Budyko Model Research Articles

Estimating potential evapotranspiration without continuous daily data: possible errors and impact on water balance simulations

Alternative approaches to estimating monthly and annual potential evapotranspiration (PE) are explored in cases where daily climate data are not routinely recorded. A database consisting of data from 222 weather stations, representing a wide variety of climatic conditions, is used to draw general conclusions. In addition, two PE formulae with different data requirements are used: the standard FAO-56 Penman-Monteith equation, and a simple temperature-based equation. First, we tested the degree of bias introduced by using climate data averaged over long time periods instead of daily data. Second, we explored the sensitivity of PE estimation with respect to variations in sampling frequency of climate variables. The results show that using mean weather data has only a limited effect on monthly and annual PE estimates. Conversely, imperfect sampling of weather data may bias monthly and to a lesser extent annual PE estimates if the sampling period exceeds 5 and 10 days, respectively. Finally, we tested the impact of erroneous weather data on the simulations of annual actual evapotranspiration obtained with the Budyko model. The impact on the Budyko model outputs depends more on the dryness index of a given location than on annual PE; for regions under water stress, the errors in estimation of actual evapotranspiration are very limited, compared to humid regions where available energy is the dominating factor and the propagation of PE errors is important. Citation Oudin, L., Moulin, L., Bendjoudi, H. & Ribstein, P. (2010) Estimating potential evapotranspiration without continuous daily data: possible errors and impact on water balance simulations. Hydrol. Sci. J. 55(2), 209–222.

Bulk Recycling Models with Incomplete Vertical Mixing. Part II: Precipitation Recycling in the Amazon Basin

Abstract An efficient method for precipitation recycling calculations based on the general bulk recycling model is developed and applied to the Amazon basin region. The results are compared with the estimates provided by simplified recycling models, and with the estimations obtained in other studies. Then the numerical procedure is adjusted to the modified recycling model incorporating some effects of incomplete vertical mixing of water in the tropospheric column as described in Part I of this paper. The modified numerical model is applied to the Amazon basin region and the results are compared with those from the unmodified model. It is seen from the results that the effects related to an incomplete vertical mixing produce significant changes in the level and distribution of precipitation recycling over the Amazon basin. The general changes in the recycling patterns occurring as a result of modifications include a significant increase in the contribution of recycled water to precipitation in the eastern part of the region and weakening continental recycling gradients. The regional recycling ratio values for the Amazon basin estimated by the modified model are significantly higher than the values provided by the unmodified model. The results of application of the models to several other regions on the globe are described in short. In particular, a comparison of the results with the estimates by the modified Budyko model is made for different regions, and it is found that the modified Budyko's model estimates are, in general, closer to the modified model numerical results than it was for the unmodified models. The results for precipitation recycling over the central United States are presented in more detail. For this region, the information on the degree of incomplete vertical mixing available from the GCM tracer transport modeling results has been used in the modified model calculations. It has been found that, as distinct from the Amazon basin, the effects related to an incomplete vertical mixing do not produce significant changes in the level and distribution of precipitation recycling over the central United States.

The Estimation of Regional Precipitation Recycling. Part I: Review of Recycling Models

Abstract This review preceding a description of a new recycling model (Part II of this paper) discusses one aspect of the regional precipitation recycling studies, namely, the mathematical modeling of the recycling process. Several recycling models developed in recent decades are discussed within a unified framework of equations of the conservation of atmospheric water vapor mass. Most of the recycling models may be considered as modifications and generalizations of Budyko's model. In spite of different forms, into which authors present their models, every recycling model is based on two equations of conservation of mass for two fractions of precipitable water in the atmosphere—written under some common assumptions—and the equation expressing the condition that these two fractions are well mixed. If any of these three equations is missing the model is incomplete and its results inconsistent. Different models differ by additional assumptions made in order to simplify either the equations or their solution ...

Estimating the Role of Local Evaporation in Precipitation for a Two-Dimensional Region

Budyko's model for estimating the contributions of locally evaporated and advected moisture to regional precipitation is extended to two dimensions. It is shown that a simple extension by analogy of the one-dimensional Budyko's formula to a two-dimensional region is inconsistent unless the flow in the region is parallel and uniform. The correct extension based on the two-dimensional equations of conservation of water vapor in the region leads to a generalization of Budyko's formula that includes a correction factor depending on the atmospheric flow structure. A general procedure for calculating the correction factor for a given atmospheric flow field is presented. Calculations of the correction factor for specific flow structures show that the deviations of the flow from the rectilinear structure can significantly affect the degree to which the local evaporation contributes to precipitation.

