<p>One suggestion on generating the monthly flows is to use a seasonal ARMA model directly (e.g. see <a href="https://faculty.fuqua.duke.edu/~rnau/Decision411_2007/seasarim.htm" rel="nofollow noreferrer">course notes</a>), since you are looking at ARMA model for stochastic generation anyway. That would allow the explicit estimation of seasonal parameters for synthetic generation, and let you skip the step of going annual --> monthly, instead go monthly and calculate annual flows from the monthly series. You may have other reasons for wanting to start with annual flows to verify those first, but that is one suggestion.</p>

<p>In terms of physical concepts at a monthly flow resolution, this is harder to comment on without knowing what physical processes are impacting your streamflows, e.g. snowmelt, river ice and freezing, spring freshet, depression storage, etc. One suggestion may be to check monthly volumes and peaks as well as timing of peaks (such as spring freshet), and ensure that any synthetic time series match these statistics within some acceptable boundary, throwing out any simulations that are deemed unacceptable.</p>

<p>This is a pretty broad (research level) question but hopefully that gives some ideas.</p>

CC BY-SA 4.0
2018-11-29T14:10:31.030Z
2018-11-29T14:10:31.030Z
Rob
<p>I've been tasked with generating synthetic streamflow scenarios through disaggregation.</p>

<p>First, I will generate 50 years of streamflow data. For that, I will probably use a simple model as AR(1) or an ARMA(1,1) and am adopting some probabilistic parameters based on streamflow data I have. These data come from the historical record a gauge station.</p>

<p>From my yearly flow, I have to generate monthly streamflows. In the end, instead of 50 streamflow realizations, each one representing an annual flow; I'll have 600 streamflow realizations, each representing a monthly stream flow.</p>

<p>Now, to get from annual to monthly stream flow, I will need a correlation matrix.</p>

<p>I could simply estimate the monthly correlation from January to December by calculating the correlation among monthly streamflows from a set of historical streamflow.</p>

<p>One could say that the physical aspects involving the (auto)correlation are implicit in the data itself. However, the data I have for this gauge station - as for any other - is only one realization of the stochastic process from which the observed streamflows were generated.</p>

<p><strong>How, then, could I enrich this monthly (auto)correlation with physical concepts stemming from the river where the gauge station is located? I should add that my question also applies to cross-correlation between two different time-series. How, in that case, could I enrich the cross-correlation matrix employing physical aspects between 2 observed time-series?</strong></p>

<hydrology><correlation>
How to obtain the correlation between monthly streamflows based on physical concepts?
Hugo
# How to obtain the correlation between monthly streamflows based on physical concepts?

(Asked by: username_0 on 2018-11-19)

I've been tasked with generating synthetic streamflow scenarios through disaggregation.

First, I will generate 50 years of streamflow data. For that, I will probably use a simple model as AR(1) or an ARMA(1,1) and am adopting some probabilistic parameters based on streamflow data I have. These data come from the historical record a gauge station.

From my yearly flow, I have to generate monthly streamflows. In the end, instead of 50 streamflow realizations, each one representing an annual flow; I'll have 600 streamflow realizations, each representing a monthly stream flow.

Now, to get from annual to monthly stream flow, I will need a correlation matrix.

I could simply estimate the monthly correlation from January to December by calculating the correlation among monthly streamflows from a set of historical streamflow.

One could say that the physical aspects involving the (auto)correlation are implicit in the data itself. However, the data I have for this gauge station - as for any other - is only one realization of the stochastic process from which the observed streamflows were generated.

**How, then, could I enrich this monthly (auto)correlation with physical concepts stemming from the river where the gauge station is located? I should add that my question also applies to cross-correlation between two different time-series. How, in that case, could I enrich the cross-correlation matrix employing physical aspects between 2 observed time-series?**

**Tags:** hydrology, correlation


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## 1 answers

### Answer by username_1 on 2018-11-29. Score: 1

One suggestion on generating the monthly flows is to use a seasonal ARMA model directly (e.g. see [course notes](https://faculty.fuqua.duke.edu/~rnau/Decision411_2007/seasarim.htm)), since you are looking at ARMA model for stochastic generation anyway. That would allow the explicit estimation of seasonal parameters for synthetic generation, and let you skip the step of going annual --> monthly, instead go monthly and calculate annual flows from the monthly series. You may have other reasons for wanting to start with annual flows to verify those first, but that is one suggestion.

In terms of physical concepts at a monthly flow resolution, this is harder to comment on without knowing what physical processes are impacting your streamflows, e.g. snowmelt, river ice and freezing, spring freshet, depression storage, etc. One suggestion may be to check monthly volumes and peaks as well as timing of peaks (such as spring freshet), and ensure that any synthetic time series match these statistics within some acceptable boundary, throwing out any simulations that are deemed unacceptable.

This is a pretty broad (research level) question but hopefully that gives some ideas.


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