# Calculating Stream Flow from Rainfall Data

I have been given the following data:

Month N T (degrees C) Monthly Rainfall (mm)
1 0.68 1.12 391.1
2 0.82 1.40 163.1
3 0.98 3.04 296.5
4 1.15 4.77 157.7

The list goes on. From this and using the Thornthwaite Equation, I calculated both I and Ep (Where Ep = monthly potential evaporation (mm), N = relative day length, T = average monthly temperature in celcius, I = monthly heat index) (3 d.p.)

Month I Ep
1 0.106 114.941
2 0.148 123.972
3 0.474 100.546
4 0.932 94.192

The list goes on.

From this I need to calculate riverflow/streamflow given as monthly rain - Ep. Thus: (3 d.p.)

Month Riverflow
1 276.159
2 39.128
3 195.954
4 63.508

The list goes on.

However, I have been asked for 2 reasons why the flow I have predicted would be inaccurate. In other words, to more accurately predict riverflow what extra data would I need?

Calculating river flow from rainfall - evaporation is a simplification. Firstly you are assuming that you can accurately measure rainfall, then that theoretical estimates of evaporation are correct which, given how much land cover and vegetation vary, is unlikely.

Next consider the pathway from raindrop hitting the soil to the river. It's clearly not instantaneous. That raindrop can evaporate directly, run off over the ground surface or soak into soil. In the soil it can be taken up by vegetation or infiltrate and become groundwater recharge. Depending on soil and aquifer characteristics this introduces a delay in the conversion of rainfall to runoff. In the real world this delay could be weeks, months or even years. In your example it's also worth thinking about low temperatures. Is rain falling as rain or is it snow?

Thirdly consider how water can get diverted from its pathway to a river. Is water abstracted from the pathway (i.e. from an aquifer), or from the river directly? Conversely reservoirs may regulate flows, either up or down depending on management.

• What is the current capacity of the soil and overburden. This will depend on the history of rainfall for the previous year or six.

• How fast can that surface absorb water? If you get 7 inches of rain in one hour (near my brother's house in N.M.) you get a lot more run off than if you get that same 7 inches in 7 days.

• I'm not sure how evaporation potential is determined. If it's calculated from temperature and relative humidity, it will seriously underestimate actual evaporation. You would need to model wind and ground level convection.

• Time of day of precip is going to matter too. A small rainfall event on warm earth will mostly evaporate, where the same rain at dawn will soak into the soil.

• Vegetation types will matter too: Plants like clover will quickly absorb rainfall and store it internally. Most trees on the other hand will not absorb moisture through their leaves, and so all of that will evaporate again.

• Steep hills will shed water into channels much faster than plains.

• Certain rocks (limestone, sandstone) can make a region that there is no surface runoff at all. (See karst landscape)

• Shape of river channel will make a difference. If you have lakes and pools, these act as 'spreaders' changing a 3 day deluge into a month of high water.

When I went canoeing in Northern Saskatchewan every year, I came up with a set of rules for checking routes:

200 km2 of water shed: The canoe would float, but I had to walk. 1000 km2 of water shed: I could paddle, but I'd be getting in and out a lot. 5000 km2 of water shed. I only worried about the places where the river constricted.

BUT: That was empirical observation of one part of the world, one month of the year (trips were in June) with most of the geology being bog and granite. (Laurentian Shield)

This is why gauge stations are important.