Technical Note: On the confounding similarity of two water balance formulas – Turc-Mezentsev vs Tixeront-Fu (original) (raw)
Related papers
A Review of Procedures for Water Balance Modelling
Water balance is another name for the principle of mass conservation in which changes of total water volume, inflow (precipitation, snow melt) and outflow (evaporation, transpiration, surface and subsurface runoff) on a given area are balanced. The study of the water balance with a previous knowledge of climatic and physical basin characteristics offers information about current and future water quantities, and added insight into the complex process of basin runoff. This paper gives a review of methods for defining water balance and its main components, a review of numerical models for water balance calculation and examples of model applications.
Hydrology
Nowadays, the balance between incoming precipitation and stream or spring discharge is a challenging aspect in many scientific disciplines related to water management. In this regard, although advances in the methodologies for water balance calculation concerning each component of the water cycle have been achieved, the Thornthwaite–Mather method remains one of the most used, especially for hydrogeological purposes. In fact, in contrast to physical-based models, which require many input parameters, the Thornthwaite–Mather method is a simple, empirical, data-driven procedure in which the error associated with its use is smaller than that associated with the measurement of input data. The disadvantage of this method is that elaboration times can be excessively long if a classical MS Excel file is used for a large amount of data. Although many authors have attempted to automatize the procedure using simple algorithms or graphical user interfaces, some bugs have been detected. For these...
Water balance calculation capability of hydrological models
Acta Agraria Kaposváriensis
Currently, in the world, there are many different hydrological models built and developed to solve problems related to the hydrological cycle. Each model has its specific mathematical foundations to describe physical processes in nature. Therefore, each model has its various characteristics: setting up the model, input data requirements, model calibration and verification, and output results. Water balance is still playing an important role in the effective management and use of water resources for agriculture. Based on the results of the hydrological parameter’s calculation, the water balance of the study basin can be calculated by the user or by the separated module of each model. Each hydrological models have its advantages and disadvantages. However, it is impossible to simulate hydrological processes and water balance completely accurately in nature. Still, simulation results can give us a view of the changing trend of hydrological components and the water balance. Model develo...
Verification of Catchment Size Using the Water Balance Equation
2016
To determine water balance equation parameters, sufficiently long time-series of monitoring data, such as river discharges at a river cross-section of interest or discharges of a spring/river source, are required along with isohyet maps of the extended area of the catchment. If isohyet maps are not available, then rain gauge or meteorological stations are needed in the considered catchment, which are rare in small and medium catchments, especially in mountainous regions. It is also extremely important to accurately define the size of the catchment but that is not an easy task in karst and arid areas. In such cases, especially karst, it is wrong to calculate water balance equation parameters using a topographic or surface water divide. Instead, the active, subsurface catchment area needs to be defined and used in subsequent calculations. One of the objectives of the paper is to take the Dojkinacka River, which drains the southern slopes of Mt. Stara Planina, as an example to demonstr...
An analysis of horizontal inflow and outflow in the groundwater-budget equation and the significance for interbasin flow are presented. Two field cases in Mexico, one in the Baja California peninsula and another in central Mexico, highlight the influence of interbasin flow where a significant proportion (approximately 70%) of the abstracted (thermal) groundwater probably originates outside the drainage basin. A conclusion is that a groundwater-balance study is an unsatisfactory method for determining some parameters, such as storativity (S). Specifically, the groundwater-balance approach provides unreliable results when vertical inflow is ignored or cannot be adequately defined. Vertical flow is indicated by the presence of groundwater temperatures as much as 23 °C higher than ambient temperature. Regional faults could be the pathways for upward flow. When vertical inflow is ignored, uncertainty in the estimation of the storativity through regional groundwater-balance calculation results. On the basis of the groundwater-balance equation, a value of S=0.19 appears to represent the confined condition of the developed part of the aquifer; this result is several orders of magnitude higher than would be reasonable according to the geological conditions. Findings are useful in evaluating whether a groundwater resource is being "overexploited". Conclusions are instructive in the application of transient-flow computer models, in which vertical flow of less dense water from beneath is not included.
