Introduction

The hydrologic cycle describes the continuous movement of water on, above, and below the surface of the earth. This project is motivated by the growing need for understanding observed patterns in precipitation and stream-water data, as well as the hydrological response of the system [1]. In this way, this project serves as an introduction into an exploration of surface hydrology. As a major component of the hydrologic cycle, precipitation is responsible for the deposition of freshwater on the surfaces of the earth. Understanding patterns of precipitation in space and time is important. Spatial and temporal comparisons allow us to ask interesting questions regarding monthly, seasonal, and annual changes in precipitation for given locations [2]. There are growing bodies of research which apply examining how understanding changing temperature, precipitation, and storms can provide assessments for effects of future climate change and economic outcomes.

Surface water hydrology describes the study of surface water movement, or the distribution of surface water in space and time. Understanding a potential link between stream flow and precipitation in the United States could be important for making inferences for recharge and system stability [2, 3]. In addition, hydrologic conditions and variations during extreme events (flooding or drought) are important to consider, as they may affect the stability of systems—which in turn can have biological and environmental impacts [4]. Runoff, a major component of the water cycle, describes water from a source (typically precipitation) that flows over the land instead of evaporating or being absorbed into the ground [5, 6]. Runoff is directly impacted by the intensity or amount of rainfall and the properties of the ground, such as permeability of soil and physical attributes (slope and presence of vegetation).

Runoff-ratios quantitatively describe the relationship between runoff and precipitation, and can be defined by the value of average runoff over the average precipitation. The runoff coefficient relates the rate of runoff to the rate of precipitation [5, 6]. Hypothetically, increasing precipitation would be reflected in increasing runoff. Similarly, less precipitation would be reflected in less runoff, should all things be considered equal in a system. For example, a ratio of 0.4 (runoff over precipitation) would imply 40% runoff, and 60% evapotranspiration (long-term). (This is theoretical, as in a steady-state system, there could be influences elsewhere, such as an aquifer.) Thus, low runoff-ratios reflect high evaporation potential, and high runoff-ratios reflect low evaporation potential.

This project aims to characterize spatial patterns in the United States for precipitation and surface water to investigate variations in surface hydrology. This study is useful for understanding processes in the hydrologic cycle and the influences of physical processes which may affect hydrology across the nation. In particular, it may be interesting to look into potential problems with runoff, including variability in surface runoff, pollution, and sedimentology [2]. Should an increase in flow correlate with increasing sediment, nutrients, bacteria, and pesticides, then large storm events could be potentially harmful to the environment and its people [4].

Data Manipulation

The data used for this project includes precipitation data from the NOAA and runoff data from the USGS. The NOAA Climate at a Glance dataset contains total precipitation collected on a monthly basis from 1895-2017 for the United States. The data is collected for each of the 344 climate divisions in the contiguous United States by daily observations, which are then computed to monthly station temperature and precipitation values. This dataset is useful for the real-time analysis of precipitation data across the country—intended for the study of climate variability and change. The USGS Water Watch describes real-time, recent, and past streamflow conditions for the United States for more than 3,000 long-term gages. Historical runoff values represent streamflow conditions from 1901 to the present-most data. The summary tables used for this project include time-series data that summarizes the conditions by state or region. Thus, this dataset will be useful for demonstrating variation through time.

USGS: State Runoff Data

USGS: Regional Runoff Data

Note: This dataset included implications not foreseen in early analysis. This data would have been useful for mapping, but it contains only the name and code for a given region– as defined by the USGS. Unfortunately, the code used for mapping implements the state codes for spatial analysis; because we do not have state codes (only regional codes) in this data set, nor do we have regions defined similarly in R packages, this data set has limited use for this project.

NOAA: Precipitation Data

## Parsed with column specification:
## cols(
##   Year = col_double(),
##   Month = col_double(),
##   Precip_inches = col_double(),
##   state_cd = col_character()
## )

Combining the Data Sets

US Map

These dataframes combine state information (state name and region code) and mapping information (boundary information for states in the U.S. from maps in base R) to allow for mapping later in the project.

“Big Data”

This project uses two large datasets from the USGS and the NOAA examine surface hydrology. The size of these datasets is demonstrated below, using facet_wrap() to display all of the time-series data on a state level.

## Warning: Removed 336 rows containing missing values (geom_point).
## Warning: Removed 7 rows containing missing values (geom_path).

## Warning: Removed 214 rows containing missing values (geom_point).
## Warning: Removed 106 rows containing missing values (geom_path).

