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Autoregressive models (AR) are extensively used to understand the behavior of streamflow. The literature abounds with examples of AR models from different families applied "everywhere" to fully understand how streamflow changes throughout the hydrologic year. One particularly well accepted model is the periodic autoregressive model, as in Hipel and McLeod (1984).

So far, from all I've ever read, all streamflow AR models will have a signficant first order lag. That is, when one calculates the PACF to find the order p of the model, p will assume a value of 1, at least.

Is there any known case registered in the literature of an AR streamflow model of order 0, i.e., AR(0) for streamflow? That is, is there a possible way that the "yesterday's flow" won't explain the "today's flow"?

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Autoregressive models are mathematical models, and like all models, are based on a conceptual model of the system. The conceptual model is that prior flow is a parameter in prediction of current flow. So it doesn't really make sense to have a model where it does not do so.

Furthermore it is difficult to conceive of a natural system where prior flow is not a predictor. This is where I disagree with Gordon's answer. Even in small catchments, prior flow is a good surrogate for the physical conditions that contribute to flow. The conditions include precipitation history, soil moisture, filling of depressions so flow can accumulate, capacity for trees to intercept precipitation (are the leaves already wet), water-table stream connectivity, etc.

If you don't see a relationship to prior flow in small catchments, that may just mean your daily timestep is too large. I care about the flow variation in very small catchments and monitor the flow on 30-minute intervals.

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  • $\begingroup$ Thanks, Haresfur. I see what you mean and you raised good points here. What do you think of intermittent rivers, though? In small, fast-draining catchments, it might be able to adjust an AR(0) for them. $\endgroup$
    – Jxson99
    Oct 10, 2016 at 14:32
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Yesterday's baseflow always influences today's baseflow because the natural recession has an exponential recession constant measured in days to months. This is evident in all but the smallest of catchments. In fast-draining very small catchments, where the time of concentration is typically measured in minutes, the antecedent conditions have little bearing on flow. They probably aren't reported in the literature, because who cares about the flow variation in very small catchments? So technically, yes, it is possible to have AR(0), but it is of no serious interest.

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  • $\begingroup$ Thanks, @Gordon. That might be the reason why I can't find any reference ascerting there won't be an AR(0) for streamflow. I wonder, however, even in a rather small catchment; if the river is permanent, it has to depend on yesterday's flow somehow, as you pointed out. Maybe the question here is that if we are to look for an AR in which the time-steps are large amouns of time, we could say an AR(0) would be appropriate. Now, small time-steps (e.g., days), it doesn't seem possible to affirm the same since the "proximity" between yesterday and today is way shorter. What do you think? $\endgroup$
    – Jxson99
    Oct 10, 2016 at 14:21
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    $\begingroup$ Further to Mason Beau and Haresfur's input, whether the river is permanent makes all the difference. If it is permanent then I would agree that there must be antecedent influence. In my answer I was thinking of some small catchments in Timor Leste which are steep hard rock in the upper catchment, and flat urban in the lower. Since there is such a small groundwater storage (next to nothing), then 24 hours after a storm there is virtually no 'hydraulic memory'. That is, zero antecedent influence. $\endgroup$
    – Gordon Stanger
    Oct 12, 2016 at 2:26

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