In Water Resources Engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is impounded. For some rivers, long-term historical records of such flow data are difficult to obtain. In contrast, meteorological data on precipitation have often been available for many yearst. Therefore, it is often useful to determine a relationship between flow and precipitation. This relationship can then be used to estimate flows for years when only precipitation measurements were made. For example, the following data are available for a river that is to be dammed:
Precipitation=[88.9 108.5 104.1 139.7 127 94 116.8 99.1]
Flow=[14.6 16.7 15.3 23.2 19.5 16.1 18.1 16.6]
How can I put the best line with linear regression to predict the annual water flow on the data?
if the drainage area is 1100 km2, estimate what fraction of the precipitation is lost via processes such as evaporation, deep groundwater infiltration, and consumptive use.
In Norway, we have maps that show runoff/km2 as l/s/km2. 1 mm of precipitation corresponds to 1000 l/km2. Use the area of the catchment and the volume of rainfall that falls on it. The runoff is the precipitation minus evapotranspiration etc.
Hello,
To put the best line with linear regression to establish an equation between precipitation and flow data, you can use software or programming tools that provide regression analysis capabilities:
1. Microsoft Excel (easy to use): You can use the built-in regression analysis tool and curve fitting through selecting the appropriate regression model.
2. SPSS, and dozens of statistical tools
3. R: Use the statistical programming language R, which has different packages like `lm()` or `stats::lm()` for linear regression modeling.
The estimation of the fraction of precipitation lost via evaporation, infiltration, percolation, and consumptive use, requires additional information and data specific to the river and upstream watershed to consider comprehensive water balance analysis (currently data is anot sufficient).
To determine the relationship between flow and precipitation, you
can analyze hydrological data and perform a correlation analysis. Here's a general approach:
It's important to note that the relationship between precipitation and flow can vary depending on factors like soil type, land use, vegetation cover, and local hydrological processes. Additionally, other factors such as antecedent conditions, groundwater contributions, and human water use can also influence streamflow. Therefore, a comprehensive analysis may involve considering multiple variables and factors beyond just precipitation to fully understand the relationship with flow.
just enter your numbers in Excel, make a scatter plot, add a line fit, add equation, R-square etc. ... for confidence intervals, p-values etc. use the "Data Analysis" add-in in Excel
about "what fraction of the precipitation is lost" = 1- beta = 85%, where beta=0.15 from the Excel fit-plot, and presumably both series share identical measurement units
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