Hydrogeology Journal, 2000
An analysis of horizontal inflow and outflow in the groundwater-budget equation and the significance for interbasin flow are presented. Two field cases in Mexico, one in the Baja California peninsula and another in central Mexico, highlight the influence of interbasin flow. A significant proportion (approximately 70%) of the abstracted (thermal) groundwater probably originates outside the drainage basin. A conclusion is that a groundwater-balance study is an unsatisfactory method for determining some parameters, such as storativity (S). Specifically, the groundwater-balance approach provides unreliable results when vertical inflow is ignored or cannot be adequately defined. Vertical flow is indicated by the presence of groundwater temperatures as much as 23 °C higher than ambient temperature. Regional faults could be the pathways for upward flow. When vertical inflow is ignored, uncertainty in the estimation of the storativity through regional groundwater-balance calculation results. On the basis of the groundwater-balance equation, a value of S=0.19 appears to represent the confined condition of the developed part of the aquifer; this result is several orders of magnitude higher than would be reasonable according to the geological conditions. Findings are useful in evaluating whether a groundwater resource is being "overexploited". Conclusions are instructive in the application of transient-flow computer models, in which vertical flow of less dense water from beneath is not included. L'article présente une analyse des entrées et des sorties horizontales dans l'équation du bilan d'une nappe et leur signification dans les écoulements entre bassins. Deux exemples provenant du Mexique, l'un dans la péninsule de Basse Californie, l'autre dans le centre du Mexique, mettent en lumière l'influence de l'écoulement entre bassins, où une proportion significative (environ 70%) de l'eau souterraine extraite, thermale, a probablement son origine hors du bassin. Une conclusion est qu'une étude par bilan de la nappe est une méthode qui n'est pas satisfaisante pour déterminer certains paramètres comme le coefficient d'emmagasinement. En particulier, l'approche par le bilan de la nappe donne des résultats qui ne sont pas fiables lorsque l'on ignore la drainance verticale ou que l'on ne peut pas la définir correctement. L'existence d'une drainance verticale est prouvée par des températures de l'eau souterraine pouvant être supérieures de 23 °C à la température ambiante. Des failles régionales peuvent permettre ces écoulements vers le haut. Lorsque l'on ignore la drainance verticale, on introduit une incertitude sur l'estimation de l'emmagasinement à partir des calculs du bilan régional de la nappe. Sur la base de l'équation du bilan de la nappe, une valeur de S=0,19 semble représenter les conditions captives de la partie développée de l'aquifère; ce résultat est plus élevé, de plusieurs ordres de grandeur, que celui que l'on peut raisonnablement attendre des conditions géologiques. Ces résultats sont utiles pour évaluer si une ressource en eau souterraine est "surexploitée". Ces conclusions sont intéressantes lorsque l'on applique des modèles d'écoulement transitoire dans lesquels on ne prend pas en compte la drainance verticale d'une eau plus légère remontant. En este trabajo, se investigan las entradas y salidas de flujo horizontal en la ecuación de balance de agua subterránea, así como el papel que desempeñan en el flujo entre cuencas. Se analizan dos ejemplos de México, uno en la Península de Baja California y otro en la parte central del país. En ambos, destaca la influencia del flujo entre cuencas, ya que se estima que una parte importante (aproximadamente el 70%) del agua termal extraída procede de una cuenca superficial externa. Se concluye que el método basado en cálculos de balance de agua subterránea no es satisfactorio para determinar algunos parámetros, como, por ejemplo, el coeficiente de almacenamiento (S). En particular, la ecuación de balance de agua subterránea proporciona resultados poco fiables cuando el flujo vertical es ignorado o no puede ser evaluado de forma adecuada. El flujo vertical se identifica por un incremento de temperatura del agua subterránea, que puede llegar a superar la temperatura ambiental en hasta 23 °C. La presencia de fallas regionales y las extracciones pueden favorecer el flujo vertical. Cuando éste es ignorado, aumenta la incertidumbre en la estimación del coeficiente de almacenamiento mediante un balance de agua subterránea. El valor obtenido con este médodo (S=0,19) es característico de acuíferos libres, pero resulta varios órdenes de magnitud mayor que el que sería esperable teniendo en cuenta las condiciones hidrogeológicas. Estos hallazgos son útiles para evaluar si los recursos de agua subterránea están siendo "sobreexplotados". Las conclusiones obtenidas son instructivas de cara a la aplicación de modelos numéricos de flujo transitorio que no consideran el flujo vertical por densidad.
Statistical analysis of parameters and residuals of conceptual hydrological models has received little effort in the hydrological research, certainly by orders of magnitude less than on many other problems like development and comparison of automatic calibration methods, optimisation algorithms, etc. Much more work is required than is presently undertaken to investigate the properties of model residuals. There is a need of an easily understandable and applicable statistical analysis scheme. In this article, a procedure is presented through which two basic issues of model evaluation are accounted for. First, different techniques used for parameter analysis are discussed. Second, methodology of residual analysis is discussed and the general behaviours of residuals are examined. To illustrate the procedure, a simple water balance model was applied to the Stabbybäcken River Basin in central Sweden.
