Nonstationarity – The Importance of Hydrologic Observations and Data to Water Management

Six years ago, Wellntel posted a blog titled “In a nonstationary world, continuity of observations is critical” – the title was a statement taken from an article in Science by Milly and others (2008). The message of the blog was that the physical drivers of hydrologic systems have increasingly been altered by climate change and as a result, greater temporal and spatial density of data are required to build the hydrologic understanding to meet local and regional groundwater challenges.

Six years on, we are all experiencing the continued disruption of climate patterns, the increasing variability of precipitation, and the growing reliance on groundwater by industry, agriculture and communities. Nonstationarity, whether inherently natural or anthropogenic, is a necessary and growing consideration in the engineering and design of water systems and infrastructure.

The stationarity/nonstationarity of hydrologic systems is a fundamental principle of water management and important to understand. So, what is the difference between a stationary and nonstationary time-series dataset? The figure above presents the difference, showing:

  • (a) a stationary time series with constant mean and variance, and
  • (b) three nonstationary time series in the form of a shift in mean (trend and step change) and a shift in variance. Solid and dashed black lines represent the mean and the variance of the time series, respectively. (Figure and explanation are copied directly from Slater and others, 2021)

Water supply and management infrastructure is designed based on best knowledge of the local hydrology. Historically, stationarity has been assumed for these plans and designs, but increasingly elements of nonstationarity, from a variety of sources, can no longer be ignored.

Through much of the last century, available data suggested that the hydroclimate and hydrologic systems were generally stationary around mean values. This stationarity was the foundation of many approaches and tools for the planning and designing of water supply and management infrastructure. But as hydrologic records became longer, the new view suggested that natural variability in the hydroclimate was not truly stationary in the sense it had been applied. According to R. M. Hirsch (2010) it has for awhile been widely recognized and accepted in the hydrologic community that the stationarity assumption may be invalid in many cases. He suggests the following three reasons why hydrologic systems may not exhibit stationarity.

1. “Human modifications to the hydrologic system upstream of the project. These modifications include urbanization (increased impervious surfaces), land-use modification such as conversion of forest land to cropland, or groundwater development leading to decreases in base flow to streams.” “These problems are relatively tractable, but they do present significant scientific challenges, particularly for some of the processes with long lag times, such as deforestation-reforestation or groundwater depletion.”

2. “Natural climate phenomena are quasi-periodic and lead to high degrees of hydrologic persistence. This category centers on phenomena such as El Niño Southern Oscillation, Pacific Decadal Oscillation, and Atlantic Multidecadal Oscillation. All of these phenomena have characteristic temporal scales, and all have documented impacts on temperature, precipitation, and hydrologic conditions on land.” “Regardless of whether this is called “non-stationarity,” it points to the importance of hydrologic analysis making maximum use of a wide range of information sources to help characterize the system. These include historic records, paleo-records, and linkages to distant land or ocean systems for which better records are available.”

3. “Climate change induced by human-driven changes in the global atmosphere, primarily the enrichment of greenhouse gases.” “Many climate researchers suggest that very intense precipitation events are becoming more common, and that prolonged periods of low precipitation are also becoming more common. However, when it comes to the response of rivers and groundwater to these changing climate phenomena, the results are much less clear.”

With these different potential sources of nonstationarity in hydrologic datasets described by Hirsch (2010), he calls it “imperative” that measurement of precipitation and streamflow, soil moisture and groundwater, and snowpack and glaciers continue with a high priority. Further, Hirsch (2010) suggests that the continuity of data and data analysis at established sites have higher priority than beginning the collection of data from more locations.

Milly and others (2015) re-emphasize the importance of data in their response to critiques of their 2008 article ‘Stationarity is Dead: Whither Water Management?’’. Because of the uniqueness and immensity of climate change on the global hydrologic and energy cycles, Milly and others (2015) state again in 2015 as they did in 2008 ‘‘In a nonstationary world, continuity of observations is critical.’’ Long-term hydrologic observations are essential to quantify, on an ongoing basis, how the physical drivers of hydrologic systems are being altered by climate change, and in turn, how approaches and tools must evolve for planning and designing water supply and management infrastructure.

From California comes an example of a response to the need for robust hydrologic observations and for the continual updating of hydrologic frequency analysis. The State Climatologist has improvements underway to the state’s hydrologic forecasting (Anderson, 2022), including adjusting Hydrologic Averages to better reflect most recent hydrologic experiences, refining statistical models using updated data, and taking new approaches to improve the forecasting of extreme weather events (10% and 90% exceedance).

Water supply and management infrastructure is designed based on best knowledge of the local hydrology. Historically, stationarity has been assumed for these plans and designs, but increasingly elements of nonstationarity, from a variety of sources, must be accounted for. The need for continuous, local hydrological data is increasing, while the ability of government agencies to collect and interpret these data is flat or declining. Even when funds for science are more readily available, state and federal agencies can not collect data at a pace and in enough places to address issues most important to local communities for water management. Fortunately, municipalities, communities, and other stakeholders can now join together to create powerful networks of Wellntel systems to provide the “continuity of observations” that focuses directly on their most critical groundwater resource concerns.

Read Dr. Dunning’s original post from May 11, 2017 here

Anderson, M. L., Forecast Improvement to Adapt to Climate Change, California Water Commission Workshop, February 16, 2022

Hirsch, R. M.: A Perspective on Nonstationarity in Water Management, Colorado Water — March / April, 2010, Volume 27, Issue 2, 5-6,  accessed on March 20, 2023 at A Perspective on Nonstationarity in Water Management (

Milly, P. C., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., and Stouffer, R. J.: Stationarity is dead: Whither water management?, 2008, Science, 319, 573–574, accessed on March 20, 2023 at

Milly, P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, R. J. Stouffer, M. D. Dettinger, and V. Krysanova, 2015, On Critiques of ‘‘Stationarity is Dead: Whither Water Management?,’’ Water Resour. Res., 51, 7785–7789, doi:10.1002/ 2015WR017408. accessed on March 20, 2023 at On Critiques of “Stationarity is Dead: Whither Water Management?” – Milly – 2015 – Water Resources Research – Wiley Online Library

Slater, L. J., Anderson, B., Buechel, M., Dadson, S., Han, S., Harrigan, S., Kelder, T., Kowal, K., Lees, T., Matthews, T., Murphy, C., and Wilby, R. L.: Nonstationary weather and water extremes: a review of methods for their detection, attribution, and management, 2021, Hydrol. Earth Syst. Sci., 25, 3897–3935, accessed on March 20, 2023 at