  • Figures 1 and 2. These facet_wrap() graphs help to demonstrate the size of the datasets we are dealing with; it is difficult to interpret the data as a whole when there are so many variables (48 states, 100+ years worth of data, and two main variables– precipitation and runoff). In order to understand the relationship between precipitation and runoff, both must be analyzed individually for spatial and temporal variation across the United States.

Exploratory Analysis

The following analyses help to individually understand trends in precipitation and runoff before examining the correlation (and ratios) between the two variables.

Precipitation Across the United States

## Warning: Column `state_cd` joining character vector and factor, coercing
## into character vector

  • Figure 3. The average precipitation values across the United States highlight wet and dry regions across the country (median values are represented in white). In general, the eastern United States receives more precipitation than the western United States. States in the southeastern U.S. appear to have the highest averages for precipitation.

Temporal Distributions in Precipitation

  • Figure 4. Seasonal variations in precipitation (a combined analysis for all states). This graph shows the averages for all states through time. In general, higher averages fall in summer months; the most variable amounts of precipitation fall in the winter.

  • Figure 5. Raster plot of annual precipitation for every state. Higher averages for precipitation are observed in blue colored tiles (ie. Washington, Tennessee, Mississippi, Louisiana, etc.). Tiles more red in color indicate states observing lower averages in precipitation (ie. Nevada, New Mexico).

  • Figure 6. Raster plot of seasonal averages of precipitation by state. This plot shows how average values vary by season for each state. Spring and summer have the highest averages of precipitation for the majority of states. Winter appears to be the dryest month. Florida and Georgia demonstrate particularly high averages during summer months.

Regional Variations in Precipitation through Time

  • Figure 7. Raster plot of annual variations in precipitation by region (defined by the grouping in base R). The West is the most dry region of the United States, with low averages through time. The North Central U.S. generally experiences variable precipitation, ranging from mid-to-low values. This graph depicts an observable increase in precipitation averages in the Northeast through time; such an observation is consistent with recent data which suggests the Northeast is experiencing more frequent and more intense precipitation events [4, 5]. Precipitation in the South generally appears to be consistent, as it experiences periods of relatively high and high average precipitation.

Runoff Across the United States

Runoff is affected by meteorological factors, including the type of precipitation and the intensity, duration, and amount of precipitation for a given event. Runoff is also impacted by physical factors—including those related to human influences, such as land use, vegetation, soil, and drainage. Urbanization and development are examples of human impacts on runoff, as these actions cause a reduction in infiltration and thus an acceleration of runoff.

Runoff by Region

  • Figure 8. Displays trends in runoff for regions (as defined by the USGS) in the United States. Some of the trends in regional runoff are consistent with trends identified in precipitation. The New England region demonstrates an increasing amount of runoff through time, which is consistent with observations regarding the increasing frequency of rainfall events in the Northeast [4]. Regions in the West and Southwest experience low runoff averages that may correspond to low precipitation averages.

Runoff by State

  • Figure 9. Map of the average runoff values (for all years on record) across the United States. Washington appears to have the highest value of average runoff. The eastern U.S. generally appears to have higher averages than states in the central and western U.S. White = median

Runoff-Ratios

Runoff-ratios are used to understand surface hydrology because they relate runoff to precipitation quantitatively. Here, we use our combined data sets (NOAA Precipitation data and USGS Runoff) to understand the relationship between precipitation and runoff for the contiguous United States.

Spatial Analysis: Runoff-Ratios

Because this project aims to understand spatial patterns across the United States, we want to see if we can identify trends in these runoff-ratios for the region– and, in particular, if these trends have changed through time. With such a large data set, mapping is the easiest, most efficient way to display useful data.

Runoff-Ratios through Time

  • Figure 15. Displays trends in runoff coefficients by state through time (color-coded by region). States in the North Central region demonstrate a general increase in ratios through time. Ratios for states in the Northeast appear steady, if not increasing (with variable scales depending on the state). Western regions show consistent decreasing trends. The South shows variable trends.

Integrated Runoff-Ratios

Because it could be unreasonable to assume the average runoff-ratio is representative of the whole system, perhaps due to variable precipitation through time, integrated runoff-ratios were calculated with statistical analysis to account for variability.

summary_table <- combined_data %>% #summary table of combined statistics (min, max, median, mean) for all states in the U.S. to demonstrate variability
  group_by(state_cd) %>% 
  summarize_at(vars(precip_mmd, runoff_mmd), funs(min, max, median, mean)) %>%
  mutate(long_term_rr = runoff_mmd_mean/precip_mmd_mean)

Individual State Data

The following section disects individual state data–including precipitation, runoff, and their respective coefficients– through time to understand the variability between states.

