<p>I'm new to hydrology and I have a question regarding the modeling of multiple reservoirs. I need to estimate the total water inflow to multiple reservoirs that will be observed tomorrow, conditional on the water inflow, temperatures and rainfalls in each reservoir today. What I have in mind is a model similar to</p>

<p><span class="math-container">$$ TotalInflow_{t} = \beta_0 + \sum_i \beta_i \cdot Inflow_{it-1} + \sum_i \gamma_i \cdot Temperature_{it-1} + \sum_i \phi_i \cdot   Rainfall_{it-1} + \epsilon_t,$$</span></p>

<p>where <span class="math-container">$i$</span> denotes each single reservoirs, <span class="math-container">$t$</span> denotes time and <span class="math-container">$\epsilon_t$</span> is a random error. Of course, I plan to augment this simple model with lags variables and fixed effects. Importantly, the reservoirs in my data are not connected (e.g., a company owns multiple dams in different rivers). However, looking into the hydrology literature, I could only find paper dealing with a single reservoir rather than the sum of the total inflows across multiple reservoirs (e.g., Coulibalya et al., 2000). What is the common approach in hydrology for this problem (e.g., ARMA models? How many lags? Differencing?)? Do you have a specific reference?</p>

<p><strong>Bibliography:</strong>
Coulibaly, Paulin, François Anctil, and Bernard Bobée. "Daily reservoir inflow forecasting using artificial neural networks with stopped training approach." Journal of Hydrology 230, no. 3-4 (2000): 244-257.</p>

CC BY-SA 4.0
2020-04-01T07:54:01.123Z
Thank you for your inputs. At this point, I'm planning to do the analysis river by river, which allows me to estimate a distribution of daily inflow given certain variables (I don't have elevation, but only precipitation, and temperature. Acceleration should be captured by some lag variables of inflow, right?). Then, if there's not a lot of cross-sectional correlation across rivers, I can compute the joint distribution of the daily inflows to the firm by convoluting the marginal distribution of each river. Would that work?
Andrew
CC BY-SA 4.0
2020-04-01T08:21:31.753Z
I don't know how but I could have deleted some comments by mistake. sorry
Andrew
CC BY-SA 4.0
2020-04-04T11:34:11.637Z
Unfortunately, I don't have access to elevation info, but only the inflow. So I was thinking of modeling in some AR(p) process. The literature is huge. Any good ref?
Andrew
CC BY-SA 4.0
2020-04-04T11:59:32.740Z
Papers like this one seem to model it as a simple AR(p) process https://www.oieau.org/eaudoc/system/files/documents/38/194116/194116_doc.pdf
Andrew
<hydrology><rivers><dams>
Modeling the total water inflow across multiple reservoirs
Andrew
# Modeling the total water inflow across multiple reservoirs

(Asked by: username_0 on 2020-03-26)

I'm new to hydrology and I have a question regarding the modeling of multiple reservoirs. I need to estimate the total water inflow to multiple reservoirs that will be observed tomorrow, conditional on the water inflow, temperatures and rainfalls in each reservoir today. What I have in mind is a model similar to

$$ TotalInflow\_{t} = \beta\_0 + \sum\_i \beta\_i \cdot Inflow\_{it-1} + \sum\_i \gamma\_i \cdot Temperature\_{it-1} + \sum\_i \phi\_i \cdot Rainfall\_{it-1} + \epsilon\_t,$$

where $i$ denotes each single reservoirs, $t$ denotes time and $\epsilon\_t$ is a random error. Of course, I plan to augment this simple model with lags variables and fixed effects. Importantly, the reservoirs in my data are not connected (e.g., a company owns multiple dams in different rivers). However, looking into the hydrology literature, I could only find paper dealing with a single reservoir rather than the sum of the total inflows across multiple reservoirs (e.g., Coulibalya et al., 2000). What is the common approach in hydrology for this problem (e.g., ARMA models? How many lags? Differencing?)? Do you have a specific reference?

**Bibliography:**
Coulibaly, Paulin, François Anctil, and Bernard Bobée. "Daily reservoir inflow forecasting using artificial neural networks with stopped training approach." Journal of Hydrology 230, no. 3-4 (2000): 244-257.

**Tags:** hydrology, rivers, dams

> **Comments:**
> **username_0**: Thank you for your inputs. At this point, I'm planning to do the analysis river by river, which allows me to estimate a distribution of daily inflow given certain variables (I don't have elevation, but only precipitation, and temperature. Acceleration should be captured by some lag variables of inflow, right?). Then, if there's not a lot of cross-sectional correlation across rivers, I can compute the joint distribution of the daily inflows to the firm by convoluting the marginal distribution of each river. Would that work?  
> **username_0**: I don't know how but I could have deleted some comments by mistake. sorry  
> **username_0**: Unfortunately, I don't have access to elevation info, but only the inflow. So I was thinking of modeling in some AR(p) process. The literature is huge. Any good ref?  
> **username_0**: Papers like this one seem to model it as a simple AR(p) process https://www.oieau.org/eaudoc/system/files/documents/38/194116/194116_doc.pdf  

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## 0 answers

