From 7edf974fe4dba27eded16759ba4f9a59cd9e5097 Mon Sep 17 00:00:00 2001 From: jerabekjak Date: Mon, 11 Mar 2024 14:14:26 +0100 Subject: [PATCH] text in separate files --- reference_manual/text_en/main.tex | 485 +----------------------------- 1 file changed, 12 insertions(+), 473 deletions(-) diff --git a/reference_manual/text_en/main.tex b/reference_manual/text_en/main.tex index 2d84f72..a8eb847 100644 --- a/reference_manual/text_en/main.tex +++ b/reference_manual/text_en/main.tex @@ -1,490 +1,27 @@ - - \section{Introduction and model overview} \input{text_en/intro.tex} +\FloatBarrier \section{Rainfall data} -\section{Hillslope hydrology and hydraulics} - - \subsection{Water balance (JJ)} - - The SMODERP2D episodic rainfall-runoff/erosion model was used for the - investigation presented here. The 2D model is based on a 1D profile version, in - which the surface runoff and the erosion were typically calculated in several - 1D profiles representing the main flow path in the hillslope \cite{Dostal2000}. - The current generation of the SMODERP2D model is pixel distributed, and is - implemented in python in order to be compatible with most GIS software. The - development is presented on the github platform at - \href{https://github.com/storm-fsv-cvut/smoderp2d}{github.com/storm-fsv-cvut/smoderp2d}. - - The SMODERP2D model is primarily designed for surface runoff and erosion - computation. The surface flow routing in the model is based on the digital - elevation model (DEM). DEM also controls the spatial discretization of the - model. The principle of the model is the cell-by-cell mass balance calculated - in each time step. The change in the water level of the shear flow in any cell - in time is controlled using the equation: - \begin{equation} - \frac{\mathrm{d}h}{\mathrm{d}t} = es_{i,t-1} + q^{in}_{i,t-1} - inf_{i,t-1} - q^{out}_{i,t-1}, - \label{eq:bilance} - \end{equation} - where h is the surface water level (L), qin and qout are the sheet overland - inflow and outflow into and out of a given raster cell ($\mathrm{L.t^{-1}}$), - ep is the effective precipitation intensity (the potential precipitation - reduced by the interception zone and the surface retention) - ($\mathrm{L.t^{-1}}$), and inf is the infiltration rate ($\mathrm{L.t^{-1}}$). - The kinematic wave approach is used in the calculation of the overland flow. - The momentum is therefore expressed by the power-law: - - \begin{equation} - q = ah^b - \label{eq:powerlaw} - \end{equation} - where a and b are power-law parameters. Equation \ref{eq:powerlaw} can be - expressed in the form of the Manning–Strickler formula - - - \begin{equation} - q = n^{-1} s^Y h^b, - \label{eq:powerlaw} - \end{equation} - where n is roughness, Y empirical parameter and s is the surface slope ($\mathrm{L.L^{-1}}$). - - The infiltration component of Equation \ref{eq:bilance} is calculated by the - Philip infiltration equation \citep{philip1957} - \begin{equation} - inf = \frac{1}{2}St^{-1/2}+K_s. - \label{eq:infiltration} - \end{equation} - - where S stands for sorptivity ($\mathrm{L.t^{1/2}}$) and ($\mathrm{K_s}$) - stands for saturation hydraulic conductivity ($\mathrm{L.t^{-1}}$). - - The SMODERP2D model is subjected to uniform rainfall. The potential - precipitation is reduced due to surface retention. The surface retention is the - storage that needs to be filled before surface runoff can occur. - - The flow routing of the surface runoff is based on the D8 one-direction flow - algorithm \cite{o1984extraction}. The inflow to cell i is defined as the sum of the sheet - outflows from the adjacent cells, as: - - \begin{equation} - q^{in}_{i,t-1} = \sum_j^m q^{out}_{j,t-1}, - \label{eq:d8} - \end{equation} - where j is the index of the adjacent up-slope cells identified by the D8 flow - algorithm. - - The time derivative in Equation \ref{eq:bilance} is calculated using an - explicit method. The computation is therefore sensitive to the size of the time - step. The size of the time step is controlled by the Courant criterion, which - needs to be kept below the theoretical maximum value of 1, while the maximum - value in practise is lower than 1 - \cite{zhang1989modeling, esteves2000overland}. - - - The sheet flow water level of the next time t + 1 step in Equation - \ref{eq:bilance} which incorporates the sum \ref{eq:d8} is calculated with the - explicit time discretisation scheme for cell i as: - \begin{equation} - h_{i,t} =h_{i,t} + \mathrm{d}t (es_{i,t-1} + \sum_j^m q^{out}_{j,t-1}- - inf_{i,t-1} - q^{out}_{i,t-1}), - \label{eq:bilance} - \end{equation} - - %The principle of the model is the cell-by-cell mass balance calculated in each - %time step. The change in the water level of the shear flow in any cell in time - %is controlled using the equation: - % - %[Equation] - % - %(1) - % - %where h is the surface water level (L), qin and qout are the sheet overland - %inflow and outflow into and out of a given raster cell (L.t−1), ep is the - %effective precipitation intensity (the potential precipitation reduced by the - %interception zone and the surface retention) (L.t−1), and inf is the - %infiltration rate (L.t−1). - % - %The SMODERP2D model is subjected to uniform rainfall. The potential - %precipitation is reduced due to surface retention. The surface retention is the - %storage that needs to be filled before surface runoff can occur. - % - %The time derivative in Equation (1) is calculated using an explicit method. The - %computation is therefore sensitive to the size of the time step. The size of - %the time step is controlled by the Courant criterion, which needs to be kept - %below the theoretical maximum value of 1, while the maximum value in practise - %is lower than 1 [46,47]. - % - %The sheet flow water level of the next time t + 1 step in Equation (1) which - %incorporates the sum (5) is calculated with the explicit time discretisation - %scheme for cell i as: - % - %[Equation] - % - %(6) - - \subsubsection{Interception component (JJ)} - \subsubsection{Infiltration component (JJ) } - - - %Phillip infiltration - % - %The infiltration component of Equation (1) is calculated by the Philip infiltration equation [44] - % - %[Equation], - % - % - %(4) - % - %where S stands for sorptivity (L.t1/2) and Ks stands for saturation hydraulic conductivity (L.t−1). - % - %GA??? - - - - \subsubsection{Surface retention component (JJ)} - \subsection{Sheet flow hydraulics (JJ)} - \subsubsection{Principle of the solution} - - %The kinematic wave approach is used in the calculation of the overland flow. The momentum is therefore expressed by the power-law: - % - %[Equation], - % - % - %(2) - % - %where a and b are power-law parameters. Equation (2) can be expressed in the form of the Manning–Strickler formula - % - %[Equation] - % - % - %(3) - % - %where b and Y are empirical parameters and s is the surface slope (L.L−1). n- Manning roughness coefficient for sheet flow - % - % - % - %XXX - tables here or link to user guide - - \subsubsection{D8/ Multiple flow approach} - - %Two (optional) types of flow direction can be used in the model solution - % - %D8 algorithm - % - %The flow routing of the surface runoff is based on the D8 one-direction flow algorithm [45]. The inflow to cell i is defined as the sum of the sheet outflows from the adjacent cells, as: - % - %[Equation], - % - % - %(5) - % - %where j is the index of the adjacent up-slope cells identified by the D8 flow algorithm. - % - %Multiple flouw algorithm - % - - - \subsection{Rill flow formation and hydraulics (JJ)} - - The rill flow is also included in the calculation. In SMODERP2D, rill flow in a - cell occurs if $h>h_{crit}$, where $h_{crit}$ is the critical water level. The - water flow corresponding to the water level above the critical water level has - enough energy to start to carry the soil particles and to create a rill. - - The critical water level $h_{crit}$ is calculated as: - \begin{equation} - h_{crit} = MIN(h_{v_{crit}},h_{\tau_{crit}}), - \label{eq:critdef} - \end{equation} - where $h_{v_{crit}}$ is the water corresponding to the critical velocity, and - $h_{\tau_{crit}}$ is the water level corresponding to the critical shear - stress. As shown in Formula \ref{eq:critdef}, $h_{crit}$ uses several values - obtained with a different approach. This approach is adopted in order to remain - on the safe side of the emergence of a rill, since $h_{v_{crit}}$ is more - sensitive to the sheet flow velocity and $h_{\tau_{crit}}$ is more sensitive to - the slope of the soil surface. - - When the condition $h>h_{crit}$ is fulfilled, a rill starts to develop in a - given cell and $h_{sheet}=h_{crit}$. In SMODERP2D, the rill is a dynamic component and - can increase as the rill flow increases. The rill volume is controlled by the - volume of water corresponding to the rill water level $h_{rill}$. This volume is - calculated as: +\input{text_en/rain.tex} +\FloatBarrier +\section{Hillslope hydrology and hydraulics} - \begin{equation} - V_{rill} = h_{rill}P, - \label{eq:rillvol} - \end{equation} - - The critical water level $h_{crit}$ is calculated as: - \begin{equation} - h_{rill} = MAX(h-h_{crit},0), - \label{eq:hrill} - \end{equation} - P stands for the size of the raster cell. The rill is simplified as a small - channel at the soil surface with a rectangular cross section. The rectangle has - width $b_{rill}$ and rill height $y_{rill} = 0.7b_{rill}$. The rill flow is as - calculated with the Manning equation: - - \begin{equation} - q_{rill} = \frac{A}{n_{rill}} s^{1/2} R_{rill}^{2/3}, - \label{eq:rillflow} - \end{equation} - where A is the cross section of the rill, $n_{rill}$ is the roughness in the - rill, s is the surface slope, and $R_{rill}$ is the hydraulic radius of the - rill. - - As stated above, the size of the rill changes as $h_{rill}$ increases. The - scheme of this change is shown in Figure \ref{fig:rill_plneni}. The change in - the rill flow varies with the change in $R_{rill}$ in Equation - \ref{eq:rillflow}, since $h_{rill}$ increases, and therefore $y_{rill}$ and - $b_{rill}$ also increase. The $R_{rill}$ for an increasing rill is calculated - as: - \begin{equation} - R_{rill} = \frac{h_{rill}b_{rill}}{2h_{rill}+b_{rill}} = - \frac{y_{rill}b_{rill}}{2y_{rill}+b_{rill}}, - \label{eq:rrill} - \end{equation} - where: - \begin{equation} - b_{rill} = h_{rill}/0.7 - \label{eq:brill} - \end{equation} - - - \begin{figure}[b] - \centering - \includegraphics[width=1\linewidth]{./img/rill_schema_plneni.png} - \caption{Scheme of the rill size during increasing surface runoff.} - \label{fig:rill_plneni} - \end{figure} - - - During the recession limb of the hydrograph, the rill size “locks”, and - $h_{rill}$ decreases until the rill is empty. The scheme of the emptying rill - and the rill flow is shown in Figure~\ref{fig:rill_prazdneni}. In this case, - $R_{rill}$ is calculated from fixed $b_{rill}$ and decreasing $h_{rill}$. - $R_{rill}$ for decreasing rill flow is calculated as: - \begin{equation} - R_{rill} = \frac{h_{rill}b_{rill}}{2h_{rill}+b_{rill}}, - \label{eq:rrill2} - \end{equation} - where: - \begin{equation} - b_{rill} = y_{rill}/0.7 - \label{eq:brill2} - \end{equation} - - \begin{figure}[t] - \includegraphics[width=1\linewidth]{./img/rill_schema_prazdneni.png} - \caption{Scheme of the rill size during the recession limb of the hydrograph.} - \label{fig:rill_prazdneni} - \end{figure} - - The total water balance in cell i, where a rill is developed, is calculated as: - - \begin{equation} - \frac{\mathrm{d}h_i}{\mathrm{d}t} = es_i + q^{in}_{sheet,i}(h_{sheet,i}) - +q^{in}_{rill,i}(h_{rill,i}) - (inf_i + q^{out}_{sheet,i}(h_{sheet,i}) + - q^{out}_{rill,i}(h_{rill,i})) - % - % - %h_{i,t} =h_{i,t} + \mathrm{d}t (es_{i,t-1} + \sum_j^m q^{out}_{j,t-1}- - %inf_{i,t-1} - q^{out}_{i,t-1}), - \end{equation} - where: - \begin{equation} - q^{in}_{sheet,i} = \sum_j^m q^{out}_{sheet, j}(h_{sheet,j}),\quad \mathrm{and} - \end{equation} - \begin{equation} - q^{in}_{rill,i} = \sum_j^m q^{out}_{rill, j}(h_{rill,j}) - \end{equation} - - and: - \begin{equation} - h = h_{rill} + h_{sheet} - \end{equation} - - The rill water level is recalculated to cover the whole cell and not just the - bottom of the rill, as shown in Figures \ref{fig:rill_plneni} and - \ref{fig:rill_prazdneni}. - - %For each soil type a critical value of the tangential stress and velocity was - %estimated. From this critical value critical height in each cell is calculated. - %In principle this is a comparison of the current level and its critical value - %at each time interval. If the critical value is exceeded, the calculation - %enters the stage at which the rill starts to form. Dimensions of the rills are - %calculated from volume of the water exceeding the critical value. Sheet surface - %runoff is then calculated using the critical value level instead of current - %height in the time step. Once the level has dropped below the critical height - %value, the calculation returns only in the calculation of surface runoff. The - %resulting rasters of rill flow and speed in the rill are stored in - %user-selected directory along with vector shapefile of created rills. - %Calculation of the flow in the rill is based on Manning equation. - - \subsubsection{Rill formation (JJ)} - - %The rill flow is also included in the