May 23, 2016

The "details lost" rainfall information in hydrological modelling

I have been interested to this topic since two years ago, and I realised now I will not find time to do it . So let me put my thought here. 

The spatial rainfall variability is well recognised field of study and it is also the one that needs further improvement in hydrology (Syed et al., 2003, Woolhiser, 1996). In the proper estimation of spatial rainfall data for modelling, there are efforts on the characterisation of rainfall field at different scale.  In the context of semi-distributed hydrological models, the rainfall inputs are usually required at some level of aggregated (i.e sub basin, HRU, hillslope). All the efforts of rainfall estimation and their spatial variability is focused mainly in the correct estimation of the 1st moment of these hydrological modelling units. Bloschl and Sivapalan (1995) formalised the upscaling activities as two steps: distributing the point measurement to the large area (units), and aggregation of spatially distributed rainfall into a single value. In the series of papers, Foufoula-Georgiou and her co-authors (Kumar and Foufoula-Georgiou, 1990, Foufoula-Georgiou and Lettenmaier, 1986, Foufoula-Georgiou and Georgakakos, 1991, Kumar and Foufoula-Georgiou, 1993b,a), in effort to understand this rainfall spatial organisation at die rent scales, they point out that spatial rainfall characterisation at larger scale provides average (smoothed process) and the "detail lost" information. While the smoothed process is representation of the areal mean rainfall at the sub basin scale, the "detail lost" is the rainfall information that is lost during the smoothing processes, which can be inferred from other statistical moments. 

It is note that in the semi-distributed model, the modelling units are based on the "hydrological similarity concepts". This mean that the units (subbasin) are statistically characterized. So far all the studies on semi-distributed models, or those uses large scale grid inputs, focused on the proper representation of the 1st statistical moment, and as to my experience, there is gaps in understanding and incorporating the sub basin variability in to the modelling environments.

With all research eorts in understanding the spatial representation of rainfall at all level of scales, however, it is clearly apparent that the effort to incorporate the rainfall spatial variability in the semi-distributed modelling solution is missed. The epistemic sources of uncertainty, i.e, uncertainty caused by the system representation and lack of skills to treat them, in hydrological model are the one we need to be concerned (Beven et al. 2011; Merz and Thieken, 2005).

What I think important is the use of probability distribution of rainfall at each time steps for each HRU(hydro logical response units) to obtain the probably of discharge time series instead of a single deterministic estimation. I have seen the use of various models to incorporate the model parameters to generate the probability band of simulation, but never seen due to the use of forcing input data. Here this figure is to show the effects of the mean (centre), the maximum and minimum (the blue band) of rainfall of each HRU of a basin in JGrass-NewAge modelling.
Fig 1: JGrass-NewAge simulation using different HRU rainfall representation. 

Keith Beven, PJ Smith, and Andrew Wood. On the colour and spin of epistemic error (and what we might do about it). Hydrology and Earth System Sciences, 15(10):3123

Gunter Bloschl and M Sivapalan. Scale issues in hydrological modelling: a review. Hydrological processes, 9(3-4):251{290, 1995.

E Foufoula-Georgiou and Konstantine P Georgakakos. Hydrologic advances in space-time precipitation modelling and forecasting. In Recent advances in the modelling of hydrologic systems, pages 47{65. Springer, 1991.

E Foufoula-Georgiou and Dennis P Lettenmaier. Continuous-time versus discrete-time point process models for rainfall occurrence series. Water Resources Research, 22(4):531

Praveen Kumar and E Foufoula-Georgiou. Fourier domain shape analysis methods: A brief review and an illustrative application to rainfall area evolution. Water Resources Research, 26(9):2219

Praveen Kumar and E Foufoula-Georgiou. A multicomponent decomposition of spatial rainfall elds: 2. self-similarity in  fluctuations. Water Resources Research, 29(8):2533{2544, 1993a.

Praveen Kumar and E Foufoula-Georgiou. A new look at rainfall  fluctuations and scaling properties of spatial rainfall using orthogonal wavelets. Journal of Applied Meteorology, 32(2):209

Bruno Merz and Annegret H Thieken. Separating natural and epistemic uncertainty in  food frequency
analysis. Journal of Hydrology, 309(1):114

Kamran H Syed, David C Goodrich, Donald E Myers, and Soroosh Sorooshian. Spatial characteristics of thunderstorm rainfall elds and their relation to runo. Journal of Hydrology, 271(1):1{21, 2003.

On the total freshwater storage deficit of Ethiopia

As it receives one of the highest rainfall amount in the continent and the region,  Ethiopia is the water tower for the greater horn of Africa and the Nile. Because of its small-holder and traditional based  agrarian economy, but recurrent drought is the main development challenge. In the last decades, hydrologists developed  many drought indexes based on various hydrological and meteorological components like rainfall, evapotranspiration, and runoff to provide indexes for decision making. some of these are: Drought Severity Index (PDSI) (Palmer, 1965), Crop Moisture Index (CMI) (Palmer, 1968), Standardized Precipitation Index (SPI) (McKee et al., 1993), and Surface Water Supply Index (SWSI) (Shafer and Dezman, 1982). There are already  some efforts  to  understand the pattern of rainfall in the region,  mainly from the long term climate change perspective, and the findings are mixed.

The total available freshwater is the residual of all the hydrological fluxes. Hence, it is the integrated indicator of the water budget system of a basin.  On the contrary,  it  is the most difficult component to measure, if obtained with huge efforts, it is very specific and point information. NASA’s Gravity Recovery and Climate Experiment (GRACE) mission (Tapley et al., 2004) provides an independent satellite observation of change of the total water storage. Recently this data has been used to estimate the total water deficit of large basin, and it is evaluated positively. Here, I analyzed GRACE data to understand the total water storage of the Ethiopia. The objectives are:1. to estimate the long term water storage mean at monthly time steps; 2. to estimate the total water deficit of each months ("drought event" if longer than the months ); 3. to calculate the total water status according to the GRACE observation for the last one decade.Here are some results, and hoping to detail the methodology and extend the results in the near future. 

Fig 1: The long term mean monthly total water storage distribution of Ethiopia according to GRACE observation.

Fig 2: the long term monthly mean storage deficit maps of Ethiopia as observed from GRACE
Fig: Time series storage deficit (below zero ) at national level . At national scale, the water storage over the long term trend is more or less at constant level
 Fig 4: the time series storage deficit at four location in the country 

To be continued…..

Palmer, W.C. Meteorological Drought; U.S. Department of Commerce, Weather Bureau: Washington, DC, USA, 1965. 

Shafer, B.A.; Dezman, L. Development of a Surface Water Supply Index (SWSI) to assess the severity of drought conditions in snowpack runoff Areas. In Proceedings of the Western Snow Conference, Reno, NV, USA, 19–23 April 1982. 

McKee, T.B., Doesken, N.J., Kleist, J., 1993. The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th Conference on Applied Climatology, American Meteorological Society, Anaheim, CA, Boston, MA, 17–22 January, pp. 179–184.

Tapley, B. D., S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins (2004), GRACE measurements of mass variability in the Earth system, Science, 305(5683), 503–505, doi:10.1126/science.1099192.

May 2, 2016

AboutHydrology: Wuletawu's Abera Ph.D. defense

AboutHydrology: Wuletawu's Abera Ph.D. defense: This illustrate the long and detailed work of Wuletawu Abera during his Ph.D. His topic was modelling the whole hydrological cycle, meaning...