Time-Series Analysis: Washington State

Why does Washington have such a high runoff-ratio? High runoff coefficents suggest low potential for evaporation, and increasing runoff. The data for Washington state can be analyzed individually to understand the relationship between runoff and precipitation for this state.

  • Figure 17. Through spatial analysis, we see Washington State has a high runoff/precipitation ratio– the highest of any state in the United States. Because the ratio is approximately 0.8, this means for every 0.8 mm of rain, there is 0.2 mm of evaporation– suggesting there is very little evaporation despite frequent precipitation (essentially, for a ratio of 0.8, it means 80% is runoff). Climatic variability may become apparent in the instance of Washington, as mountain ranges, including the Cascades rain shadow, likely play an important role in determining where rain falls in the region—-keeping the inlands dry [2].

  • Figure 18. Displays the variation in the runoff-ratio of Washington state through time (1901-2017). For some of the earlier years on record, the runoff-ratio is above 1.0 (where a ratio of 1 indicates 100% runoff for rain falling). In general, this indicates Washington may see little-to-no evaporation despite having frequent rainfall. Additionally, the runoff-ratio for Washington state appears to be decreasing through time– perhaps due to human influences [5, 6]. (There may be variability in the beginning of the dataset due to WA not being well-studied.)

  • Displays the annual totals for precipitation in Washington State. This data should be considered in terms of the high runoff-ratio for Washington state because it demonstrates significant variability for the intensity of rainfall events (although consistency in earlier data is questionable, as WA may not have been well-studied).
## Warning: Removed 1 rows containing missing values (geom_point).

  • Q-Q plot for Washington State which demonstrates the distributions of precipitation and runoff. The probability distributions will be analyzed in the Discussion.

Time-Series Analysis: New York State

  • Figure 19. The relationship between precipitation and runoff is more easily understood looking at data on the state-level. Looking at precipitation and runoff together (precipitation being the top line and runoff being the bottom line, intuitively), we can see increased precipitation events usually correlate with increased runoff. New York has a relatively high average runoff-ratio compared to other states (within the top 10 average ratios across the United States).
## Warning: Removed 1 rows containing missing values (geom_point).

  • Q-Q plot for New York, demonstrating the distributions of precipitation and runoff. The probability distributions will be analyzed in the Discussion.

Time-Series Analysis: New Mexico

New Mexico displayed the lowest runoff-ratio out of all of the states; low runoff-ratios are indicative of high evaporation potential, and less runoff.

  • Figure 20. New Mexico averaged the lowest runoff-ratio out of all of the states in the U.S. Individual state data for all of the years on record displays especially low runoff values and relatively low averages in rainfall. The runoff-ratio calculated essentially follows the runoff data.

Integrated State Values

The single averages values of precipitation and runoff for each state were plotted to determine if there were clear populations or spatial trends.

Spatial and Temporal Analysis: Runoff-Ratios through Time

Because an animated choropleth map did not prove to be successful, we can approximate the change in the runoff-ratio through time and map this data to get a sense of which regions are experiencing the greatest amount of change through time.

## Warning: Column `state_cd` joining factor and character vector, coercing
## into character vector

Discussion and Conclusions

The goal of this project was to calculate and examine the runoff-ratios of states in the contiguous United States based on a combined synthesis of datasets for runoff and precipitation data from the USGS and the NOAA, respectively. Results suggest, for most of the contiguous United States, precipitation is the primary factor causing temporal variation. In this way, trends in the runoff-ratio correlate with trends consistent with a changing climate. In addition, human influences are responsible for changes in the runoff-ratio, as identified in the central U.S. [5].

Q-Q plots are statistical probability plots that compare two probability distributions. For precipitation and runoff, Q-Q plots were created for New York State and Washington State allow for a greater analysis into the distribution between precipitation and runoff. Because precipitation forces runoff, distributions are skewed toward increasing precipitation. Thus, it is possible the distribution of precipitation suggests precipitation is the driving force of runoff and runoff variability.

Spatial Variability

Based on annual averages of precipitation from the National Climate Assessment and general observations from the precipitation map, the eastern half of the United States gets more precipitation than the western half of the United States. To the west of Mississippi, the United States appears to be much dryer annually. In this way, there is clear spatial variability. Temporal variability may also become apparent for these data set, as it is possible the intensity of precipitation events has increased or decreased since the beginning of the data set to today, and thus there may be increasing variability in the changes manifested in the runoff-ratios.

