Figure 2. Temporal evolution of the inundation fraction from GIEMS and
Noah-MP modelled \(F_{\text{sat}}\) in the Prairie Pothole Region.
Therefore, we propose a new formula for the saturated fraction\(F_{\text{sat}}\), based on the first layer soil saturation, instead of
water table depth:
\(F_{\text{sat}}=F_{\text{satmx}}*(\frac{SH_{2}O-\text{SM}_{\text{wlt}}}{\text{SM}_{\text{ref}}-\text{SM}_{\text{wlt}}})\)(7)
The first layer soil moisture (\(\text{SH}_{2}O\)) responds more rapidly
to surface hydrological processes, such as snowmelt infiltration and
evapotranspiration, than groundwater level. \(F_{\text{sat}}\) is
determined by the maximum saturated fraction (\(F_{\text{satmx}}\)) and
a relative soil moisture saturation condition, normalized by the soil
moisture wilting point (\(\text{SM}_{\text{wlt}}\)) and field capacity
(\(\text{SM}_{\text{ref}}\)). This assumes the mean soil moisture
saturation in the first layer soil can empirically represent spatial
heterogeneity of soil saturation at the sub-grid scale.
2.5 Implementing the surface wetland storage scheme
In this study, we incorporate a sub-grid bucket-style surface water
storage scheme to represent the surface water dynamics in Prairie
Pothole wetlands in North America by capturing three important processes
in its water balance: (1) wetland storage receives water from snowmelt
runoff and rainfall; (2) water in wetland storage would evaporate at the
potential rate, calculated using the Penman equation in equation (10);
(3) when the water exceeds the wetland maximum storage capacity
(\(W_{\text{cap}}\)), it will spill out and become the outflow term.
This wetland storage scheme operates at the sub-grid scale and uses\(F_{\text{sat}}\) to determine the inflow of water input from
precipitation and snowmelt and contributes to the latent heat flux as a
weighted average over all three sub-grid types, similar to the treatment
in Pitman (1991). The sensible heat flux is calculated as the residual
term from the energy balance equation.
\(Q_{\text{insur}}=Q_{\text{snowmelt}}+Q_{\text{rain}}\) (8)
\(Q_{\text{inflow}}=Q_{\text{insur}}*F_{\text{sat}}\) (9)
\(Q_{\text{evap}}=\frac{mR_{n}+\rho c_{p}(e)g_{a}}{\lambda_{v}(m+\gamma)}\)(10)
\(\text{LH}_{\text{all}}={(1-F_{\text{sat}})(F}_{\text{veg}}\left(\text{LE}_{g,v}+\text{LE}_{v}\right)+(1-F_{\text{veg}})\text{LE}_{g,b})+F_{\text{sat}}*Q_{\text{evap}}\lambda_{v}\)(11)
\(Q_{\text{outflow}}={max(Q}_{\text{inflow}}-W_{\text{cap}},0)\)(12)
\(W_{\text{surf}}=Q_{\text{inflow}}-Q_{\text{evap}}*F_{\text{sat}}-Q_{\text{outflow}}\)(13)
In many traditional LSM treatments, surface runoff is treated as a
drainage term that leaves the grid cell and is lost to the water
balance. In our new scheme, the surface runoff from snowmelt and
rainfall becomes the inflow to surface water storage
(\(Q_{\text{inflow}}\)). The water in surface wetlands evaporates to the
atmosphere at the potential rate, calculated by the Penman equation. The
outflow is a result of total water exceeding the maximum water storage
(\(W_{\text{cap}}\)), characterizing the “fill-and-spill” process.
Note this surface wetland storage scheme is not connected to other
wetland storage or a river network, so that the outflow term will leave
the grid point and is lost to the water balance, as parameterized in the
default Noah-MP. The change of surface water storage\((W_{\text{surf}})\) is calculated by the net balance of inflow,
evaporation, and outflow.
Figure 3 illustrates the difference between the default Noah-MP and the
modified surface runoff scheme in this study. The left-hand side shows
the default Noah-MP surface runoff scheme based on the TOPMODEL
saturation-excess concept. The inflow from rain and snowmelt
(\(Q_{\text{insur}}\)) will be partitioned into infiltration (in the
1-\(F_{\text{sat}}\) portion), which enters soil moisture, and to
surface runoff (in the \(F_{\text{sat}}\) portion), which eventually
leaves the grid cell. The right-hand side shows the two modifications in
our study: (1) the modified \(F_{\text{sat}}\) parameterization based on
first layer soil saturation; (2) creating a surface water storage\(W_{\text{cap}}\) representing surface wetland dynamics. The\(F_{\text{sat}}\) portion of the inflow will now be collected within
the \(W_{\text{cap}}\) storage and evaporate to the atmosphere with a
weighted function. The water amount exceeding the maximum capacity will
become the outflow from the wetland (also referred to as the new runoff
term, \(R_{\text{srf}}\)).