calculation. In SMODERP2D, rill flow in a - %cell occurs if [Equation], where [Equation] is the critical water level. The - %water flow corresponding to the water level above the critical water level has - %enough energy to start to carry the soil particles and to create a rill. - % - %The critical water level [Equation] is calculated as: - % - %[Equation] - % - % - %(7) - % - %where [Equation] is the water corresponding to the critical velocity, and - %[Equation] is the water level corresponding to the critical shear stress. As - %shown in Formula (7), [Equation] uses several values obtained with a different - %approach. This approach is adopted in order to remain on the safe side of the - %emergence of a rill, since [Equation] is more sensitive to the sheet flow - %velocity and [Equation] is more sensitive to the slope of the soil surface. - % - %When the condition [Equation] is fulfilled, a rill starts to develop in a given - %cell and [Equation]. In SMODERP2D, the rill is a dynamic component and can - %increase as the rill flow increases. The rill volume is controlled by the - %volume of water corresponding to the rill water level [Equation] This volume is - %calculated as: - % - %[Equation] - % - % - %(8) - % - %where: - % - %[Equation] - % - % - %(9) - % - %P stands for the size of the raster cell. - - \subsubsection{Rill hydraulics (JJ)} - - %The rill is simplified as a small channel at the soil surface with a - %rectangular cross section. The rectangle has width[Equation] and rill height - %[Equation]. The rill flow is as calculated with the Manning equation: - % - %[Equation] - % - % - %(10) - % - %where A is the cross section of the rill, [Equation] is the - %roughness in the rill, s is the surface slope, and [Equation] is the - %hydraulic radius of the rill. - % - %As stated above, the size of the rill changes as [Equation] increases. The - %scheme of this change is shown in Figure 1. The change in the rill flow varies - %with the change in [Equation] in Equation (10), since [Equation] increases, and - %therefore [Equation] and [Equation] also increase. The [Equation] for an - %increasing rill is calculated as: - % - %[Equation] - % - % - %(11) - % - %where: - % - %[Equation] - % - % - %(12) - % - % - % - %Figure 1. Scheme of the rill size during increasing surface runoff. - % - %During the recession limb of the hydrograph, the rill size - %“locks”, and [Equation] decreases until the rill is empty. The scheme - %of the emptying rill and the rill flow is shown in Figure 2. In this - %case, [Equation] is calculated from fixed [Equation] and decreasing - %[Equation]. [Equation] for decreasing rill flow is calculated as: - % - %[Equation] - % - % - %(13) - % - %where: - % - %[Equation] - % - % - %(14) - % - % - % - %Figure 2. Scheme of the rill size during the recession limb of the hydrograph. - % - %The total water balance in cell i, where a rill is developed, is calculated as: - % - %[Equation] - % - % - %(15) - % - %where: - % - %[Equation] - % - % - %(16) - % - %[Equation] - % - % - %(17) - % - % - % - %and: - % - %[Equation] - % - % - %(18) - % - % - % - %The rill water level is recalculated to cover the whole cell and not just the bottom of the rill, as shown in Figures 1 and 2. - - - - \subsection{Kinematic / Diffuse approach} - - \subsubsection{Kinematic} - \subsubsection{Diffuse} - - \subsection{Implicit /Explicit approach} - - \subsubsection{Implicit} - \subsubsection{Explicit} - - \subsection{Impute data requirements and description} - - \subsubsection{DMR} - \subsubsection{Soil} - \subsubsection{Land Use} - \subsubsection{Soil and Land Use combination} +\input{text_en/hillhyd.tex} +\FloatBarrier \section{Stream hydrology and hydraulics} \subsection{Segmentation} \subsection{Kinematic approach - Manning formula} - \subsection{Stream shape} - \subsection{Stream characteristics} - -\section{Impute data requirements and description} + \subsubsection{Stream shape} + \subsubsection{Stream characteristics} + \subsection{Impute data requirements and description} +\FloatBarrier \section{Output data description} \subsection{Basic data} @@ -492,12 +29,14 @@ \section{Output data description} \subsection{Control} \subsection{Temporary data} +\FloatBarrier \section{Numerical solution and source code description} \subsection{Source code architecture} \subsection{NumPy solution} \subsection{Implicit method numerical solution} +\FloatBarrier \section{Reference}