# Total Basin Water

## What are the changes in the total amount of water in the basins?

The overall problem is to compute the water budget, or “balance,” for each geographic sector of interest, as changes in each component of the terrestrial hydrologic cycle. The process to measure each term of the water balance must be identified.

__Governing Equations__

The “highest level” expression of the water budget is the changes in the total mass of water in a basin, including water at or near the surface (open water, soil moisture, snow) and groundwater (shallow, deep, including aquifers). Clearly there are very different time scales, on which these respective pools change. Total Water Storage (TWS; e.g., mm or m3/mo), summarized as:

Eq 1. dS/dt = d(TWS)/dt = ΔS_{LAND} = ΔS_{SW} + ΔS_{SWE} + ΔS_{SM} + ΔS_{GW}

where ΔSLAND is the change in the water balance (TWS) across the landscape, as composed of changes in ΔSSNOW = snow water equivalents (SWE), ΔS_{SW} = surface water, ΔS_{SM} = soil moisture, and ΔS_{GW }= ground water.

Net changes in the water balance are constrained as the time rate of change of the inputs to and outputs from the respective sector. In an unmanaged system,

Eq. 2. P = ET + RTRF + ΔS_{SWE} + ΔS_{SM}

where P = precipitation (snow, rain), ET = evapotranspiration (including from irrigated regions), and RTRF is total runoff. Note RTRF represents (the computation of) runoff, and not a priori river discharge at a specific point or gauge, where a model might be calibrated. This is particularly relevant in a system with a series of reservoirs, or where there are inter-basin transfers.

__Partioning of Flows__

Practically, we are interested in not only the overall water budgets, but in partitioning the flows into components of specific relevance.

In the Amu Darya and Syr Darya, runoff is derived from both direct rainfall and from snowmelt. RTRF is composed of baseflow (BF) and surface flow (SF), and can be further partitioned into runoff derived from rainfall and snowmelt terms:

Eq. 3. RT_{RF} = R_{RAIN} + R_{SNOW}

The Aral basin has extensive current and planned hydropower development. Provision of these dams must be included, for both mass and routing considerations (as well as, of course, energy generation and irrigation). In an unmanaged system, RT_{RF} is a loss (in the mass balance sense) to that sector, and ΔS_{RIV} can be considered to be quite small, as it is only the water actually in river channels. But in a system with a series of dams, that isn’t a priori the case, as the runoff is essentially retained in that (or a neighboring) sector, in a reservoir.

To evaluate the inclusion of reservoirs, surface water can be partitioned as

Eq. 4. ΔS_{SW} = ΔS_{RIV} + ΔS_{RES}

where ΔSRIV = change in amount of water stored in river channels and ΔSRES = change in amount stored in reservoirs (dams). To highlight this point, the initial TWS equation (Eq. 1) can be recombined with Eq. 4; for example as:

Eq. 5. (ΔS_{GW }+ ΔS_{RES}) = ΔS_{LAND} – ( ΔS_{SWE} + ΔS_{SM} + ΔS_{RIV})

__Evaluation of Terms__

The challenge is how to assess each term.

It has historically been very difficult (if not impossible) to evaluate the change in TWS (especially groundwater and aquifers), as expressed in Eq. 1. But the capability of the GRACE satellite now allows an evaluation of overall TWS (at least at large scales), which allows further partitioning of the respective components (by specific means – measurements, models). The hydrology modeling environment (VIC) allows the computation of the individual terms of Eq. 2 (with the obvious dependency on the quality of the data sets used in the actual modeling). It should be noted that while each term of the model uses a common setup and forcing, the actual computation of the terms is independent (i.e’ not computed as variable b = 1 – variable a).

For comparative evaluation purposes, it is useful to rearrange Eq. 2 as:

Eq.6. P - ET - RT_{RF} = ΔS_{SWE} + ΔS_{SM}

And then to evaluate Eq 1 as:

Eq. 7 [ ΔS_{LAND]}GRACE = [(ΔS_{RIV} + ΔS_{RES }) + ΔS_{SWE} + ΔS_{SM }+ ΔS_{GW}]VIC

If changes in reservoir storage and (deep) groundwater are minimal, then terms of Eq 7 would be in approximate equilibrium. If either are significant, then GRACE should be able to detect any anomalies.

__Preliminary Results__

To compare the water balance terms computed from the VIC model with the GRACE moisture anomaly, the years 2003 through 2006 were used when the two data categories coincide. The GRACE water balance anomaly showed delay of one to five months in its peak and low season for both Amu and Syr Darya basins. The delay might have been created by the change in surface water storages and/or groundwater. The SM_SNOW which is the sum of the soil moisture storage and snow water equivalent change is well-correlated with the P-ET-RF (precipitation minus evapotranspiration and runoff). The correlation between monthly time series of GRACE moisture anomaly and P-ET-RF or SWE_SM is 0.70 and 0.78 for Amu and Syr Darya basins respectively.