Global vegetation change predicted by the modified Budyko model

A modified Budyko global vegetation model is used to predict changes in global vegetation patterns resulting from climate change (CO2 doubling). Vegetation patterns are predicted using a model based on a dryness index and potential evaporation determined by solving radiation balance equations. Climate change scenarios are derived from predictions from four General Circulation Models (GCM's) of the atmosphere (GFDL, GISS, OSU, and UKMO). Global vegetation maps after climate change are compared to the current climate vegetation map using the kappa statistic for judging agreement, as well as by calculating area statistics. All four GCM scenarios show similar trends in vegetation shifts and in areas that remain stable, although the UKMO scenario predicts greater warming than the others. Climate change maps produced by all four GCM scenarios show good agreement with the current climate vegetation map for the globe as a whole, although over half of the vegetation classes show only poor to fair agreement. The most stable areas are Desert and Ice/Polar Desert. Because most of the predicted warming is concentrated in the Boreal and Temperate zones, vegetation there is predicted to undergo the greatest change. Specifically, all Boreal vegetation classes are predicted to shrink. The interrelated classes of Tundra, Taiga, and Temperate Forest are predicted to replace much of their poleward (mostly northern) neighbors. Most vegetation classes in the Subtropics and Tropics are predicted to expand. Any shift in the Tropics favoring either Forest over Savanna, or vice versa, will be determined by the magnitude of the increased precipitation accompanying global warming. Although the model predicts equilibrium conditions to which many plant species cannot adjust (through migration or microevolution) in the 50–100 y needed for CO2 doubling, it is nevertheless not clear if projected global warming will result in drastic or benign vegetation change.

Special Paper: A Global Vegetation Model Based on the Climatological Approach of Budyko

A global vegetation model based on the climato- logical approach of Budyko is developed. The major vege- tation zones of the world are predicted by a two- dimensional ordination of a Dryness Index and Potential Evaporation, which is derived from radiation balance. Mean temperature of the warmest month is also used to separate the Ice/Polar Desert, Tundra, and Taiga zones. Pre- dictions of vegetation distributions are made using a global climate database interpolated to a 0.5? by 0.5? terrestrial grid. The overall impression from examining the resulting global vegetation map is that the modified Budyko model predicts the location and distribution of the world's vegeta- tion fairly well. Comparison between model predictions and Olson's actual vegetation map were based on Kappa statistics and indicate good agreement for Ice/Polar Desert, Tundra, Taiga, and Desert (even though we predict too much Desert). Agreement with Olson's map was fair for predicting the specific location of Tropical Rain Forest and Tropical Savannas, and was good for predicting their general location at a larger scale. Agreement between Olson's map and model predictions were poor for Steppe, Temperate Forest, Tropical Seasonal Forest, and Xerophy- tic Shrubs, although the predictions for Temperate Forest and Tropical Seasonal Forest improved to fair at a larger scale for judging agreement. Agreement with the baseline map of Olson was poor for Steppe and Xerophytic Shrubs at all scales of comparison. Based on Kappa statistics, overall agreement between model predictions and Olson's map is between fair and good, depending on the scale of comparison. The model performed well in comparison to other global vegetation models. Apparently the calculation of radiation balance and the resulting Dryness Index and Potential Evaporation provides important information for predicting the distribution of the major vegetation zones of the world.

The influence of climatic conditions on the heat balance of the human body

The structure of heat exchange between the human body and its surroundings has been studied according to M.I. Budyko's model. Comparative measurements were carried out in the Polish Lakeland (maritime, temperate warm climate), in Central Mongolia (continental, temperate cool climate), and in the Kara Kum desert (dry subtropical climate). The results deal with the summer and early autumn seasons. The calculations indicate that the quantitative apportionment of various forms of heat exchange depend on specific weather conditions, which are typical for the distinguished climatic zones.

Analytical Analysis of a Budyko-Type Climate Model

For a given value of the solar constant we have found that the Budyko-type climate model gives two positions for the edge of the polar ice sheet. The results of the Budyko model suggest that with a decrease in the solar constant of about 1.6%, the ice cap reaches a latitude of about 50°. At this point the model breaks down and the solution for the position of the edge of the polar ice sheet becomes complex. We have based our conclusions on analytic investigations. Numerical calculations were used only to support our analytic results.

Energy input-output climates of the world: A preliminary attempt

A genetic climatic classification is presented which uses the fluxes of energy and moisture at the interface as its basis. Long and short wave inputs are abstracted into net radiation, whereas latent heat flux, vertical sensible heat flux and horizontal sensible heat flux (at interface level) are used as output components in this global classification. Six climatic groups and sixty-two climates result. For purposes of demonstration of the system, Budyko's model was used to derive the necessary data. It is believed, until future models generate more accurate data, that the main global features portrayed by the scheme are consistent and show reasonable trends.