared FDCs in Lewis and Esralew (2009). Although this alternate method is potentially less accurate, the entire rationale for these estimates is not to replace hydrologic modeling, but to provide initial low-cost water supply estimates that can signal the need for more in-depth hydrologic modeling and drought planning. 3.5. Using drought-influenced flow duration curves for water supply analysis There are 437 surface water public water supply permits currently in Oklahoma (OWRB, 2016c) (Table 4). Of those, 321 obtain water from reservoirs with the remaining 116 utilizing water directly from streams. A few USGS gages are located near those stream diversions and an additional few are upstream of water source reservoirs, offering an opportunity to use drought-influenced FDCs to estimate the effects of drought on public water supplies that are dependent on surface water.
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Table 4 Public water supply permits and allowable diversion volumes in Oklahoma utilizing surface water sources with source types (percent of total shown in parentheses). The majority of permits and the largest volume of water diversion utilize reservoir sources.
Total Permits Reservoir Source Stream Source
Number of Permits
Total Diversion, m3 × 106
Mean Diversion, m3 × 106
Standard Deviation
437 321 (73) 116 (27)
2167 1829 (84) 338 (16)
5.0 5.7 2.9
16.8 19.2 6.2
For instance, the USGS gage Illinois River near Tahlequah, OK (7196500) is located about 1.7 km upstream of three runof-river diversion points on the Illinois River that supply the city of Tahlequah, OK with 55% of its water requirements: maximum annual diversion of 21 M m3 , or an average of ∼0.06 M m3 d−1 . Reduced flow at this point of the stream will have a direct impact on the municipal water supply. The median flow at the gage calculated with the full record is 12.2 m3 s−1 , but when calculated with the CD 6 average difference from normal of 9.0% (Table 1), the median is only 9.5 m3 s−1 , representing a 23% reduction in flow. Assuming constant flow at these rates, the 99% exceedance drought-influenced flow (0.05 M m3 d−1 ) would not equal the average daily withdrawal for the City of Tahlequah, and withdrawals taken at the 90% exceedance daily total flow (0.25 M m3 d−1 ) would remove more than 20% of the flow. These values are concerning, since water needs can be high during seasonal low-flow periods. The USGS gage Kiamichi River near Antlers, OK (7336200) is close to permitted stream withdrawal sites for two local rural water districts with permitted withdrawals totaling 1.3 M m3 annually (0.003 M m3 d−1 ). The Kiamichi River is also the main tributary to Hugo Lake, and the City of Hugo, OK is permitted to withdraw 37.6 M m3 annually (0.1 M m3 d−1 ) from the lake storage. The cumulative annual volume for the median discharges for the full-record and drought-influenced FDCs at the Antlers gage are 273 and 182 M m3 , respectively. However, flows at the gage may be inadequate for the stream withdrawals on an annual basis, especially if drought conditions exist. According to the FDCs, flows exceeded 98% of the time based on the full record (0.004 M m3 d−1 ) and 90% based on the drought-influenced record (0.005 M m3 d−1 ) will just meet the surface water demand. Vulnerability of the water supply for the City of Hugo is more difficult to evaluate with the drought-influenced records, since lake storage provides a buffer and is related to cumulative flow and especially to low frequency high volume flow. Calculating the total annual flow from the gage records, then comparing the full record to the drought-influenced years, one can see that the total inflow to Hugo Lake is much reduced, and over a multi-year drought there may be water supply issues for the City of Hugo (Fig. 9).
4. Conclusions Flow duration curves are a useful tool for water resource planning, particularly when the timing of streamflow is not the primary requirement (Vogel and Fennessey, 1995) and they portray the probability of a given flow in terms of the percent of time that it is likely to be exceeded. For this project, drought-influenced FDCs were prepared by selecting daily average streamflow records from years with below-average precipitation according to long-term precipitation records compiled for each of Oklahoma’s nine Climate Divisions. The drought-influenced flows were consistently smaller for a given exceedance, and when the “normal” exceedance for each flow was calculated the distributions were significantly different. The normal exceedances for all gages across the state and within each CD were averaged and the intercept of a line parallel to the 1:1 line calculated. The intercept is equivalent to an “offset” that may be added to an exceedance value on the full-record FDC to estimate the drought-influenced flow. Full-record FDCs are available for Oklahoma in Lewis and Esralew (2009) and those can be used to make drought-influenced flow estimates through linear interpolation. A simpler method is explored that is based on the 10% increments in the published FDCs (Lewis and Esralew, 2009). Noting that a 10% offset is within one standard deviation of the state average, and most of the individual CD offsets, a user can estimate a droughtinfluenced flow directly from a published FDC simply by reading the exceedance that is 10% greater, although it should be noted that this method is potentially less accurate. Additionally, this methodology for investigating drought-influenced streamflows could be applied to any region with long streamflow and precipitation records. The intent of this work is to provide a low-cost means for estimating drought streamflows for small water users and suppliers, and thus increase the likelihood for planning in advance of drought. Small water providers are the least likely to use their scarce budgets to contract hydrological investigations without a strong sense of need. At present, this tool can provide drought flow estimates only at stream gage sites. To be truly useful for the numerous small water suppliers who depend on streamflow, this tool will need to provide estimates at any stream location, and be widely available. Thus, next steps include regional analysis and outreach to the responsible state agency in Oklahoma to incorporate this tool into the Drought Planning toolkit.
Funding This work was supported by NSF EPSCoR [Grant No. OIA-1301789].
R.B. Miller, G.A. Fox / Journal of Hydrology: Regional Studies 10 (2017) 35–46
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Fig. 9. Histogram of total annual flow recorded at the USGS gage Kiamichi River near Antlers, OK, which represent the major inflows to Hugo Lake. Shown are the distributions for the full record (a), and the drought-influenced record (b). Reduced total inflow to Lake Hugo during drought may impair water supplies for Hugo, OK.
Appendix A. Supplementary data Supplementary data associated with http://dx.doi.org/10.1016/j.ejrh.2017.01.001.
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