Perhaps one of the most interesting results from this analysis stems from the idea that plenty of states receive the same amount of rainfall, but do not get the same amount of runoff (Figures 11, 21). On average, for 3 mm of precipitation, the North Central region of the U.S. experiences low runoff; for the same 3 mm of rain, the South experiences more runoff, and the Northeast experiences even more still. States in the Pacific Northwest (such as Washington and Oregon– our outliers), receive even greater amounts of runoff, still. This variability demonstrates an important difference in the evaporation potential likely due to climatic differences.

Implications and Future Research

This project works to understand the relationship between precipitation and runoff by simulating average ratios for each state, but it is likely the mean variations for the runoff-ratio change through time. Future research on this subject may include trying to understand the temporal variations in relation to human influences, as it has been recognized that humans can impact the runoff coefficient [5]. Studies focusing on understanding how land use, vegetation, and development can impact runoff-ratios over time may be useful as we continue to face such changes.

It is interesting to consider the effects of having “wet” or “dry” years in relation to the value of the runoff-ratio. One would assume wetter years would allow for a higher ratio (more precipitation may cause increased runner), while dryer years may allow for a lower ratio (less precipitation may cause less runoff). In a previous lab, it was understood that the Pacific Northwest (and especially Washington) seems like an excessively “wet” region. A general observation for the precipitation data of Washington indicates it may not be the “amount” of precipitation that gives Washington its reputation—it is likely the number of dayss with rain [8]. In this way, Washington may have the reputation of being particularly rainy because it rains frequently, but there is not a significant amount of rain during the events. The lag of the hydrologic system describes how long it takes for events to be recognized in a system. Future research on this topic should implement temporal analysis on the lag between runoff-ratios (based on “wet” or “dry” years in terms of precipitation events) in order to understand the memory of the system. Because Washington may not have been well-studied previously (1901-1950), there may be inconsistency in the data. While a double mass curve was not created for this project, it may be useful for understanding adjustments needed for inconsistent precipitation data.

The Effects of Runoff

The analysis indicates precipitation is the driving force of runoff in the United States; with increasing precipitation following a changing climate in many parts of the U.S., increasing runoff may have environmental consequences. Water erosion and pollution, should flowing runoff can pick up contaminants, are primary consequences which contribute to human and environmental risks. Increasing development in areas where runoff is already high may increase the frequency of flooding events. Future research on this subject should work to understand potential risks associated with different regions depending on human influences on runoff.

This project is significant because it works to understand patterns in surface hydrology for the United States, and applies quantitative analysis to characterize such trends. Hydrology, the study of water, is essential because water is one of the most important natural resources. This analysis demonstrates the need to understand the complex water systems on a regional scale, and evaluates the implications of such on our future [7].

References

[1] Grayson, R. and Blöschl, G. eds., 2001. Spatial patterns in catchment hydrology: observations and modelling. CUP Archive.

[2] Barlow, M., Nigam, S. and Berbery, E.H., 2001. ENSO, Pacific decadal variability, and US summertime precipitation, drought, and stream flow. Journal of climate, 14(9), pp.2105-2128.

[3] Woolhiser, D.A. and Goodrich, D.C., 1988. Effect of storm rainfall intensity patterns on surface runoff. Journal of Hydrology, 102(1-4), pp.335-354.

[4] Faurès, J.M., Goodrich, D.C., Woolhiser, D.A. and Sorooshian, S., 1995. Impact of small-scale spatial rainfall variability on runoff modeling. Journal of hydrology, 173(1-4), pp.309-326.

[5] McCabe, G.J. and Wolock, D.M., 2016. Variability and trends in runoff efficiency in the conterminous United States. JAWRA Journal of the American Water Resources Association, 52(5), pp.1046-1055.

[6] Hamlet, A.F., Mote, P.W., Clark, M.P. and Lettenmaier, D.P., 2007. Twentieth-century trends in runoff, evapotranspiration, and soil moisture in the western United States. Journal of Climate, 20(8), pp.1468-1486.

[7] Velpuri, N.M. and Senay, G.B., 2013. Analysis of long-term trends (1950–2009) in precipitation, runoff and runoff coefficient in major urban watersheds in the United States. Environmental Research Letters, 8(2), p.024020.

[8] Mote, Phillip, and Snover, Amy (2018). “Projected Climate Change: Northwest” and “Water-related Challenges.” The National Climate Assessment.