In this age of computerized detail, it is easy to find numbers presented with little or no thought on level of significance. You May note stream measurement during higher flows, you find water level changes surging, leaves and debris perhaps, sediment and channel shifting perhaps, velocity changing with location and depth in cross section, and usually short duration of gauging measurements as water level changes shift during storm or flood hydrograph. Perhaps only one or two figures are significant, so a discharge measurement of 127,500.00 cfs may be really best reported as 130,000 (rounded) or even 100,000 cfs if figures of significance would be considered and reported. The 127,500 cfs might be calculated from stage discharge relationship or could be from a flood measurement. If one goes into the flood measurement data, one gets an idea of the various sources of potential error as stage is seldom stable. Most high flow measurements are designed by professionals to attempt to be within plus or minus 10%, recognizing at times of vary rapid change in stage, plus or minus 20% or less may be more realistic. So unless you are dealing with very low and stable flows, values reported to two decimal places are more for show, than significance.

However, when adding up all the changes in flow through time series, I don’t see anything wrong with using non-significant numbers or decimal places from stage discharge relationship to estimate water yield or stormflow, then after calculations, do some rounding or dropping off numbers to better reflect significance. For most discharge measurements, there should probably be only one to maybe at best three significant figures.

If you review various sites of stream gauging by USGS, I think you will find instances of variability in discharge numbers reported related to stage, and sometimes differences in reported values at a single stage. If these sites were specifically selected for their ease of access as well as stability of site, one can assume that the variability presented in the results are probably related to measuring flows and the combination of dynamic change during storm hydrographs.

In this age of computerized detail, it is easy to find numbers presented with little or no thought on level of significance. You May note stream measurement during higher flows, you find water level changes surging, leaves and debris perhaps, sediment and channel shifting perhaps, velocity changing with location and depth in cross section, and usually short duration of gauging measurements as water level changes shift during storm or flood hydrograph. Perhaps only one or two figures are significant, so a discharge measurement of 127,500.00 cfs may be really best reported as 130,000 (rounded) or even 100,000 cfs if figures of significance would be considered and reported. The 127,500 cfs might be calculated from stage discharge relationship or could be from a flood measurement. If one goes into the flood measurement data, one gets an idea of the various sources of potential error as stage is seldom stable. Most high flow measurements are designed by professionals to attempt to be within plus or minus 10%, recognizing at times of vary rapid change in stage, plus or minus 20% or less may be more realistic. So unless you are dealing with very low and stable flows, values reported to two decimal places are more for show, than significance.

However, when adding up all the changes in flow through time series, I don’t see anything wrong with using non-significant numbers or decimal places from stage discharge relationship to estimate water yield or stormflow, then after calculations, do some rounding or dropping off numbers to better reflect significance. For most discharge measurements, there should probably be only one to maybe at best three significant figures.

If you review various sites of stream gauging by USGS, I think you will find instances of variability in discharge numbers reported related to stage, and sometimes differences in reported values at a single stage. If these sites were specifically selected for their ease of access as well as stability of site, one can assume that the variability presented in the results are probably related to measuring flows and the combination of dynamic change during storm hydrographs.

I think there is a general rule for that. Such as 10,000,000 kg sediment may be simply written as 10,000 tons or 10^6 kg.

I would like to advocate for the use of probabilistic estimation whenever necessary and possible (as it probably is in this case). There is a lot of uncertainty in the forcings, equations, parameters, initial states, etc. of flood models, and the output should reflect this. More than rounded results, you should aim at providing confidence intervals, error bars, or even probability densities of your most important outputs. In the following article they demonstrated the value of probabilistic estimates over higher-resolution ones: Zhu, Y., Toth, Z., Wobus, R., Richardson, D., and Mylne, K. (2002), “The economic value of ensemble-based weather forecasts,” Bulletin of the American Meteorological Society, 83, 73–83. https://doi.org/10.1175/1520-0477(2002)0832.3.CO;2.

If you could assemble a few scenarios that capture the range of possible assignments to input precipitation values and other key variables in the model, you could run them all and then extract a few statistics from the multiple results to provide decision makers an stochastic estimation of the conditions to expect. The same applies to your next analysis: the few scenarios predicted by your flood model could be used to run the analysis several times and provide a spread of possible outcomes there as well. Of course, there is a large wealth of research on Monte Carlo methods and ensemble forecasting if you would like to go further down this rabbit hole...

Thanks all for providing very good answers!

That all are the context I meant.

Since there might be various sources uncertainty from the input data and the model itself, we could consider the use of stochastic estimation as Felipe Hernández pointed out. Monte Carlo methods and ensemble forecasting might be very promising as we deal with such kind of estimations.

Thanks for your detail and practical explanation Magfira Syarifuddin .

I would like to use the numerical result for building some empirical equation statistically.

It's exactly like what you said. It seems that I can rounded up the 1.5234 m inundation depth to 1.5 as 2.34 cm is not so much significant for the impact on some land use.

Thus, using that rounded up value, I would use it as predictors for some damage function.

Thanks William F. Hansen

M.Hassan Nasermoaddeli

That's exceptional explanation!

It is the actual situation in a site measurement and its use.

However, how to deal with the such kind of different standard applied in some observation as we need a consistency spatially and temporally? Especially in undeveloped region that has both manual and automated gauges.