THE WATER BALANCE FOR RESERVOIRS AND ITS APPLICATION TO TROPICAL LATITUDES
The hydrological balance for large water bodies, including reservoirs, requires the identification and accounting of water volumes and flows entering and leaving the water body control volume over a given period of time. These flows are varied in mechanisms and dynamics and they are highly dependent on conditions of the basin such as geology, weather, morphometry, land use, geographic location and time. A dynamic equilibrium is established between water inputs and outputs, which can be combined into a differential equation that describes reservoir water balance. Based on a thorough identification of the most likely water inputs and outputs for a reservoir, this paper reviews the methods of calculation, estimation and modeling for all such flows and volume terms involved in reservoir water balance. These methods are either deterministic, statistical or stochastic in nature, depending upon the element of the water balance. The solutions to such methods range historically from graphical to analytical to numerical to complex computer software models. This paper also analyzes the recent application and uses of modeling efforts in different basins for various types of water bodies in tropical and subtropical latitudes.
Agricultural Water Management, 2001
The hydrology of the Earth's surface is quite dynamic. Attempts to model the hydrology have been only partially successful. Many of the existing detailed numerical models require so many input parameters that they are not practical for use at speci®c locations, and the simpli®ed models do not well describe the dynamic surface hydrology. Here, we present a modi®ed statisticaldynamic model that is simple to use. We evaluate how well the modi®ed statistical-dynamic model describes surface hydrology by comparing it to a more advanced numerical model and to ®eld measurements. Our model is developed by making speci®c modi®cations to the Eagleson statisticaldynamic water balance model. Speci®c modi®cations to the earlier model include: the addition of precipitation periods that can account for seasonal variations in precipitation and water balance, a change in how soil water properties and¯ow are computed, and how a limited water supply in¯uences plant transpiration so that transpiration rates can be less than the potential transpiration rates. Mass conservation and a step by step prediction-correction algorithm are used to calculate the mean water balance and its partitioning as well as the average soil moisture in the precipitation periods. All of these modi®cations improve the statistical-dynamic model and make it more¯exible and potentially useful. Comparisons of the modi®ed model are made with numerical simulations of the WAVES model and with 10-year ®eld measurements from an eco-hydrological system on the Loess Plateau. The data from a long-term fertility experiment of winter wheat at Changwu Agroecological Station on the Loess Plateau are used to test the modi®ed statistical-dynamic water balance model. In both comparisons the correspondence is remarkably good. The modi®ed statistical-dynamic water balance model accurately predicts the mean water balance components and the dynamic processes of the mean soil moisture for speci®c wheat-fertility-productivity Agricultural Water Management 48 (2001) 21±35 : S 0 3 7 8 -3 7 7 4 ( 0 0 ) 0 0 1 1 1 -6 conditions. The statistical-dynamic water balance model is simple to use, fast and ef®cient, requires less input than complex numerical models, and is shown to be quite accurate in predicting dynamic soil moisture storage. #
Spatial distribution of the energy and flows of the hydrologic cycle in the form of evapotranspiration, runoff and infiltration within a region is a function of the climate (precipitation, temperature and evaporation) and landscape (relief, soil, land cover) of the area, and constitutes the hydrological cycle. The general model evaluating each of these sections and flows is the water balance. Methods for calculating the water balance in a region are based on either mass transference or energy transference. The aim of the present work was to calculate the spatially distributed regional water balance in a poorly gauged basin by each of three methods, and to evaluate these methods by comparing the results. Spatial modelling of the hydrometeorological variables used the ArcView 3.2 geographic information system; hydrological modelling made using HEC system version 3.1.0. The first approach was based on analysis of the information recorded at the available meteorological stations, point estimation of the monthly water balance according to the Thornthwaite and Mather method, and the use of Thiessen polygons. The second approach was based on the calculation and distribution of the parameters for the Thornthwaite and Mather method. The third approach used the FAO–Penman equation. The models were applied to the Lake Cuitzeo basin. The result obtained by the third method indicated a mean annual volume of runoff of 229.05 hm3. This volume is only 8.5 hm3 less than that estimated as necessary for maintaining a depth of 1 m throughout the Lake Cuitzeo water body. This difference represents a possible fluctuation of 2 cm in the mean level of the surface of the lake. The HEC model represents an alternative for modelling the basin since it requires relatively few inputs, of which the main ones (temperature, precipitation, potential evapotranspiration, evapotranspiration) are obtainable or deducible by means of one or other of the approaches presented here.